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Counter Strike : Global Offensive Source Code
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csgo/cstrike15_src/mathlib/mathlib_base.cpp

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//===== Copyright � 1996-2005, Valve Corporation, All rights reserved. ======//
//
// Purpose: Math primitives.
//
//===========================================================================//
/// FIXME: As soon as all references to mathlib.c are gone, include it in here
#include <math.h>
#include <float.h> // needed for flt_epsilon
#include "tier0/basetypes.h"
//#include <memory.h>
#include "tier0/dbg.h"
#include "tier0/vprof.h"
//#define _VPROF_MATHLIB
#if !defined(__SPU__)
#pragma warning(disable:4244) // "conversion from 'const int' to 'float', possible loss of data"
#pragma warning(disable:4730) // "mixing _m64 and floating point expressions may result in incorrect code"
#endif
#include "mathlib/mathlib.h"
#include "mathlib/vector.h"
#include "mathlib/vplane.h"
#if !defined(__SPU__)
#include "mathlib/vmatrix.h"
#endif
#if !defined( _X360 )
#include "sse.h"
#endif
#include "mathlib/ssemath.h"
#include "mathlib/ssequaternion.h"
// memdbgon must be the last include file in a .cpp file!!!
#include "tier0/memdbgon.h"
bool s_bMathlibInitialized = false;
#ifdef PARANOID
// User must provide an implementation of Sys_Error()
void Sys_Error (char *error, ...);
#endif
const Vector vec3_origin(0,0,0);
const QAngle vec3_angle(0,0,0);
const Quaternion quat_identity(0,0,0,1);
const Vector vec3_invalid( FLT_MAX, FLT_MAX, FLT_MAX );
const int nanmask = 255<<23;
const matrix3x4a_t g_MatrixIdentity(
1,0,0,0,
0,1,0,0,
0,0,1,0
);
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Standard C implementations of optimized routines:
//-----------------------------------------------------------------------------
float _sqrtf(float _X)
{
Assert( s_bMathlibInitialized );
return sqrtf(_X);
}
float _rsqrtf(float x)
{
Assert( s_bMathlibInitialized );
return 1.f / _sqrtf( x );
}
#ifndef PLATFORM_PPC
float VectorNormalize (Vector& vec)
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "_VectorNormalize", "Mathlib" );
#endif
Assert( s_bMathlibInitialized );
float radius = sqrtf(vec.x*vec.x + vec.y*vec.y + vec.z*vec.z);
// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
float iradius = 1.f / ( radius + FLT_EPSILON );
vec.x *= iradius;
vec.y *= iradius;
vec.z *= iradius;
return radius;
}
#endif
// TODO: Add fast C VectorNormalizeFast.
// Perhaps use approximate rsqrt trick, if the accuracy isn't too bad.
void FASTCALL _VectorNormalizeFast (Vector& vec)
{
Assert( s_bMathlibInitialized );
// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
float iradius = 1.f / ( sqrtf(vec.x*vec.x + vec.y*vec.y + vec.z*vec.z) + FLT_EPSILON );
vec.x *= iradius;
vec.y *= iradius;
vec.z *= iradius;
}
float _InvRSquared(const float* v)
{
Assert( s_bMathlibInitialized );
float r2 = DotProduct(v, v);
return r2 < 1.f ? 1.f : 1/r2;
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Function pointers selecting the appropriate implementation
//-----------------------------------------------------------------------------
void (FASTCALL *pfVectorNormalizeFast)(Vector& v) = _VectorNormalizeFast;
float SinCosTable[SIN_TABLE_SIZE];
void InitSinCosTable()
{
for( int i = 0; i < SIN_TABLE_SIZE; i++ )
{
SinCosTable[i] = sin(i * 2.0 * M_PI / SIN_TABLE_SIZE);
}
}
#endif // !defined(__SPU__)
qboolean VectorsEqual( const float *v1, const float *v2 )
{
Assert( s_bMathlibInitialized );
return ( ( v1[0] == v2[0] ) &&
( v1[1] == v2[1] ) &&
( v1[2] == v2[2] ) );
}
#endif // #if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: Generates Euler angles given a left-handed orientation matrix. The
// columns of the matrix contain the forward, left, and up vectors.
// Input : matrix - Left-handed orientation matrix.
// angles[PITCH, YAW, ROLL]. Receives right-handed counterclockwise
// rotations in degrees around Y, Z, and X respectively.
//-----------------------------------------------------------------------------
void MatrixAngles( const matrix3x4_t& matrix, RadianEuler &angles, Vector &position )
{
MatrixGetColumn( matrix, 3, position );
MatrixAngles( matrix, angles );
}
void MatrixAngles( const matrix3x4_t &matrix, Quaternion &q, Vector &pos )
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "MatrixQuaternion", "Mathlib" );
#endif
float trace;
trace = matrix[0][0] + matrix[1][1] + matrix[2][2] + 1.0f;
if( trace > 1.0f + FLT_EPSILON )
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion A",1);
q.x = ( matrix[2][1] - matrix[1][2] );
q.y = ( matrix[0][2] - matrix[2][0] );
q.z = ( matrix[1][0] - matrix[0][1] );
q.w = trace;
}
else if ( matrix[0][0] > matrix[1][1] && matrix[0][0] > matrix[2][2] )
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion B",1);
trace = 1.0f + matrix[0][0] - matrix[1][1] - matrix[2][2];
q.x = trace;
q.y = (matrix[1][0] + matrix[0][1] );
q.z = (matrix[0][2] + matrix[2][0] );
q.w = (matrix[2][1] - matrix[1][2] );
}
else if (matrix[1][1] > matrix[2][2])
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion C",1);
trace = 1.0f + matrix[1][1] - matrix[0][0] - matrix[2][2];
q.x = (matrix[0][1] + matrix[1][0] );
q.y = trace;
q.z = (matrix[2][1] + matrix[1][2] );
q.w = (matrix[0][2] - matrix[2][0] );
}
else
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion D",1);
trace = 1.0f + matrix[2][2] - matrix[0][0] - matrix[1][1];
q.x = (matrix[0][2] + matrix[2][0] );
q.y = (matrix[2][1] + matrix[1][2] );
q.z = trace;
q.w = (matrix[1][0] - matrix[0][1] );
}
QuaternionNormalize( q );
#if 0
// check against the angle version
RadianEuler ang;
MatrixAngles( matrix, ang );
Quaternion test;
AngleQuaternion( ang, test );
float d = QuaternionDotProduct( q, test );
Assert( fabs(d) > 0.99 && fabs(d) < 1.01 );
#endif
MatrixGetColumn( matrix, 3, pos );
}
void MatrixAngles( const matrix3x4_t& matrix, float *angles )
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "MatrixAngles", "Mathlib" );
#endif
Assert( s_bMathlibInitialized );
float forward[3];
float left[3];
float up[3];
//
// Extract the basis vectors from the matrix. Since we only need the Z
// component of the up vector, we don't get X and Y.
//
forward[0] = matrix[0][0];
forward[1] = matrix[1][0];
forward[2] = matrix[2][0];
left[0] = matrix[0][1];
left[1] = matrix[1][1];
left[2] = matrix[2][1];
up[2] = matrix[2][2];
float xyDist = sqrtf( forward[0] * forward[0] + forward[1] * forward[1] );
// enough here to get angles?
if ( xyDist > 0.001f )
{
// (yaw) y = ATAN( forward.y, forward.x ); -- in our space, forward is the X axis
angles[1] = RAD2DEG( atan2f( forward[1], forward[0] ) );
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
// (roll) z = ATAN( left.z, up.z );
angles[2] = RAD2DEG( atan2f( left[2], up[2] ) );
}
else // forward is mostly Z, gimbal lock-
{
// (yaw) y = ATAN( -left.x, left.y ); -- forward is mostly z, so use right for yaw
angles[1] = RAD2DEG( atan2f( -left[0], left[1] ) );
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
angles[2] = 0;
}
}
Vector MatrixNormalize( const matrix3x4_t &in, matrix3x4_t &out )
{
Vector vScale;
vScale.x = sqrt( in[ 0 ][ 0 ] * in[ 0 ][ 0 ] + in[ 1 ][ 0 ] * in[ 1 ][ 0 ] + in[ 2 ][ 0 ] * in[ 2 ][ 0 ] );
vScale.y = sqrt( in[ 0 ][ 1 ] * in[ 0 ][ 1 ] + in[ 1 ][ 1 ] * in[ 1 ][ 1 ] + in[ 2 ][ 1 ] * in[ 2 ][ 1 ] );
vScale.z = sqrt( in[ 0 ][ 2 ] * in[ 0 ][ 2 ] + in[ 1 ][ 2 ] * in[ 1 ][ 2 ] + in[ 2 ][ 2 ] * in[ 2 ][ 2 ] );
matrix3x4_t norm;
float flInvScaleX = 1.0f / vScale.x;
float flInvScaleY = 1.0f / vScale.y;
float flInvScaleZ = 1.0f / vScale.z;
out[ 0 ][ 0 ] = in[ 0 ][ 0 ] * flInvScaleX; out[ 1 ][ 0 ] = in[ 1 ][ 0 ] * flInvScaleX; out[ 2 ][ 0 ] = in[ 2 ][ 0 ] * flInvScaleX;
out[ 0 ][ 1 ] = in[ 0 ][ 1 ] * flInvScaleY; out[ 1 ][ 1 ] = in[ 1 ][ 1 ] * flInvScaleY; out[ 2 ][ 1 ] = in[ 2 ][ 1 ] * flInvScaleY;
out[ 0 ][ 2 ] = in[ 0 ][ 2 ] * flInvScaleZ; out[ 1 ][ 2 ] = in[ 1 ][ 2 ] * flInvScaleZ; out[ 2 ][ 2 ] = in[ 2 ][ 2 ] * flInvScaleZ;
out[ 0 ][ 3 ] = in[ 0 ][ 3 ]; out[ 1 ][ 3 ] = in[ 1 ][ 3 ]; out[ 2 ][ 3 ] = in[ 2 ][ 3 ];
return vScale;
}
#if !defined(__SPU__)
// transform in1 by the matrix in2
void VectorTransform (const float * RESTRICT in1, const matrix3x4_t& in2, float * RESTRICT out)
{
Assert( s_bMathlibInitialized );
float x = DotProduct(in1, in2[0]) + in2[0][3];
float y = DotProduct(in1, in2[1]) + in2[1][3];
float z = DotProduct(in1, in2[2]) + in2[2][3];
out[ 0 ] = x;
out[ 1 ] = y;
out[ 2 ] = z;
}
// assuming the matrix is orthonormal, transform in1 by the transpose (also the inverse in this case) of in2.
void VectorITransform (const float *in1, const matrix3x4_t& in2, float *out)
{
Assert( s_bMathlibInitialized );
float in1t[3];
in1t[0] = in1[0] - in2[0][3];
in1t[1] = in1[1] - in2[1][3];
in1t[2] = in1[2] - in2[2][3];
float x = in1t[0] * in2[0][0] + in1t[1] * in2[1][0] + in1t[2] * in2[2][0];
float y = in1t[0] * in2[0][1] + in1t[1] * in2[1][1] + in1t[2] * in2[2][1];
float z = in1t[0] * in2[0][2] + in1t[1] * in2[1][2] + in1t[2] * in2[2][2];
out[ 0 ] = x;
out[ 1 ] = y;
out[ 2 ] = z;
}
#endif // #if !defined(__SPU__)
// assume in2 is a rotation and rotate the input vector
void VectorRotate( const float * RESTRICT in1, const matrix3x4_t& in2, float * RESTRICT out )
{
Assert( s_bMathlibInitialized );
float x = DotProduct( in1, in2[ 0 ] );
float y = DotProduct( in1, in2[ 1 ] );
float z = DotProduct( in1, in2[ 2 ] );
out[ 0 ] = x;
out[ 1 ] = y;
out[ 2 ] = z;
}
#if !defined(__SPU__)
// assume in2 is a rotation and rotate the input vector
void VectorRotate( const Vector &in1, const QAngle &in2, Vector &out )
{
matrix3x4_t matRotate;
AngleMatrix( in2, matRotate );
VectorRotate( in1, matRotate, out );
}
// assume in2 is a rotation and rotate the input vector
void VectorRotate( const Vector &in1, const Quaternion &in2, Vector &out )
{
#if WE_WANT_OUR_CODE_TO_BE_POINTLESSLY_SLOW
matrix3x4_t matRotate;
QuaternionMatrix( in2, matRotate );
VectorRotate( in1, matRotate, out );
#else
// rotation is q * v * q^-1
Quaternion conjugate = in2.Conjugate();
// do the rotation as unrolled flop code ( QuaternionMult is a function call, which murders instruction scheduling )
// first q*v
Quaternion temp;
temp.x = in2.y * in1.z - in2.z * in1.y + in2.w * in1.x;
temp.y = -in2.x * in1.z + in2.z * in1.x + in2.w * in1.y;
temp.z = in2.x * in1.y - in2.y * in1.x + in2.w * in1.z;
temp.w = -in2.x * in1.x - in2.y * in1.y - in2.z * in1.z;
// now (qv)(q*)
out.x = temp.x * conjugate.w + temp.y * conjugate.z - temp.z * conjugate.y + temp.w * conjugate.x;
out.y = -temp.x * conjugate.z + temp.y * conjugate.w + temp.z * conjugate.x + temp.w * conjugate.y;
out.z = temp.x * conjugate.y - temp.y * conjugate.x + temp.z * conjugate.w + temp.w * conjugate.z;
Assert( fabs(-temp.x * conjugate.x - temp.y * conjugate.y - temp.z * conjugate.z + temp.w * conjugate.w) < 0.0001 );
#endif
}
// rotate by the inverse of the matrix
void VectorIRotate( const float * RESTRICT in1, const matrix3x4_t& in2, float * RESTRICT out )
{
Assert( s_bMathlibInitialized );
Assert( in1 != out );
out[0] = in1[0]*in2[0][0] + in1[1]*in2[1][0] + in1[2]*in2[2][0];
out[1] = in1[0]*in2[0][1] + in1[1]*in2[1][1] + in1[2]*in2[2][1];
out[2] = in1[0]*in2[0][2] + in1[1]*in2[1][2] + in1[2]*in2[2][2];
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
// transform a set of angles in the output space of parentMatrix to the input space
QAngle TransformAnglesToLocalSpace( const QAngle &angles, const matrix3x4_t &parentMatrix )
{
matrix3x4_t angToWorld, worldToParent, localMatrix;
MatrixInvert( parentMatrix, worldToParent );
AngleMatrix( angles, angToWorld );
ConcatTransforms( worldToParent, angToWorld, localMatrix );
QAngle out;
MatrixAngles( localMatrix, out );
return out;
}
// transform a set of angles in the input space of parentMatrix to the output space
QAngle TransformAnglesToWorldSpace( const QAngle &angles, const matrix3x4_t &parentMatrix )
{
matrix3x4_t angToParent, angToWorld;
AngleMatrix( angles, angToParent );
ConcatTransforms( parentMatrix, angToParent, angToWorld );
QAngle out;
MatrixAngles( angToWorld, out );
return out;
}
#endif // VECTOR_NO_SLOW_OPERATIONS
void MatrixInitialize( matrix3x4_t &mat, const Vector &vecOrigin, const Vector &vecXAxis, const Vector &vecYAxis, const Vector &vecZAxis )
{
MatrixSetColumn( vecXAxis, 0, mat );
MatrixSetColumn( vecYAxis, 1, mat );
MatrixSetColumn( vecZAxis, 2, mat );
MatrixSetColumn( vecOrigin, 3, mat );
}
void MatrixCopy( const matrix3x4_t& in, matrix3x4_t& out )
{
Assert( s_bMathlibInitialized );
memcpy( out.Base(), in.Base(), sizeof( float ) * 3 * 4 );
}
//-----------------------------------------------------------------------------
// Matrix equality test
//-----------------------------------------------------------------------------
bool MatricesAreEqual( const matrix3x4_t &src1, const matrix3x4_t &src2, float flTolerance )
{
for ( int i = 0; i < 3; ++i )
{
for ( int j = 0; j < 4; ++j )
{
if ( fabs( src1[i][j] - src2[i][j] ) > flTolerance )
return false;
}
}
return true;
}
#endif // #if !defined(__SPU__)
// NOTE: This is just the transpose not a general inverse
void MatrixInvert( const matrix3x4_t& in, matrix3x4_t& out )
{
Assert( s_bMathlibInitialized );
if ( &in == &out )
{
V_swap(out[0][1],out[1][0]);
V_swap(out[0][2],out[2][0]);
V_swap(out[1][2],out[2][1]);
}
else
{
// transpose the matrix
out[0][0] = in[0][0];
out[0][1] = in[1][0];
out[0][2] = in[2][0];
out[1][0] = in[0][1];
out[1][1] = in[1][1];
out[1][2] = in[2][1];
out[2][0] = in[0][2];
out[2][1] = in[1][2];
out[2][2] = in[2][2];
}
// now fix up the translation to be in the other space
float tmp[3];
tmp[0] = in[0][3];
tmp[1] = in[1][3];
tmp[2] = in[2][3];
out[0][3] = -DotProduct( tmp, out[0] );
out[1][3] = -DotProduct( tmp, out[1] );
out[2][3] = -DotProduct( tmp, out[2] );
}
void MatrixGetColumn( const matrix3x4_t& in, int column, Vector &out )
{
out.x = in[0][column];
out.y = in[1][column];
out.z = in[2][column];
}
void MatrixSetColumn( const Vector &in, int column, matrix3x4_t& out )
{
out[0][column] = in.x;
out[1][column] = in.y;
out[2][column] = in.z;
}
#if !defined(__SPU__)
int VectorCompare (const float *v1, const float *v2)
{
Assert( s_bMathlibInitialized );
int i;
for (i=0 ; i<3 ; i++)
if (v1[i] != v2[i])
return 0;
return 1;
}
void CrossProduct (const float* v1, const float* v2, float* cross)
{
Assert( s_bMathlibInitialized );
Assert( v1 != cross );
Assert( v2 != cross );
cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
}
size_t Q_log2( unsigned int val )
{
#ifdef _X360 // use hardware
// both zero and one return zero (per old implementation)
return ( val == 0 ) ? 0 : 31 - _CountLeadingZeros( val );
#else // use N. Compoop's algorithm ( inherited from days of yore )
int answer=0;
while (val>>=1)
answer++;
return answer;
#endif
}
// Matrix is right-handed x=forward, y=left, z=up. We a left-handed convention for vectors in the game code (forward, right, up)
void MatrixVectorsFLU( const matrix3x4_t &matrix, Vector* pForward, Vector *pLeft, Vector *pUp )
{
MatrixGetColumn( matrix, FORWARD_AXIS, *pForward );
MatrixGetColumn( matrix, LEFT_AXIS, *pLeft );
MatrixGetColumn( matrix, UP_AXIS, *pUp );
}
// Matrix is right-handed x=forward, y=left, z=up. We a left-handed convention for vectors in the game code (forward, right, up)
void MatrixVectors( const matrix3x4_t &matrix, Vector* pForward, Vector *pRight, Vector *pUp )
{
MatrixGetColumn( matrix, 0, *pForward );
MatrixGetColumn( matrix, 1, *pRight );
MatrixGetColumn( matrix, 2, *pUp );
*pRight *= -1.0f;
}
void VectorVectors( const Vector &forward, Vector &right, Vector &up )
{
Assert( s_bMathlibInitialized );
Vector tmp;
if ( fabs( forward[0] ) < 1e-6 && fabs( forward[1] ) < 1e-6 )
{
// pitch 90 degrees up/down from identity
right[0] = 0;
right[1] = -1;
right[2] = 0;
up[0] = -forward[2];
up[1] = 0;
up[2] = 0;
}
else
{
tmp[0] = 0; tmp[1] = 0; tmp[2] = 1.0;
CrossProduct( forward, tmp, right );
VectorNormalize( right );
CrossProduct( right, forward, up );
VectorNormalize( up );
}
}
void VectorMatrix( const Vector &forward, matrix3x4_t& matrix)
{
Assert( s_bMathlibInitialized );
Vector right, up;
VectorVectors(forward, right, up);
MatrixSetColumn( forward, 0, matrix );
MatrixSetColumn( -right, 1, matrix );
MatrixSetColumn( up, 2, matrix );
}
void VectorPerpendicularToVector( Vector const &in, Vector *pvecOut )
{
float flY = in.y * in.y;
pvecOut->x = RemapVal( flY, 0, 1, in.z, 1 );
pvecOut->y = 0;
pvecOut->z = -in.x;
pvecOut->NormalizeInPlace();
float flDot = DotProduct( *pvecOut, in );
*pvecOut -= flDot * in;
pvecOut->NormalizeInPlace();
}
//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors. Each vector is optional
//-----------------------------------------------------------------------------
void AngleVectorsFLU( const QAngle &angles, Vector *pForward, Vector *pLeft, Vector *pUp )
{
Assert( s_bMathlibInitialized );
float sr, sp, sy, cr, cp, cy;
#ifdef _X360
fltx4 radians, scale, sine, cosine;
radians = LoadUnaligned3SIMD( angles.Base() );
scale = ReplicateX4( M_PI_F / 180.f );
radians = MulSIMD( radians, scale );
SinCos3SIMD( sine, cosine, radians );
sp = SubFloat( sine, 0 ); sy = SubFloat( sine, 1 ); sr = SubFloat( sine, 2 );
cp = SubFloat( cosine, 0 ); cy = SubFloat( cosine, 1 ); cr = SubFloat( cosine, 2 );
#else
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
#endif
if ( pForward )
{
(*pForward)[FORWARD_AXIS] = cp*cy;
(*pForward)[LEFT_AXIS] = cp*sy;
(*pForward)[UP_AXIS] = -sp;
}
if ( pLeft )
{
(*pLeft)[FORWARD_AXIS] = (sr*sp*cy+cr*-sy);
(*pLeft)[LEFT_AXIS] = (sr*sp*sy+cr*cy);
(*pLeft)[UP_AXIS] = sr*cp;
}
if ( pUp )
{
(*pUp)[FORWARD_AXIS] = (cr*sp*cy+-sr*-sy);
(*pUp)[LEFT_AXIS] = (cr*sp*sy+-sr*cy);
(*pUp)[UP_AXIS] = cr*cp;
}
}
void VectorAngles( const float *forward, float *angles )
{
Assert( s_bMathlibInitialized );
float tmp, yaw, pitch;
if (forward[1] == 0 && forward[0] == 0)
{
yaw = 0;
if (forward[2] > 0)
pitch = 270;
else
pitch = 90;
}
else
{
yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
if (yaw < 0)
yaw += 360;
tmp = sqrt (forward[0]*forward[0] + forward[1]*forward[1]);
pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
if (pitch < 0)
pitch += 360;
}
angles[0] = pitch;
angles[1] = yaw;
angles[2] = 0;
}
/*
================
R_ConcatRotations
================
*/
void ConcatRotations (const float in1[3][3], const float in2[3][3], float out[3][3])
{
Assert( s_bMathlibInitialized );
Assert( in1 != out );
Assert( in2 != out );
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
in1[0][2] * in2[2][0];
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
in1[0][2] * in2[2][1];
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
in1[0][2] * in2[2][2];
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
in1[1][2] * in2[2][0];
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
in1[1][2] * in2[2][1];
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
in1[1][2] * in2[2][2];
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
in1[2][2] * in2[2][0];
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
in1[2][2] * in2[2][1];
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
in1[2][2] * in2[2][2];
}
#endif // #if !defined(__SPU__)
void ConcatTransforms_Aligned( const matrix3x4a_t &m0, const matrix3x4a_t &m1, matrix3x4a_t &out )
{
AssertAligned( &m0 );
AssertAligned( &m1 );
AssertAligned( &out );
fltx4 lastMask = *(fltx4 *)(&g_SIMD_ComponentMask[3]);
fltx4 rowA0 = LoadAlignedSIMD( m0.m_flMatVal[0] );
fltx4 rowA1 = LoadAlignedSIMD( m0.m_flMatVal[1] );
fltx4 rowA2 = LoadAlignedSIMD( m0.m_flMatVal[2] );
fltx4 rowB0 = LoadAlignedSIMD( m1.m_flMatVal[0] );
fltx4 rowB1 = LoadAlignedSIMD( m1.m_flMatVal[1] );
fltx4 rowB2 = LoadAlignedSIMD( m1.m_flMatVal[2] );
// now we have the rows of m0 and the columns of m1
// first output row
fltx4 A0 = SplatXSIMD(rowA0);
fltx4 A1 = SplatYSIMD(rowA0);
fltx4 A2 = SplatZSIMD(rowA0);
fltx4 mul00 = MulSIMD( A0, rowB0 );
fltx4 mul01 = MulSIMD( A1, rowB1 );
fltx4 mul02 = MulSIMD( A2, rowB2 );
fltx4 out0 = AddSIMD( mul00, AddSIMD(mul01,mul02) );
// second output row
A0 = SplatXSIMD(rowA1);
A1 = SplatYSIMD(rowA1);
A2 = SplatZSIMD(rowA1);
fltx4 mul10 = MulSIMD( A0, rowB0 );
fltx4 mul11 = MulSIMD( A1, rowB1 );
fltx4 mul12 = MulSIMD( A2, rowB2 );
fltx4 out1 = AddSIMD( mul10, AddSIMD(mul11,mul12) );
// third output row
A0 = SplatXSIMD(rowA2);
A1 = SplatYSIMD(rowA2);
A2 = SplatZSIMD(rowA2);
fltx4 mul20 = MulSIMD( A0, rowB0 );
fltx4 mul21 = MulSIMD( A1, rowB1 );
fltx4 mul22 = MulSIMD( A2, rowB2 );
fltx4 out2 = AddSIMD( mul20, AddSIMD(mul21,mul22) );
// add in translation vector
A0 = AndSIMD(rowA0,lastMask);
A1 = AndSIMD(rowA1,lastMask);
A2 = AndSIMD(rowA2,lastMask);
out0 = AddSIMD(out0, A0);
out1 = AddSIMD(out1, A1);
out2 = AddSIMD(out2, A2);
StoreAlignedSIMD( out.m_flMatVal[0], out0 );
StoreAlignedSIMD( out.m_flMatVal[1], out1 );
StoreAlignedSIMD( out.m_flMatVal[2], out2 );
}
/*
================
R_ConcatTransforms
================
*/
void ConcatTransforms (const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out)
{
#if 0
// test for ones that'll be 2x faster
if ( (((size_t)&in1) % 16) == 0 && (((size_t)&in2) % 16) == 0 && (((size_t)&out) % 16) == 0 )
{
ConcatTransforms_Aligned( in1, in2, out );
return;
}
#endif
fltx4 lastMask = *(fltx4 *)(&g_SIMD_ComponentMask[3]);
fltx4 rowA0 = LoadUnalignedSIMD( in1.m_flMatVal[0] );
fltx4 rowA1 = LoadUnalignedSIMD( in1.m_flMatVal[1] );
fltx4 rowA2 = LoadUnalignedSIMD( in1.m_flMatVal[2] );
fltx4 rowB0 = LoadUnalignedSIMD( in2.m_flMatVal[0] );
fltx4 rowB1 = LoadUnalignedSIMD( in2.m_flMatVal[1] );
fltx4 rowB2 = LoadUnalignedSIMD( in2.m_flMatVal[2] );
// now we have the rows of m0 and the columns of m1
// first output row
fltx4 A0 = SplatXSIMD(rowA0);
fltx4 A1 = SplatYSIMD(rowA0);
fltx4 A2 = SplatZSIMD(rowA0);
fltx4 mul00 = MulSIMD( A0, rowB0 );
fltx4 mul01 = MulSIMD( A1, rowB1 );
fltx4 mul02 = MulSIMD( A2, rowB2 );
fltx4 out0 = AddSIMD( mul00, AddSIMD(mul01,mul02) );
// second output row
A0 = SplatXSIMD(rowA1);
A1 = SplatYSIMD(rowA1);
A2 = SplatZSIMD(rowA1);
fltx4 mul10 = MulSIMD( A0, rowB0 );
fltx4 mul11 = MulSIMD( A1, rowB1 );
fltx4 mul12 = MulSIMD( A2, rowB2 );
fltx4 out1 = AddSIMD( mul10, AddSIMD(mul11,mul12) );
// third output row
A0 = SplatXSIMD(rowA2);
A1 = SplatYSIMD(rowA2);
A2 = SplatZSIMD(rowA2);
fltx4 mul20 = MulSIMD( A0, rowB0 );
fltx4 mul21 = MulSIMD( A1, rowB1 );
fltx4 mul22 = MulSIMD( A2, rowB2 );
fltx4 out2 = AddSIMD( mul20, AddSIMD(mul21,mul22) );
// add in translation vector
A0 = AndSIMD(rowA0,lastMask);
A1 = AndSIMD(rowA1,lastMask);
A2 = AndSIMD(rowA2,lastMask);
out0 = AddSIMD(out0, A0);
out1 = AddSIMD(out1, A1);
out2 = AddSIMD(out2, A2);
// write to output
StoreUnalignedSIMD( out.m_flMatVal[0], out0 );
StoreUnalignedSIMD( out.m_flMatVal[1], out1 );
StoreUnalignedSIMD( out.m_flMatVal[2], out2 );
}
/*
===================
FloorDivMod
Returns mathematically correct (floor-based) quotient and remainder for
numer and denom, both of which should contain no fractional part. The
quotient must fit in 32 bits.
====================
*/
#if !defined(__SPU__)
void FloorDivMod (double numer, double denom, int *quotient,
int *rem)
{
Assert( s_bMathlibInitialized );
int q, r;
double x;
#ifdef PARANOID
if (denom <= 0.0)
Sys_Error ("FloorDivMod: bad denominator %d\n", denom);
// if ((floor(numer) != numer) || (floor(denom) != denom))
// Sys_Error ("FloorDivMod: non-integer numer or denom %f %f\n",
// numer, denom);
#endif
if (numer >= 0.0)
{
x = floor(numer / denom);
q = (int)x;
r = Floor2Int(numer - (x * denom));
}
else
{
//
// perform operations with positive values, and fix mod to make floor-based
//
x = floor(-numer / denom);
q = -(int)x;
r = Floor2Int(-numer - (x * denom));
if (r != 0)
{
q--;
r = (int)denom - r;
}
}
*quotient = q;
*rem = r;
}
/*
===================
GreatestCommonDivisor
====================
*/
int GreatestCommonDivisor (int i1, int i2)
{
Assert( s_bMathlibInitialized );
if (i1 > i2)
{
if (i2 == 0)
return (i1);
return GreatestCommonDivisor (i2, i1 % i2);
}
else
{
if (i1 == 0)
return (i2);
return GreatestCommonDivisor (i1, i2 % i1);
}
}
bool IsDenormal( const float &val )
{
const int x = *reinterpret_cast <const int *> (&val); // needs 32-bit int
const int abs_mantissa = x & 0x007FFFFF;
const int biased_exponent = x & 0x7F800000;
return ( biased_exponent == 0 && abs_mantissa != 0 );
}
int SignbitsForPlane (cplane_t *out)
{
Assert( s_bMathlibInitialized );
int bits, j;
// for fast box on planeside test
bits = 0;
for (j=0 ; j<3 ; j++)
{
if (out->normal[j] < 0)
bits |= 1<<j;
}
return bits;
}
/*
==================
BoxOnPlaneSide
Returns 1, 2, or 1 + 2
==================
*/
int __cdecl BoxOnPlaneSide (const float *emins, const float *emaxs, const cplane_t *p)
{
Assert( s_bMathlibInitialized );
float dist1, dist2;
int sides;
// fast axial cases
if (p->type < 3)
{
if (p->dist <= emins[p->type])
return 1;
if (p->dist >= emaxs[p->type])
return 2;
return 3;
}
// general case
switch (p->signbits)
{
case 0:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
break;
case 1:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
break;
case 2:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
break;
case 3:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
break;
case 4:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
break;
case 5:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
break;
case 6:
dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
break;
case 7:
dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
break;
default:
dist1 = dist2 = 0; // shut up compiler
Assert( 0 );
break;
}
sides = 0;
if (dist1 >= p->dist)
sides = 1;
if (dist2 < p->dist)
sides |= 2;
Assert( sides != 0 );
return sides;
}
//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors
//-----------------------------------------------------------------------------
void AngleVectors (const QAngle &angles, Vector *forward)
{
Assert( s_bMathlibInitialized );
Assert( forward );
float sp, sy, cp, cy;
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
forward->x = cp*cy;
forward->y = cp*sy;
forward->z = -sp;
}
//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors. Each vector is optional
//-----------------------------------------------------------------------------
void AngleVectors( const QAngle &angles, Vector *forward, Vector *right, Vector *up )
{
Assert( s_bMathlibInitialized );
float sr, sp, sy, cr, cp, cy;
#ifdef _X360
fltx4 radians, scale, sine, cosine;
radians = LoadUnaligned3SIMD( angles.Base() );
scale = ReplicateX4( M_PI_F / 180.f );
radians = MulSIMD( radians, scale );
SinCos3SIMD( sine, cosine, radians );
sp = SubFloat( sine, 0 ); sy = SubFloat( sine, 1 ); sr = SubFloat( sine, 2 );
cp = SubFloat( cosine, 0 ); cy = SubFloat( cosine, 1 ); cr = SubFloat( cosine, 2 );
#else
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
#endif
if (forward)
{
forward->x = cp*cy;
forward->y = cp*sy;
forward->z = -sp;
}
if (right)
{
right->x = (-1*sr*sp*cy+-1*cr*-sy);
right->y = (-1*sr*sp*sy+-1*cr*cy);
right->z = -1*sr*cp;
}
if (up)
{
up->x = (cr*sp*cy+-sr*-sy);
up->y = (cr*sp*sy+-sr*cy);
up->z = cr*cp;
}
}
//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors transposed
//-----------------------------------------------------------------------------
void AngleVectorsTranspose (const QAngle &angles, Vector *forward, Vector *right, Vector *up)
{
Assert( s_bMathlibInitialized );
float sr, sp, sy, cr, cp, cy;
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
if (forward)
{
forward->x = cp*cy;
forward->y = (sr*sp*cy+cr*-sy);
forward->z = (cr*sp*cy+-sr*-sy);
}
if (right)
{
right->x = cp*sy;
right->y = (sr*sp*sy+cr*cy);
right->z = (cr*sp*sy+-sr*cy);
}
if (up)
{
up->x = -sp;
up->y = sr*cp;
up->z = cr*cp;
}
}
//-----------------------------------------------------------------------------
// Forward direction vector -> Euler angles
//-----------------------------------------------------------------------------
void VectorAngles( const Vector& forward, QAngle &angles )
{
Assert( s_bMathlibInitialized );
float tmp, yaw, pitch;
if (forward[1] == 0 && forward[0] == 0)
{
yaw = 0;
if (forward[2] > 0)
pitch = 270;
else
pitch = 90;
}
else
{
yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
if (yaw < 0)
yaw += 360;
tmp = FastSqrt (forward[0]*forward[0] + forward[1]*forward[1]);
pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
if (pitch < 0)
pitch += 360;
}
angles[0] = pitch;
angles[1] = yaw;
angles[2] = 0;
}
//-----------------------------------------------------------------------------
// Forward direction vector with a reference up vector -> Euler angles
//-----------------------------------------------------------------------------
void VectorAngles( const Vector &forward, const Vector &pseudoup, QAngle &angles )
{
Assert( s_bMathlibInitialized );
Vector left;
CrossProduct( pseudoup, forward, left );
VectorNormalizeFast( left );
float xyDist = sqrtf( forward[0] * forward[0] + forward[1] * forward[1] );
// enough here to get angles?
if ( xyDist > 0.001f )
{
// (yaw) y = ATAN( forward.y, forward.x ); -- in our space, forward is the X axis
angles[1] = RAD2DEG( atan2f( forward[1], forward[0] ) );
// The engine does pitch inverted from this, but we always end up negating it in the DLL
// UNDONE: Fix the engine to make it consistent
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
float up_z = (left[1] * forward[0]) - (left[0] * forward[1]);
// (roll) z = ATAN( left.z, up.z );
angles[2] = RAD2DEG( atan2f( left[2], up_z ) );
}
else // forward is mostly Z, gimbal lock-
{
// (yaw) y = ATAN( -left.x, left.y ); -- forward is mostly z, so use right for yaw
angles[1] = RAD2DEG( atan2f( -left[0], left[1] ) ); //This was originally copied from the "void MatrixAngles( const matrix3x4_t& matrix, float *angles )" code, and it's 180 degrees off, negated the values and it all works now (Dave Kircher)
// The engine does pitch inverted from this, but we always end up negating it in the DLL
// UNDONE: Fix the engine to make it consistent
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
angles[2] = 0;
}
}
#endif // #if !defined(__SPU__)
void SetIdentityMatrix( matrix3x4_t& matrix )
{
memset( matrix.Base(), 0, sizeof(float)*3*4 );
matrix[0][0] = 1.0;
matrix[1][1] = 1.0;
matrix[2][2] = 1.0;
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Builds a scale matrix
//-----------------------------------------------------------------------------
void SetScaleMatrix( float x, float y, float z, matrix3x4_t &dst )
{
dst[0][0] = x; dst[0][1] = 0.0f; dst[0][2] = 0.0f; dst[0][3] = 0.0f;
dst[1][0] = 0.0f; dst[1][1] = y; dst[1][2] = 0.0f; dst[1][3] = 0.0f;
dst[2][0] = 0.0f; dst[2][1] = 0.0f; dst[2][2] = z; dst[2][3] = 0.0f;
}
//-----------------------------------------------------------------------------
// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
//
// | ax2 + (1 - ax2)cosQ axay(1 - cosQ) - azsinQ azax(1 - cosQ) + aysinQ |
// Ra(Q) = | axay(1 - cosQ) + azsinQ ay2 + (1 - ay2)cosQ ayaz(1 - cosQ) - axsinQ |
// | azax(1 - cosQ) - aysinQ ayaz(1 - cosQ) + axsinQ az2 + (1 - az2)cosQ |
//
// Input : mat -
// vAxisOrRot -
// angle -
//-----------------------------------------------------------------------------
void MatrixBuildRotationAboutAxis( const Vector &vAxisOfRot, float angleDegrees, matrix3x4_t &dst )
{
float radians;
float axisXSquared;
float axisYSquared;
float axisZSquared;
float fSin;
float fCos;
radians = angleDegrees * ( M_PI / 180.0 );
fSin = sin( radians );
fCos = cos( radians );
axisXSquared = vAxisOfRot[0] * vAxisOfRot[0];
axisYSquared = vAxisOfRot[1] * vAxisOfRot[1];
axisZSquared = vAxisOfRot[2] * vAxisOfRot[2];
// Column 0:
dst[0][0] = axisXSquared + (1 - axisXSquared) * fCos;
dst[1][0] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) + vAxisOfRot[2] * fSin;
dst[2][0] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) - vAxisOfRot[1] * fSin;
// Column 1:
dst[0][1] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) - vAxisOfRot[2] * fSin;
dst[1][1] = axisYSquared + (1 - axisYSquared) * fCos;
dst[2][1] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) + vAxisOfRot[0] * fSin;
// Column 2:
dst[0][2] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) + vAxisOfRot[1] * fSin;
dst[1][2] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) - vAxisOfRot[0] * fSin;
dst[2][2] = axisZSquared + (1 - axisZSquared) * fCos;
// Column 3:
dst[0][3] = 0;
dst[1][3] = 0;
dst[2][3] = 0;
}
//-----------------------------------------------------------------------------
// Computes the transpose
//-----------------------------------------------------------------------------
void MatrixTranspose( matrix3x4_t& mat )
{
vec_t tmp;
tmp = mat[0][1]; mat[0][1] = mat[1][0]; mat[1][0] = tmp;
tmp = mat[0][2]; mat[0][2] = mat[2][0]; mat[2][0] = tmp;
tmp = mat[1][2]; mat[1][2] = mat[2][1]; mat[2][1] = tmp;
}
void MatrixTranspose( const matrix3x4_t& src, matrix3x4_t& dst )
{
dst[0][0] = src[0][0]; dst[0][1] = src[1][0]; dst[0][2] = src[2][0]; dst[0][3] = 0.0f;
dst[1][0] = src[0][1]; dst[1][1] = src[1][1]; dst[1][2] = src[2][1]; dst[1][3] = 0.0f;
dst[2][0] = src[0][2]; dst[2][1] = src[1][2]; dst[2][2] = src[2][2]; dst[2][3] = 0.0f;
}
#endif // #if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: converts engine euler angles into a matrix
// Input : vec3_t angles - PITCH, YAW, ROLL
// Output : *matrix - left-handed column matrix
// the basis vectors for the rotations will be in the columns as follows:
// matrix[][0] is forward
// matrix[][1] is left
// matrix[][2] is up
//-----------------------------------------------------------------------------
void AngleMatrix( RadianEuler const &angles, const Vector &position, matrix3x4_t& matrix )
{
AngleMatrix( angles, matrix );
MatrixSetColumn( position, 3, matrix );
}
void AngleMatrix( const RadianEuler& angles, matrix3x4_t& matrix )
{
QAngle quakeEuler( RAD2DEG( angles.y ), RAD2DEG( angles.z ), RAD2DEG( angles.x ) );
AngleMatrix( quakeEuler, matrix );
}
void AngleMatrix( const QAngle &angles, const Vector &position, matrix3x4_t& matrix )
{
AngleMatrix( angles, matrix );
MatrixSetColumn( position, 3, matrix );
}
void AngleMatrix( const QAngle &angles, matrix3x4_t& matrix )
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "AngleMatrix", "Mathlib" );
#endif
Assert( s_bMathlibInitialized );
float sr, sp, sy, cr, cp, cy;
#ifdef _X360
fltx4 radians, scale, sine, cosine;
radians = LoadUnaligned3SIMD( angles.Base() );
scale = ReplicateX4( M_PI_F / 180.f );
radians = MulSIMD( radians, scale );
SinCos3SIMD( sine, cosine, radians );
sp = SubFloat( sine, 0 ); sy = SubFloat( sine, 1 ); sr = SubFloat( sine, 2 );
cp = SubFloat( cosine, 0 ); cy = SubFloat( cosine, 1 ); cr = SubFloat( cosine, 2 );
#else
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
#endif
// matrix = (YAW * PITCH) * ROLL
matrix[0][0] = cp*cy;
matrix[1][0] = cp*sy;
matrix[2][0] = -sp;
// NOTE: Do not optimize this to reduce multiplies! optimizer bug will screw this up.
matrix[0][1] = sr*sp*cy+cr*-sy;
matrix[1][1] = sr*sp*sy+cr*cy;
matrix[2][1] = sr*cp;
matrix[0][2] = (cr*sp*cy+-sr*-sy);
matrix[1][2] = (cr*sp*sy+-sr*cy);
matrix[2][2] = cr*cp;
matrix[0][3] = 0.0f;
matrix[1][3] = 0.0f;
matrix[2][3] = 0.0f;
}
#if !defined(__SPU__)
void AngleIMatrix( const RadianEuler& angles, matrix3x4_t& matrix )
{
QAngle quakeEuler( RAD2DEG( angles.y ), RAD2DEG( angles.z ), RAD2DEG( angles.x ) );
AngleIMatrix( quakeEuler, matrix );
}
void AngleIMatrix (const QAngle& angles, matrix3x4_t& matrix )
{
Assert( s_bMathlibInitialized );
float sr, sp, sy, cr, cp, cy;
SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
// matrix = (YAW * PITCH) * ROLL
matrix[0][0] = cp*cy;
matrix[0][1] = cp*sy;
matrix[0][2] = -sp;
matrix[1][0] = sr*sp*cy+cr*-sy;
matrix[1][1] = sr*sp*sy+cr*cy;
matrix[1][2] = sr*cp;
matrix[2][0] = (cr*sp*cy+-sr*-sy);
matrix[2][1] = (cr*sp*sy+-sr*cy);
matrix[2][2] = cr*cp;
matrix[0][3] = 0.f;
matrix[1][3] = 0.f;
matrix[2][3] = 0.f;
}
void AngleIMatrix (const QAngle &angles, const Vector &position, matrix3x4_t &mat )
{
AngleIMatrix( angles, mat );
Vector vecTranslation;
VectorRotate( position, mat, vecTranslation );
vecTranslation *= -1.0f;
MatrixSetColumn( vecTranslation, 3, mat );
}
#endif // #if !defined(__SPU__)
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Bounding box construction methods
//-----------------------------------------------------------------------------
void ClearBounds (Vector& mins, Vector& maxs)
{
Assert( s_bMathlibInitialized );
mins[0] = mins[1] = mins[2] = FLT_MAX;
maxs[0] = maxs[1] = maxs[2] = -FLT_MAX;
}
void AddPointToBounds (const Vector& v, Vector& mins, Vector& maxs)
{
Assert( s_bMathlibInitialized );
int i;
vec_t val;
for (i=0 ; i<3 ; i++)
{
val = v[i];
if (val < mins[i])
mins[i] = val;
if (val > maxs[i])
maxs[i] = val;
}
}
bool AreBoundsValid( const Vector &vMin, const Vector &vMax )
{
for ( int i = 0; i < 3; ++ i )
{
if ( vMin[i] > vMax[i] )
{
return false;
}
}
return true;
}
bool IsPointInBounds( const Vector &vPoint, const Vector &vMin, const Vector &vMax )
{
for ( int i = 0; i < 3; ++ i )
{
if ( vPoint[i] < vMin[i] || vPoint[i] > vMax[i] )
{
return false;
}
}
return true;
}
// solve a x^2 + b x + c = 0
bool SolveQuadratic( float a, float b, float c, float &root1, float &root2 )
{
Assert( s_bMathlibInitialized );
if (a == 0)
{
if (b != 0)
{
// no x^2 component, it's a linear system
root1 = root2 = -c / b;
return true;
}
if (c == 0)
{
// all zero's
root1 = root2 = 0;
return true;
}
return false;
}
float tmp = b * b - 4.0f * a * c;
if (tmp < 0)
{
// imaginary number, bah, no solution.
return false;
}
tmp = sqrt( tmp );
root1 = (-b + tmp) / (2.0f * a);
root2 = (-b - tmp) / (2.0f * a);
return true;
}
// solves for "a, b, c" where "a x^2 + b x + c = y", return true if solution exists
bool SolveInverseQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c )
{
float det = (x1 - x2)*(x1 - x3)*(x2 - x3);
// FIXME: check with some sort of epsilon
if (det == 0.0)
return false;
a = (x3*(-y1 + y2) + x2*(y1 - y3) + x1*(-y2 + y3)) / det;
b = (x3*x3*(y1 - y2) + x1*x1*(y2 - y3) + x2*x2*(-y1 + y3)) / det;
c = (x1*x3*(-x1 + x3)*y2 + x2*x2*(x3*y1 - x1*y3) + x2*(-(x3*x3*y1) + x1*x1*y3)) / det;
return true;
}
bool SolveInverseQuadraticMonotonic( float x1, float y1, float x2, float y2, float x3, float y3,
float &a, float &b, float &c )
{
// use SolveInverseQuadratic, but if the sigm of the derivative at the start point is the wrong
// sign, displace the mid point
// first, sort parameters
if (x1>x2)
{
V_swap(x1,x2);
V_swap(y1,y2);
}
if (x2>x3)
{
V_swap(x2,x3);
V_swap(y2,y3);
}
if (x1>x2)
{
V_swap(x1,x2);
V_swap(y1,y2);
}
// this code is not fast. what it does is when the curve would be non-monotonic, slowly shifts
// the center point closer to the linear line between the endpoints. Should anyone need htis
// function to be actually fast, it would be fairly easy to change it to be so.
for(float blend_to_linear_factor=0.0;blend_to_linear_factor<=1.0;blend_to_linear_factor+=0.05)
{
float tempy2=(1-blend_to_linear_factor)*y2+blend_to_linear_factor*FLerp(y1,y3,x1,x3,x2);
if (!SolveInverseQuadratic(x1,y1,x2,tempy2,x3,y3,a,b,c))
return false;
float derivative=2.0*a+b;
if ( (y1<y2) && (y2<y3)) // monotonically increasing
{
if (derivative>=0.0)
return true;
}
else
{
if ( (y1>y2) && (y2>y3)) // monotonically decreasing
{
if (derivative<=0.0)
return true;
}
else
return true;
}
}
return true;
}
// solves for "a, b, c" where "1/(a x^2 + b x + c ) = y", return true if solution exists
bool SolveInverseReciprocalQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c )
{
float det = (x1 - x2)*(x1 - x3)*(x2 - x3)*y1*y2*y3;
// FIXME: check with some sort of epsilon
if (det == 0.0)
return false;
a = (x1*y1*(y2 - y3) + x3*(y1 - y2)*y3 + x2*y2*(-y1 + y3)) / det;
b = (x2*x2*y2*(y1 - y3) + x3*x3*(-y1 + y2)*y3 + x1*x1*y1*(-y2 + y3)) / det;
c = (x2*(x2 - x3)*x3*y2*y3 + x1*x1*y1*(x2*y2 - x3*y3) + x1*(-(x2*x2*y1*y2) + x3*x3*y1*y3)) / det;
return true;
}
// Rotate a vector around the Z axis (YAW)
void VectorYawRotate( const Vector &in, float flYaw, Vector &out)
{
Assert( s_bMathlibInitialized );
if (&in == &out )
{
Vector tmp;
tmp = in;
VectorYawRotate( tmp, flYaw, out );
return;
}
float sy, cy;
SinCos( DEG2RAD(flYaw), &sy, &cy );
out.x = in.x * cy - in.y * sy;
out.y = in.x * sy + in.y * cy;
out.z = in.z;
}
float Bias( float x, float biasAmt )
{
// WARNING: not thread safe
static float lastAmt = -1;
static float lastExponent = 0;
if( lastAmt != biasAmt )
{
lastExponent = log( biasAmt ) * -1.4427f; // (-1.4427 = 1 / log(0.5))
}
return pow( x, lastExponent );
}
float Gain( float x, float biasAmt )
{
// WARNING: not thread safe
if( x < 0.5 )
return 0.5f * Bias( 2*x, 1-biasAmt );
else
return 1 - 0.5f * Bias( 2 - 2*x, 1-biasAmt );
}
float SmoothCurve( float x )
{
return (1 - cos( x * M_PI )) * 0.5f;
}
inline float MovePeak( float x, float flPeakPos )
{
// Todo: make this higher-order?
if( x < flPeakPos )
return x * 0.5f / flPeakPos;
else
return 0.5 + 0.5 * (x - flPeakPos) / (1 - flPeakPos);
}
float SmoothCurve_Tweak( float x, float flPeakPos, float flPeakSharpness )
{
float flMovedPeak = MovePeak( x, flPeakPos );
float flSharpened = Gain( flMovedPeak, flPeakSharpness );
return SmoothCurve( flSharpened );
}
#endif // !defined(__SPU__)
//-----------------------------------------------------------------------------
// make sure quaternions are within 180 degrees of one another, if not, reverse q
//-----------------------------------------------------------------------------
void QuaternionAlign( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
// FIXME: can this be done with a quat dot product?
int i;
// decide if one of the quaternions is backwards
float a = 0;
float b = 0;
for (i = 0; i < 4; i++)
{
a += (p[i]-q[i])*(p[i]-q[i]);
b += (p[i]+q[i])*(p[i]+q[i]);
}
if (a > b)
{
for (i = 0; i < 4; i++)
{
qt[i] = -q[i];
}
}
else if (&qt != &q)
{
for (i = 0; i < 4; i++)
{
qt[i] = q[i];
}
}
}
//-----------------------------------------------------------------------------
// Do a piecewise addition of the quaternion elements. This actually makes little
// mathematical sense, but it's a cheap way to simulate a slerp.
//-----------------------------------------------------------------------------
void QuaternionBlend( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
#if ALLOW_SIMD_QUATERNION_MATH
fltx4 psimd, qsimd, qtsimd;
psimd = LoadUnalignedSIMD( p.Base() );
qsimd = LoadUnalignedSIMD( q.Base() );
qtsimd = QuaternionBlendSIMD( psimd, qsimd, t );
StoreUnalignedSIMD( qt.Base(), qtsimd );
#else
// decide if one of the quaternions is backwards
Quaternion q2;
QuaternionAlign( p, q, q2 );
QuaternionBlendNoAlign( p, q2, t, qt );
#endif
}
void QuaternionBlendNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
float sclp, sclq;
int i;
// 0.0 returns p, 1.0 return q.
sclp = 1.0f - t;
sclq = t;
for (i = 0; i < 4; i++) {
qt[i] = sclp * p[i] + sclq * q[i];
}
QuaternionNormalize( qt );
}
void QuaternionIdentityBlend( const Quaternion &p, float t, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
float sclp;
sclp = 1.0f - t;
qt.x = p.x * sclp;
qt.y = p.y * sclp;
qt.z = p.z * sclp;
if (qt.w < 0.0)
{
qt.w = p.w * sclp - t;
}
else
{
qt.w = p.w * sclp + t;
}
QuaternionNormalize( qt );
}
//-----------------------------------------------------------------------------
// Quaternion sphereical linear interpolation
//-----------------------------------------------------------------------------
void QuaternionSlerp( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
Quaternion q2;
// 0.0 returns p, 1.0 return q.
// decide if one of the quaternions is backwards
QuaternionAlign( p, q, q2 );
QuaternionSlerpNoAlign( p, q2, t, qt );
}
void QuaternionSlerpNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
float omega, cosom, sinom, sclp, sclq;
int i;
// 0.0 returns p, 1.0 return q.
cosom = p[0]*q[0] + p[1]*q[1] + p[2]*q[2] + p[3]*q[3];
if ((1.0f + cosom) > 0.000001f) {
if ((1.0f - cosom) > 0.000001f) {
omega = acos( cosom );
sinom = sin( omega );
sclp = sin( (1.0f - t)*omega) / sinom;
sclq = sin( t*omega ) / sinom;
}
else {
// TODO: add short circuit for cosom == 1.0f?
sclp = 1.0f - t;
sclq = t;
}
for (i = 0; i < 4; i++) {
qt[i] = sclp * p[i] + sclq * q[i];
}
}
else {
Assert( &qt != &q );
qt[0] = -q[1];
qt[1] = q[0];
qt[2] = -q[3];
qt[3] = q[2];
sclp = sin( (1.0f - t) * (0.5f * M_PI));
sclq = sin( t * (0.5f * M_PI));
for (i = 0; i < 3; i++) {
qt[i] = sclp * p[i] + sclq * qt[i];
}
}
Assert( qt.IsValid() );
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: Returns the angular delta between the two normalized quaternions in degrees.
//-----------------------------------------------------------------------------
float QuaternionAngleDiff( const Quaternion &p, const Quaternion &q )
{
#if 1
// this code path is here for 2 reasons:
// 1 - acos maps 1-epsilon to values much larger than epsilon (vs asin, which maps epsilon to itself)
// this means that in floats, anything below ~0.05 degrees truncates to 0
// 2 - normalized quaternions are frequently slightly non-normalized due to float precision issues,
// and the epsilon off of normalized can be several percents of a degree
Quaternion qInv, diff;
QuaternionConjugate( q, qInv );
QuaternionMult( p, qInv, diff );
// Note if the quaternion is slightly non-normalized the square root below may be more than 1,
// the value is clamped to one otherwise it may result in asin() returning an undefined result.
float sinang = MIN( 1.0f, sqrt( diff.x * diff.x + diff.y * diff.y + diff.z * diff.z ) );
float angle = RAD2DEG( 2 * asin( sinang ) );
return angle;
#else
Quaternion q2;
QuaternionAlign( p, q, q2 );
Assert( s_bMathlibInitialized );
float cosom = p.x * q2.x + p.y * q2.y + p.z * q2.z + p.w * q2.w;
if ( cosom > -1.0f )
{
if ( cosom < 1.0f )
{
float omega = 2 * fabs( acos( cosom ) );
return RAD2DEG( omega );
}
return 0.0f;
}
return 180.0f;
#endif
}
void QuaternionConjugate( const Quaternion &p, Quaternion &q )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
q.x = -p.x;
q.y = -p.y;
q.z = -p.z;
q.w = p.w;
}
void QuaternionInvert( const Quaternion &p, Quaternion &q )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
QuaternionConjugate( p, q );
float magnitudeSqr = QuaternionDotProduct( p, p );
Assert( magnitudeSqr );
if ( magnitudeSqr )
{
float inv = 1.0f / magnitudeSqr;
q.x *= inv;
q.y *= inv;
q.z *= inv;
q.w *= inv;
}
}
void QuaternionMultiply( const Quaternion &q, const Vector &v, Vector &result )
{
Vector t, t2;
CrossProduct( q.ImaginaryPart(), v, t );
t *= 2.0f;
VectorMA( v, q.RealPart(), t, result );
CrossProduct( q.ImaginaryPart(), t, t2 );
result += t2;
}
#endif // #if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Make sure the quaternion is of unit length
//-----------------------------------------------------------------------------
float QuaternionNormalize( Quaternion &q )
{
Assert( s_bMathlibInitialized );
float radius, iradius;
Assert( q.IsValid() );
radius = q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
if ( radius ) // > FLT_EPSILON && ((radius < 1.0f - 4*FLT_EPSILON) || (radius > 1.0f + 4*FLT_EPSILON))
{
radius = sqrt(radius);
iradius = 1.0f/radius;
q[3] *= iradius;
q[2] *= iradius;
q[1] *= iradius;
q[0] *= iradius;
}
return radius;
}
void QuaternionScale( const Quaternion &p, float t, Quaternion &q )
{
Assert( s_bMathlibInitialized );
#if 0
Quaternion p0;
Quaternion q;
p0.Init( 0.0, 0.0, 0.0, 1.0 );
// slerp in "reverse order" so that p doesn't get realigned
QuaternionSlerp( p, p0, 1.0 - fabs( t ), q );
if (t < 0.0)
{
q.w = -q.w;
}
#else
float r;
// FIXME: nick, this isn't overly sensitive to accuracy, and it may be faster to
// use the cos part (w) of the quaternion (sin(omega)*N,cos(omega)) to figure the new scale.
float sinom = sqrt( DotProduct( &p.x, &p.x ) );
sinom = MIN( sinom, 1.f );
float sinsom = sin( asin( sinom ) * t );
t = sinsom / (sinom + FLT_EPSILON);
VectorScale( &p.x, t, &q.x );
// rescale rotation
r = 1.0f - sinsom * sinsom;
// Assert( r >= 0 );
if (r < 0.0f)
r = 0.0f;
r = sqrt( r );
// keep sign of rotation
if (p.w < 0)
q.w = -r;
else
q.w = r;
#endif
Assert( q.IsValid() );
return;
}
void QuaternionAdd( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
Assert( p.IsValid() );
Assert( q.IsValid() );
// decide if one of the quaternions is backwards
Quaternion q2;
QuaternionAlign( p, q, q2 );
// is this right???
qt[0] = p[0] + q2[0];
qt[1] = p[1] + q2[1];
qt[2] = p[2] + q2[2];
qt[3] = p[3] + q2[3];
return;
}
float QuaternionDotProduct( const Quaternion &p, const Quaternion &q )
{
Assert( s_bMathlibInitialized );
Assert( p.IsValid() );
Assert( q.IsValid() );
return p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w;
}
// qt = p * q
void QuaternionMult( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
Assert( s_bMathlibInitialized );
Assert( p.IsValid() );
Assert( q.IsValid() );
if (&p == &qt)
{
Quaternion p2 = p;
QuaternionMult( p2, q, qt );
return;
}
// decide if one of the quaternions is backwards
Quaternion q2;
QuaternionAlign( p, q, q2 );
qt.x = p.x * q2.w + p.y * q2.z - p.z * q2.y + p.w * q2.x;
qt.y = -p.x * q2.z + p.y * q2.w + p.z * q2.x + p.w * q2.y;
qt.z = p.x * q2.y - p.y * q2.x + p.z * q2.w + p.w * q2.z;
qt.w = -p.x * q2.x - p.y * q2.y - p.z * q2.z + p.w * q2.w;
}
#if !defined(__SPU__)
void QuaternionExp( const Quaternion &p, Quaternion &q )
{
float r = sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
float et = exp(p[3]);
float s = r>=0.00001f? et*sin(r)/r: 0.f;
q.Init( s*p[0],s*p[1],s*p[2], et*cos( r ) );
}
void QuaternionLn( const Quaternion &p, Quaternion &q )
{
float r = sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
float t = r>0.00001f? atan2(r,p[3])/r: 0.f;
float norm = p[0]*p[0] + p[1]*p[1] + p[2]*p[2] + p[3]*p[3];
q.Init( t*p[0],t*p[1],t*p[2],0.5*log(norm) );
}
// Average using exponential method
// Qave = exp( 1 / n * log( Q1 ) + ... + 1 / n * log( Qn ) ) where
// if pflWeights passed in 1/n is replaced by normalized weighting
void QuaternionAverageExponential( Quaternion &q, int nCount, const Quaternion *pQuaternions, const float *pflWeights /*=NULL*/ )
{
Assert( nCount >= 1 );
Assert( pQuaternions );
// Nothing to do if only one input quaternions
if ( nCount == 1 )
{
q = pQuaternions[ 0 ];
return;
}
float ooWeightSum = 1.0f;
float flWeightSum = 0.0f;
for ( int i = 0 ; i < nCount; ++i )
{
if ( pflWeights )
{
flWeightSum += pflWeights[ i ];
}
else
{
flWeightSum += 1.0f;
}
}
if ( flWeightSum > 0.0f )
{
ooWeightSum = 1.0f / flWeightSum;
}
Quaternion sum( 0, 0, 0, 0 );
// Now sum the ln of the quaternions
for ( int i = 0; i < nCount; ++i )
{
float weight = ooWeightSum;
if ( pflWeights )
{
weight *= pflWeights[ i ];
}
// Make sure all quaternions are aligned with the
// first to avoid blending the wrong direction.
Quaternion alignedQuat;
QuaternionAlign( pQuaternions[ 0 ], pQuaternions[ i ], alignedQuat );
Quaternion qLn;
QuaternionLn( alignedQuat, qLn );
for ( int j = 0; j < 4; ++j )
{
sum[ j ] += ( qLn[ j ] * weight );
}
}
// then exponentiate to get final value
QuaternionExp( sum, q );
}
// Given a vector and a pseudo-up reference vector, create a quaternion which represents
// the orientation of the forward vector. Note, will be unstable if vecForward is close
// to referenceUp
void QuaternionLookAt( const Vector &vecForward, const Vector &referenceUp, Quaternion &q )
{
Vector forward = vecForward;
forward.NormalizeInPlace();
float ratio = DotProduct( forward, referenceUp );
Vector up = referenceUp - ( forward * ratio );
up.NormalizeInPlace();
Vector right = forward.Cross( up );
right.NormalizeInPlace();
const Vector &x = right;
const Vector &y = forward;
const Vector &z = up;
float tr = x.x + y.y + z.z;
q.Init( y.z - z.y , z.x - x.z, x.y - y.x, tr + 1.0f );
QuaternionNormalize( q );
/*
Vector z = vecForward;
z.NormalizeInPlace();
Vector x = referenceUp.Cross( z );
x.NormalizeInPlace();
Vector y = z.Cross( x );
y.NormalizeInPlace();
float tr = x.x + y.y + z.z;
q.Init( y.z - z.y , z.x - x.z, x.y - y.x, tr + 1.0f );
QuaternionNormalize( q );
*/
}
#endif // !defined(__SPU__)
void QuaternionMatrix( const Quaternion &q, const Vector &pos, matrix3x4_t& matrix )
{
Assert( pos.IsValid() );
QuaternionMatrix( q, matrix );
matrix[0][3] = pos.x;
matrix[1][3] = pos.y;
matrix[2][3] = pos.z;
}
void QuaternionMatrix( const Quaternion &q, const Vector &pos, const Vector &vScale, matrix3x4_t& mat )
{
Assert( pos.IsValid() );
Assert( q.IsValid() );
Assert( vScale.IsValid() );
QuaternionMatrix( q, mat );
mat[ 0 ][ 0 ] *= vScale.x; mat[ 1 ][ 0 ] *= vScale.x; mat[ 2 ][ 0 ] *= vScale.x;
mat[ 0 ][ 1 ] *= vScale.y; mat[ 1 ][ 1 ] *= vScale.y; mat[ 2 ][ 1 ] *= vScale.y;
mat[ 0 ][ 2 ] *= vScale.z; mat[ 1 ][ 2 ] *= vScale.z; mat[ 2 ][ 2 ] *= vScale.z;
mat[ 0 ][ 3 ] = pos.x; mat[ 1 ][ 3 ] = pos.y; mat[ 2 ][ 3 ] = pos.z;
}
void QuaternionMatrix( const Quaternion &q, matrix3x4_t& matrix )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "QuaternionMatrix", "Mathlib" );
#endif
// Original code
// This should produce the same code as below with optimization, but looking at the assmebly,
// it doesn't. There are 7 extra multiplies in the release build of this, go figure.
#if 1
matrix[0][0] = 1.0 - 2.0 * q.y * q.y - 2.0 * q.z * q.z;
matrix[1][0] = 2.0 * q.x * q.y + 2.0 * q.w * q.z;
matrix[2][0] = 2.0 * q.x * q.z - 2.0 * q.w * q.y;
matrix[0][1] = 2.0f * q.x * q.y - 2.0f * q.w * q.z;
matrix[1][1] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.z * q.z;
matrix[2][1] = 2.0f * q.y * q.z + 2.0f * q.w * q.x;
matrix[0][2] = 2.0f * q.x * q.z + 2.0f * q.w * q.y;
matrix[1][2] = 2.0f * q.y * q.z - 2.0f * q.w * q.x;
matrix[2][2] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.y * q.y;
matrix[0][3] = 0.0f;
matrix[1][3] = 0.0f;
matrix[2][3] = 0.0f;
#else
float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// precalculate common multiplitcations
x2 = q.x + q.x;
y2 = q.y + q.y;
z2 = q.z + q.z;
xx = q.x * x2;
xy = q.x * y2;
xz = q.x * z2;
yy = q.y * y2;
yz = q.y * z2;
zz = q.z * z2;
wx = q.w * x2;
wy = q.w * y2;
wz = q.w * z2;
matrix[0][0] = 1.0 - (yy + zz);
matrix[0][1] = xy - wz;
matrix[0][2] = xz + wy;
matrix[0][3] = 0.0f;
matrix[1][0] = xy + wz;
matrix[1][1] = 1.0 - (xx + zz);
matrix[1][2] = yz - wx;
matrix[1][3] = 0.0f;
matrix[2][0] = xz - wy;
matrix[2][1] = yz + wx;
matrix[2][2] = 1.0 - (xx + yy);
matrix[2][3] = 0.0f;
#endif
}
const Vector Quaternion::GetForward()const
{
Vector vAxisX;
vAxisX.x = 1.0 - 2.0 * y * y - 2.0 * z * z;
vAxisX.y = 2.0 * x * y + 2.0 * w * z;
vAxisX.z = 2.0 * x * z - 2.0 * w * y;
return vAxisX;
}
const Vector Quaternion::GetLeft()const
{
Vector vAxisY;
vAxisY.x = 2.0f * x * y - 2.0f * w * z;
vAxisY.y = 1.0f - 2.0f * x * x - 2.0f * z * z;
vAxisY.z = 2.0f * y * z + 2.0f * w * x;
return vAxisY;
}
const Vector Quaternion::GetUp()const
{
Vector vAxisZ;
vAxisZ.x = 2.0f * x * z + 2.0f * w * y;
vAxisZ.y = 2.0f * y * z - 2.0f * w * x;
vAxisZ.z = 1.0f - 2.0f * x * x - 2.0f * y * y;
return vAxisZ;
}
const Quaternion RotateBetween( const Vector& v1, const Vector& v2 )
{
// Find quaternion that rotates v1 into v2
Quaternion qOut;
Vector vBisector = 0.5f * ( v1 + v2 );
if ( vBisector.LengthSqr() > 1e-9f )
{
qOut.Init( CrossProduct( v1, vBisector ), DotProduct( v1, vBisector ) );
}
else
{
// Anti-parallel: Use a perpendicular vector
if ( fabsf( v1.x ) > 0.5f )
{
qOut.x = v1.y;
qOut.y = -v1.x;
qOut.z = 0.0f;
}
else
{
qOut.x = 0.0f;
qOut.y = v1.z;
qOut.z = -v1.y;
}
qOut.w = 0.0f;
}
// The algorithm is simplified and made more accurate by normalizing at the end
QuaternionNormalize( qOut );
Assert( ( VectorTransform( v1, QuaternionMatrix( qOut ) ) - v2 ).Length() < 2e-3f );
return qOut;
}
void UnitTestQuatExpLog()
{
for ( int i = 0; i < 300000; ++i )
{
Quaternion q = RandomQuaternion();
Vector l = QuaternionLog( q );
Quaternion q2 = Exp( l );
Assert( QuaternionLength( q - q2 ) < 0.0001f );
}
}
void UnitTestRotateBetween()
{
RandomSeed( 1 );
float flMaxError = 0;
int nMaxError;
for ( int i = 0; i < 3000000; ++i )
{
Vector u = RandomVectorOnUnitSphere(), v = RandomVectorOnUnitSphere();
Quaternion q = RotateBetween( u, v );
float flError = ( VectorTransform( u, QuaternionMatrix( q ) ) - v ).Length();
if ( flMaxError < flError )
{
flMaxError = flError;
nMaxError = i;
}
}
Assert( flMaxError < 0.001f );
}
//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion into engine angles
// Input : *quaternion - q3 + q0.i + q1.j + q2.k
// *outAngles - PITCH, YAW, ROLL
//-----------------------------------------------------------------------------
void QuaternionAngles( const Quaternion &q, QAngle &angles )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "QuaternionAngles", "Mathlib" );
#endif
#if 1
// FIXME: doing it this way calculates too much data, needs to do an optimized version...
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
MatrixAngles( matrix, angles );
#else
float m11, m12, m13, m23, m33;
m11 = ( 2.0f * q.w * q.w ) + ( 2.0f * q.x * q.x ) - 1.0f;
m12 = ( 2.0f * q.x * q.y ) + ( 2.0f * q.w * q.z );
m13 = ( 2.0f * q.x * q.z ) - ( 2.0f * q.w * q.y );
m23 = ( 2.0f * q.y * q.z ) + ( 2.0f * q.w * q.x );
m33 = ( 2.0f * q.w * q.w ) + ( 2.0f * q.z * q.z ) - 1.0f;
// FIXME: this code has a singularity near PITCH +-90
angles[YAW] = RAD2DEG( atan2(m12, m11) );
angles[PITCH] = RAD2DEG( asin(-m13) );
angles[ROLL] = RAD2DEG( atan2(m23, m33) );
#endif
Assert( angles.IsValid() );
}
float QuaternionionGetYaw( const Quaternion &q )
{
// FIXME: doing it this way calculates too much data, need to do an optimized version...
QAngle angles;
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
MatrixAngles( matrix, angles );
return angles[ YAW ];
}
float QuaternionionGetPitch( const Quaternion &q )
{
// FIXME: doing it this way calculates too much data, need to do an optimized version...
QAngle angles;
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
MatrixAngles( matrix, angles );
return angles[ PITCH ];
}
float QuaternionionGetRoll( const Quaternion &q )
{
// FIXME: doing it this way calculates too much data, need to do an optimized version...
QAngle angles;
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
MatrixAngles( matrix, angles );
return angles[ ROLL ];
}
//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion into FLU vectors
// Input : *quaternion - q3 + q0.i + q1.j + q2.k
// basis vectors, each vector is optional
//-----------------------------------------------------------------------------
void QuaternionVectorsFLU( Quaternion const &q, Vector *pForward, Vector *pLeft, Vector *pUp )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
#ifdef _VPROF_MATHLIB
// @TODO: VPROF_BUDGET( "QuaternionVectorsFLU", "Mathlib" );
#endif
// Note: it's pretty much identical to just computing the quaternion matrix and assigning its columns to the vectors
*pForward = q.GetForward();
*pLeft = q.GetLeft();
*pUp = q.GetUp();
#ifdef DBGFLAG_ASSERT
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
Vector forward, left, up;
MatrixVectorsFLU( matrix, &forward, &left, &up );
Assert( ( forward - *pForward ).Length() + ( left - *pLeft ).Length() + ( up - *pUp ).Length() < 1e-4f );
#endif
}
void QuaternionVectorsForward( const Quaternion& q, Vector *pForward )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
#ifdef _VPROF_MATHLIB
// @TODO: VPROF_BUDGET( "QuaternionVectorsForward", "Mathlib" );
#endif
*pForward = q.GetForward();
#ifdef DBGFLAG_ASSERT
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
Assert( ( MatrixGetColumn( matrix, FORWARD_AXIS ) - *pForward ).Length() < 1e-4f );
#endif
}
void UnitTestVectorFLU()
{
for ( int i = 0; i < 100000; ++i )
{
Quaternion q = RandomQuaternion();
Vector forward, left, up;
QuaternionVectorsForward( q, &forward );
QuaternionVectorsFLU( q, &forward, &left, &up );
}
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion to an axis / angle in degrees
// (exponential map)
//-----------------------------------------------------------------------------
void QuaternionAxisAngle( const Quaternion &q, Vector &axis, float &angle )
{
angle = RAD2DEG(2 * acos(q.w));
if ( angle > 180 )
{
angle -= 360;
}
axis.x = q.x;
axis.y = q.y;
axis.z = q.z;
VectorNormalize( axis );
}
//-----------------------------------------------------------------------------
// Purpose: Converts an exponential map (ang/axis) to a quaternion
//-----------------------------------------------------------------------------
void AxisAngleQuaternion( const Vector &axis, float angle, Quaternion &q )
{
float sa, ca;
SinCos( DEG2RAD(angle) * 0.5f, &sa, &ca );
q.x = axis.x * sa;
q.y = axis.y * sa;
q.z = axis.z * sa;
q.w = ca;
}
#endif // #if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: Converts radian-euler axis aligned angles to a quaternion
// Input : *pfAngles - Right-handed Euler angles in radians
// *outQuat - quaternion of form (i,j,k,real)
//-----------------------------------------------------------------------------
void AngleQuaternion( const RadianEuler &angles, Quaternion &outQuat )
{
Assert( s_bMathlibInitialized );
// Assert( angles.IsValid() );
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "AngleQuaternion", "Mathlib" );
#endif
float sr, sp, sy, cr, cp, cy;
#ifdef _X360
fltx4 radians, scale, sine, cosine;
radians = LoadUnaligned3SIMD( &angles.x );
scale = ReplicateX4( 0.5f );
radians = MulSIMD( radians, scale );
SinCos3SIMD( sine, cosine, radians );
// NOTE: The ordering here is *different* from the AngleQuaternion below
// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
sr = SubFloat( sine, 0 ); sp = SubFloat( sine, 1 ); sy = SubFloat( sine, 2 );
cr = SubFloat( cosine, 0 ); cp = SubFloat( cosine, 1 ); cy = SubFloat( cosine, 2 );
#else
SinCos( angles.z * 0.5f, &sy, &cy );
SinCos( angles.y * 0.5f, &sp, &cp );
SinCos( angles.x * 0.5f, &sr, &cr );
#endif
// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
float srXcp = sr * cp, crXsp = cr * sp;
outQuat.x = srXcp*cy-crXsp*sy; // X
outQuat.y = crXsp*cy+srXcp*sy; // Y
float crXcp = cr * cp, srXsp = sr * sp;
outQuat.z = crXcp*sy-srXsp*cy; // Z
outQuat.w = crXcp*cy+srXsp*sy; // W (real component)
}
#ifdef _X360
//-----------------------------------------------------------------------------
// Purpose: Converts radian-euler axis aligned angles to a quaternion, returning
// it on a vector register.
// Input : *vAngles - Right-handed Euler angles in radians (roll pitch yaw)
//
// Algorithm based on that found in the XDK (which really uses RPY order, as
// opposed to this which takes the parameters in RPY order but catenates them
// in PYR order).
//-----------------------------------------------------------------------------
fltx4 AngleQuaternionSIMD( FLTX4 vAngles )
{
Assert( s_bMathlibInitialized );
// Assert( angles.IsValid() );
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "AngleQuaternion", "Mathlib" );
#endif
// we compute the sin and cos of half all the angles.
// in the comments I'll call these components
// sr = sin(r/2), cp = cos(p/2), sy = sin(y/2), etc.
fltx4 OneHalf = __vspltisw(1);
OneHalf = __vcfsx(OneHalf, 1);
fltx4 HalfAngles = MulSIMD(vAngles, OneHalf);
fltx4 sine,cosine;
SinCos3SIMD(sine, cosine, HalfAngles);
fltx4 SignMask = __vspltisw(-1);
fltx4 Zero = __vspltisw(0);
SignMask = __vslw(SignMask, SignMask); // shift left so 1 is only in the sign bit
SignMask = __vrlimi(SignMask, Zero, 0x5, 0); // { -1, 0, -1, 0 }
fltx4 Rc, Pc, Yc, Rs, Ps, Ys, retsum, retval;
Rc = __vspltw(cosine, 0); // cr cr cr cr
Pc = __vspltw(cosine, 1); // cp cp cp cp
Yc = __vspltw(cosine, 2); // cy cy cy cy
Rs = __vspltw(sine, 0); // sr sr sr sr
Ps = __vspltw(sine, 1); // sp sp sp sp
Ys = __vspltw(sine, 2); // sy sy sy sy
Rc = __vrlimi(Rc, sine, 0x8, 0); // sr cr cr cr
Rs = __vrlimi(Rs, cosine, 0x8, 0); // cr sr sr sr
Pc = __vrlimi(Pc, sine, 0x4, 0); // cp sp cp cp
Ps = __vrlimi(Ps, cosine, 0x4, 0); // sp cp sp sp
Yc = __vrlimi(Yc, sine, 0x2, 0); // cy cy sy cy
Ys = __vrlimi(Ys, cosine, 0x2, 0); // sy sy cy sy
retsum = __vxor(Rs, SignMask); // -cr sr -sr sr
retval = __vmulfp(Pc, Yc); // cp*cy sp*cy cp*sy cp*cy
retsum = __vmulfp(retsum, Ys); // -cr*sy sr*sy -sr*cy sr*sy
retval = __vmulfp(retval, Rc); // cp*cy*sr sp*cy*cr cp*sy*cr cp*cy*cr
retval = __vmaddfp(retsum, Ps, retval); // cp*cy*sr + -cr*sy*sp ...
return retval;
}
inline fltx4 AngleQuaternionSIMD( const RadianEuler &angles )
{
return AngleQuaternionSIMD(LoadUnaligned3SIMD(angles.Base()));
}
#endif
//-----------------------------------------------------------------------------
// Purpose: Converts engine-format euler angles to a quaternion
// Input : angles - Right-handed Euler angles in degrees as follows:
// [0]: PITCH: Clockwise rotation around the Y axis.
// [1]: YAW: Counterclockwise rotation around the Z axis.
// [2]: ROLL: Counterclockwise rotation around the X axis.
// *outQuat - quaternion of form (i,j,k,real)
//-----------------------------------------------------------------------------
void AngleQuaternion( const QAngle &angles, Quaternion &outQuat )
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET( "AngleQuaternion", "Mathlib" );
#endif
float sr, sp, sy, cr, cp, cy;
#ifdef _X360
fltx4 radians, scale, sine, cosine;
radians = LoadUnaligned3SIMD( angles.Base() );
scale = ReplicateX4( 0.5f * M_PI_F / 180.f );
radians = MulSIMD( radians, scale );
SinCos3SIMD( sine, cosine, radians );
// NOTE: The ordering here is *different* from the AngleQuaternion above
// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
sp = SubFloat( sine, 0 ); sy = SubFloat( sine, 1 ); sr = SubFloat( sine, 2 );
cp = SubFloat( cosine, 0 ); cy = SubFloat( cosine, 1 ); cr = SubFloat( cosine, 2 );
#else
SinCos( DEG2RAD( angles.y ) * 0.5f, &sy, &cy );
SinCos( DEG2RAD( angles.x ) * 0.5f, &sp, &cp );
SinCos( DEG2RAD( angles.z ) * 0.5f, &sr, &cr );
#endif
// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
float srXcp = sr * cp, crXsp = cr * sp;
outQuat.x = srXcp*cy-crXsp*sy; // X
outQuat.y = crXsp*cy+srXcp*sy; // Y
float crXcp = cr * cp, srXsp = sr * sp;
outQuat.z = crXcp*sy-srXsp*cy; // Z
outQuat.w = crXcp*cy+srXsp*sy; // W (real component)
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: Converts a basis to a quaternion
//-----------------------------------------------------------------------------
void BasisToQuaternion( const Vector &vecForward, const Vector &vecRight, const Vector &vecUp, Quaternion &q )
{
Assert( fabs( vecForward.LengthSqr() - 1.0f ) < 1e-3 );
Assert( fabs( vecRight.LengthSqr() - 1.0f ) < 1e-3 );
Assert( fabs( vecUp.LengthSqr() - 1.0f ) < 1e-3 );
Vector vecLeft;
VectorMultiply( vecRight, -1.0f, vecLeft );
// FIXME: Don't know why, but this doesn't match at all with other result
// so we can't use this super-fast way.
/*
// Find the trace of the matrix:
float flTrace = vecForward.x + vecLeft.y + vecUp.z + 1.0f;
if ( flTrace > 1e-6 )
{
float flSqrtTrace = FastSqrt( flTrace );
float s = 0.5f / flSqrtTrace;
q.x = ( vecUp.y - vecLeft.z ) * s;
q.y = ( vecForward.z - vecUp.x ) * s;
q.z = ( vecLeft.x - vecForward.y ) * s;
q.w = 0.5f * flSqrtTrace;
}
else
{
if (( vecForward.x > vecLeft.y ) && ( vecForward.x > vecUp.z ) )
{
float flSqrtTrace = FastSqrt( 1.0f + vecForward.x - vecLeft.y - vecUp.z );
float s = 0.5f / flSqrtTrace;
q.x = 0.5f * flSqrtTrace;
q.y = ( vecForward.y + vecLeft.x ) * s;
q.z = ( vecUp.x + vecForward.z ) * s;
q.w = ( vecUp.y - vecLeft.z ) * s;
}
else if ( vecLeft.y > vecUp.z )
{
float flSqrtTrace = FastSqrt( 1.0f + vecLeft.y - vecForward.x - vecUp.z );
float s = 0.5f / flSqrtTrace;
q.x = ( vecForward.y + vecLeft.x ) * s;
q.y = 0.5f * flSqrtTrace;
q.z = ( vecUp.y + vecLeft.z ) * s;
q.w = ( vecForward.z - vecUp.x ) * s;
}
else
{
float flSqrtTrace = FastSqrt( 1.0 + vecUp.z - vecForward.x - vecLeft.y );
float s = 0.5f / flSqrtTrace;
q.x = ( vecUp.x + vecForward.z ) * s;
q.y = ( vecUp.y + vecLeft.z ) * s;
q.z = 0.5f * flSqrtTrace;
q.w = ( vecLeft.x - vecForward.y ) * s;
}
}
QuaternionNormalize( q );
*/
// Version 2: Go through angles
matrix3x4_t mat;
MatrixSetColumn( vecForward, 0, mat );
MatrixSetColumn( vecLeft, 1, mat );
MatrixSetColumn( vecUp, 2, mat );
QAngle angles;
MatrixAngles( mat, angles );
// Quaternion q2;
AngleQuaternion( angles, q );
// Assert( fabs(q.x - q2.x) < 1e-3 );
// Assert( fabs(q.y - q2.y) < 1e-3 );
// Assert( fabs(q.z - q2.z) < 1e-3 );
// Assert( fabs(q.w - q2.w) < 1e-3 );
}
// FIXME: Optimize!
void MatrixQuaternion( const matrix3x4_t &mat, Quaternion &q )
{
QAngle angles;
MatrixAngles( mat, angles );
AngleQuaternion( angles, q );
}
#endif // #if !defined(__SPU__)
void MatrixQuaternionFast( const matrix3x4_t &mat, Quaternion &q )
{
float t;
if ( mat[ 2 ][ 2 ] < 0 )
{
if ( mat[ 0 ][ 0 ] > mat[ 1 ][ 1 ] )
{
t = 1 + mat[ 0 ][ 0 ] - mat[ 1 ][ 1 ] - mat[ 2 ][ 2 ];
q.Init( t, mat[ 0 ][ 1 ] + mat[ 1 ][ 0 ], mat[ 2 ][ 0 ] + mat[ 0 ][ 2 ], mat[ 2 ][ 1 ] - mat[ 1 ][ 2 ] );
}
else
{
t = 1 - mat[ 0 ][ 0 ] + mat[ 1 ][ 1 ] - mat[ 2 ][ 2 ];
q.Init( mat[ 0 ][ 1 ] + mat[ 1 ][ 0 ], t, mat[ 1 ][ 2 ] + mat[ 2 ][ 1 ], mat[ 0 ][ 2 ] - mat[ 2 ][ 0 ] );
}
}
else
{
if ( mat[ 0 ][ 0 ] < -mat[ 1 ][ 1 ] )
{
t = 1 - mat[ 0 ][ 0 ] - mat[ 1 ][ 1 ] + mat[ 2 ][ 2 ];
q.Init( mat[ 2 ][ 0 ] + mat[ 0 ][ 2 ], mat[ 1 ][ 2 ] + mat[ 2 ][ 1 ], t, mat[ 1 ][ 0 ] - mat[ 0 ][ 1 ] );
}
else
{
t = 1 + mat[ 0 ][ 0 ] + mat[ 1 ][ 1 ] + mat[ 2 ][ 2 ];
q.Init( mat[ 2 ][ 1 ] - mat[ 1 ][ 2 ], mat[ 0 ][ 2 ] - mat[ 2 ][ 0 ], mat[ 1 ][ 0 ] - mat[ 0 ][ 1 ], t );
}
}
q = q * ( 0.5f / sqrtf( t ) );
}
float MatrixQuaternionTest( uint nCount )
{
float flMaxError = 0, flSumError = 0;
for ( uint i = 0; i < nCount; ++i )
{
Quaternion q = RandomQuaternion(), r;
Assert( fabsf( q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w - 1 ) < 1e-5f );
matrix3x4_t mat;
QuaternionMatrix( q, mat );
MatrixQuaternion( mat, r );
if ( QuaternionDotProduct( q, r ) < 0 )
{
r = -r;
}
float flError = Sqr( q.x - r.x ) + Sqr( q.y - r.y ) + Sqr( q.z - r.z ) + Sqr( q.w - r.w );
flSumError += flError;
if ( flError > flMaxError )
{
flMaxError = flError;
}
}
NOTE_UNUSED( flMaxError ); NOTE_UNUSED( flSumError );
return flSumError / nCount;
}
float MatrixQuaternionFastTest( uint nCount )
{
float flMaxError = 0, flSumError = 0;
for ( uint i = 0; i < nCount; ++i )
{
Quaternion q = RandomQuaternion(), r;
Assert( fabsf( q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w - 1 ) < 1e-5f );
matrix3x4_t mat;
QuaternionMatrix( q, mat );
MatrixQuaternionFast( mat, r );
if ( QuaternionDotProduct( q, r ) < 0 )
{
r = -r;
}
float flError = Sqr( q.x - r.x ) + Sqr( q.y - r.y ) + Sqr( q.z - r.z ) + Sqr( q.w - r.w );
flSumError += flError;
if ( flError > flMaxError )
{
flMaxError = flError;
}
}
NOTE_UNUSED( flMaxError ); NOTE_UNUSED( flSumError );
return flSumError / nCount;
}
// the same as MatrixQuaternionTest, but uses inline helper functions that return matrix and quaternion instead of using return-by-reference versions
// on MSVC10, this generates the same code as MatrixQuaternionTest, but it's easier to read, write and maintain code
float MatrixQuaternionTest2( uint nCount )
{
float flMaxError = 0, flSumError = 0;
for ( uint i = 0; i < nCount; ++i )
{
Quaternion q = RandomQuaternion(), r;
Assert( fabsf( q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w - 1 ) < 1e-5f );
matrix3x4_t mat = QuaternionMatrix( q );
r = MatrixQuaternion( mat );
if ( QuaternionDotProduct( q, r ) < 0 )
{
r = -r;
}
float flError = Sqr( q.x - r.x ) + Sqr( q.y - r.y ) + Sqr( q.z - r.z ) + Sqr( q.w - r.w );
flSumError += flError;
if ( flError > flMaxError )
{
flMaxError = flError;
}
}
NOTE_UNUSED( flMaxError ); NOTE_UNUSED( flSumError );
return flSumError / nCount;
}
//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion into engine angles
// Input : *quaternion - q3 + q0.i + q1.j + q2.k
// *outAngles - PITCH, YAW, ROLL
//-----------------------------------------------------------------------------
void QuaternionAngles( const Quaternion &q, RadianEuler &angles )
{
Assert( s_bMathlibInitialized );
Assert( q.IsValid() );
// FIXME: doing it this way calculates too much data, needs to do an optimized version...
matrix3x4_t matrix;
QuaternionMatrix( q, matrix );
MatrixAngles( matrix, angles );
Assert( angles.IsValid() );
}
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: A helper function to normalize p2.x->p1.x and p3.x->p4.x to
// be the same length as p2.x->p3.x
// Input : &p2 -
// &p4 -
// p4n -
//-----------------------------------------------------------------------------
void Spline_Normalize(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
Vector& p1n,
Vector& p4n )
{
float dt = p3.x - p2.x;
p1n = p1;
p4n = p4;
if ( dt != 0.0 )
{
if (p1.x != p2.x)
{
// Equivalent to p1n = p2 - (p2 - p1) * (dt / (p2.x - p1.x));
VectorLerp( p2, p1, dt / (p2.x - p1.x), p1n );
}
if (p4.x != p3.x)
{
// Equivalent to p4n = p3 + (p4 - p3) * (dt / (p4.x - p3.x));
VectorLerp( p3, p4, dt / (p4.x - p3.x), p4n );
}
}
}
#endif // #if !defined(__SPU__)
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose:
// Input :
//-----------------------------------------------------------------------------
void Catmull_Rom_Spline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float tSqr = t*t*0.5f;
float tSqrSqr = t*tSqr;
t *= 0.5f;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
VectorScale( p1, -tSqrSqr, a ); // 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
VectorScale( p2, tSqrSqr*3, b );
VectorScale( p3, tSqrSqr*-3, c );
VectorScale( p4, tSqrSqr, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 2
VectorScale( p1, tSqr*2, a ); // 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
VectorScale( p2, tSqr*-5, b );
VectorScale( p3, tSqr*4, c );
VectorScale( p4, -tSqr, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 3
VectorScale( p1, -t, a ); // 0.5 t * [ (-1*p1) + p3 ]
VectorScale( p3, t, b );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
// matrix row 4
VectorAdd( p2, output, output ); // p2
}
void Catmull_Rom_Spline_Tangent(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float tOne = 3*t*t*0.5f;
float tTwo = 2*t*0.5f;
float tThree = 0.5;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
VectorScale( p1, -tOne, a ); // 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
VectorScale( p2, tOne*3, b );
VectorScale( p3, tOne*-3, c );
VectorScale( p4, tOne, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 2
VectorScale( p1, tTwo*2, a ); // 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
VectorScale( p2, tTwo*-5, b );
VectorScale( p3, tTwo*4, c );
VectorScale( p4, -tTwo, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 3
VectorScale( p1, -tThree, a ); // 0.5 t * [ (-1*p1) + p3 ]
VectorScale( p3, tThree, b );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
}
// area under the curve [0..t]
void Catmull_Rom_Spline_Integral(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
output = p2*t
-0.25f*(p1 - p3)*t*t
+ (1.0f/6.0f)*(2.0f*p1 - 5.0f*p2 + 4.0f*p3 - p4)*t*t*t
- 0.125f*(p1 - 3.0f*p2 + 3.0f*p3 - p4)*t*t*t*t;
}
// area under the curve [0..1]
void Catmull_Rom_Spline_Integral(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
Vector& output )
{
output = (-0.25f * p1 + 3.25f * p2 + 3.25f * p3 - 0.25f * p4) * (1.0f / 6.0f);
}
void Catmull_Rom_Spline_Normalize(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
float dt = p3.DistTo(p2);
Vector p1n, p4n;
VectorSubtract( p1, p2, p1n );
VectorSubtract( p4, p3, p4n );
VectorNormalize( p1n );
VectorNormalize( p4n );
VectorMA( p2, dt, p1n, p1n );
VectorMA( p3, dt, p4n, p4n );
Catmull_Rom_Spline( p1n, p2, p3, p4n, t, output );
}
void Catmull_Rom_Spline_Integral_Normalize(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
float dt = p3.DistTo(p2);
Vector p1n, p4n;
VectorSubtract( p1, p2, p1n );
VectorSubtract( p4, p3, p4n );
VectorNormalize( p1n );
VectorNormalize( p4n );
VectorMA( p2, dt, p1n, p1n );
VectorMA( p3, dt, p4n, p4n );
Catmull_Rom_Spline_Integral( p1n, p2, p3, p4n, t, output );
}
void Catmull_Rom_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Vector p1n, p4n;
Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
Catmull_Rom_Spline( p1n, p2, p3, p4n, t, output );
}
#endif // !defined(__SPU__)
//-----------------------------------------------------------------------------
// Purpose: basic hermite spline. t = 0 returns p1, t = 1 returns p2,
// d1 and d2 are used to entry and exit slope of curve
// Input :
//-----------------------------------------------------------------------------
void Hermite_Spline(
const Vector &p1,
const Vector &p2,
const Vector &d1,
const Vector &d2,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float tSqr = t*t;
float tCube = t*tSqr;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &d1 );
Assert( &output != &d2 );
float b1 = 2.0f*tCube-3.0f*tSqr+1.0f;
float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
float b3 = tCube-2*tSqr+t;
float b4 = tCube-tSqr;
VectorScale( p1, b1, output );
VectorMA( output, b2, p2, output );
VectorMA( output, b3, d1, output );
VectorMA( output, b4, d2, output );
}
float Hermite_Spline(
float p1,
float p2,
float d1,
float d2,
float t )
{
Assert( s_bMathlibInitialized );
float output;
float tSqr = t*t;
float tCube = t*tSqr;
float b1 = 2.0f*tCube-3.0f*tSqr+1.0f;
float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
float b3 = tCube-2*tSqr+t;
float b4 = tCube-tSqr;
output = p1 * b1;
output += p2 * b2;
output += d1 * b3;
output += d2 * b4;
return output;
}
void Hermite_SplineBasis( float t, float basis[4] )
{
float tSqr = t*t;
float tCube = t*tSqr;
basis[0] = 2.0f*tCube-3.0f*tSqr+1.0f;
basis[1] = 1.0f - basis[0]; // -2*tCube+3*tSqr;
basis[2] = tCube-2*tSqr+t;
basis[3] = tCube-tSqr;
}
//-----------------------------------------------------------------------------
// Purpose: simple three data point hermite spline.
// t = 0 returns p1, t = 1 returns p2,
// slopes are generated from the p0->p1 and p1->p2 segments
// this is reasonable C1 method when there's no "p3" data yet.
// Input :
//-----------------------------------------------------------------------------
// BUG: the VectorSubtract()'s calls go away if the global optimizer is enabled
#if !defined(__SPU__)
#pragma optimize( "g", off )
#endif
void Hermite_Spline( const Vector &p0, const Vector &p1, const Vector &p2, float t, Vector& output )
{
Vector e10, e21;
VectorSubtract( p1, p0, e10 );
VectorSubtract( p2, p1, e21 );
Hermite_Spline( p1, p2, e10, e21, t, output );
}
#if !defined(__SPU__)
#pragma optimize( "", on )
#endif
float Hermite_Spline( float p0, float p1, float p2, float t )
{
return Hermite_Spline( p1, p2, p1 - p0, p2 - p1, t );
}
void Hermite_Spline( const Quaternion &q0, const Quaternion &q1, const Quaternion &q2, float t, Quaternion &output )
{
// cheap, hacked version of quaternions
Quaternion q0a;
Quaternion q1a;
QuaternionAlign( q2, q0, q0a );
QuaternionAlign( q2, q1, q1a );
output.x = Hermite_Spline( q0a.x, q1a.x, q2.x, t );
output.y = Hermite_Spline( q0a.y, q1a.y, q2.y, t );
output.z = Hermite_Spline( q0a.z, q1a.z, q2.z, t );
output.w = Hermite_Spline( q0a.w, q1a.w, q2.w, t );
QuaternionNormalize( output );
}
#if !defined(__SPU__)
// See http://en.wikipedia.org/wiki/Kochanek-Bartels_curves
//
// Tension: -1 = Round -> 1 = Tight
// Bias: -1 = Pre-shoot (bias left) -> 1 = Post-shoot (bias right)
// Continuity: -1 = Box corners -> 1 = Inverted corners
//
// If T=B=C=0 it's the same matrix as Catmull-Rom.
// If T=1 & B=C=0 it's the same as Cubic.
// If T=B=0 & C=-1 it's just linear interpolation
//
// See http://news.povray.org/povray.binaries.tutorials/attachment/%[email protected]%3E/Splines.bas.txt
// for example code and descriptions of various spline types...
//
void Kochanek_Bartels_Spline(
float tension,
float bias,
float continuity,
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float ffa, ffb, ffc, ffd;
ffa = ( 1.0f - tension ) * ( 1.0f + continuity ) * ( 1.0f + bias );
ffb = ( 1.0f - tension ) * ( 1.0f - continuity ) * ( 1.0f - bias );
ffc = ( 1.0f - tension ) * ( 1.0f - continuity ) * ( 1.0f + bias );
ffd = ( 1.0f - tension ) * ( 1.0f + continuity ) * ( 1.0f - bias );
float tSqr = t*t*0.5f;
float tSqrSqr = t*tSqr;
t *= 0.5f;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
VectorScale( p1, tSqrSqr * -ffa, a );
VectorScale( p2, tSqrSqr * ( 4.0f + ffa - ffb - ffc ), b );
VectorScale( p3, tSqrSqr * ( -4.0f + ffb + ffc - ffd ), c );
VectorScale( p4, tSqrSqr * ffd, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 2
VectorScale( p1, tSqr* 2 * ffa, a );
VectorScale( p2, tSqr * ( -6 - 2 * ffa + 2 * ffb + ffc ), b );
VectorScale( p3, tSqr * ( 6 - 2 * ffb - ffc + ffd ), c );
VectorScale( p4, tSqr * -ffd, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 3
VectorScale( p1, t * -ffa, a );
VectorScale( p2, t * ( ffa - ffb ), b );
VectorScale( p3, t * ffb, c );
// p4 unchanged
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
// matrix row 4
// p1, p3, p4 unchanged
// p2 is multiplied by 1 and added, so just added it directly
VectorAdd( p2, output, output );
}
void Kochanek_Bartels_Spline_NormalizeX(
float tension,
float bias,
float continuity,
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Vector p1n, p4n;
Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
Kochanek_Bartels_Spline( tension, bias, continuity, p1n, p2, p3, p4n, t, output );
}
void Cubic_Spline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float tSqr = t*t;
float tSqrSqr = t*tSqr;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
VectorScale( p2, tSqrSqr * 2, b );
VectorScale( p3, tSqrSqr * -2, c );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
// matrix row 2
VectorScale( p2, tSqr * -3, b );
VectorScale( p3, tSqr * 3, c );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
// matrix row 3
// no influence
// p4 unchanged
// matrix row 4
// p1, p3, p4 unchanged
VectorAdd( p2, output, output );
}
void Cubic_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Vector p1n, p4n;
Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
Cubic_Spline( p1n, p2, p3, p4n, t, output );
}
void BSpline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float oneOver6 = 1.0f / 6.0f;
float tSqr = t * t * oneOver6;
float tSqrSqr = t*tSqr;
t *= oneOver6;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
VectorScale( p1, -tSqrSqr, a );
VectorScale( p2, tSqrSqr * 3.0f, b );
VectorScale( p3, tSqrSqr * -3.0f, c );
VectorScale( p4, tSqrSqr, d );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
VectorAdd( d, output, output );
// matrix row 2
VectorScale( p1, tSqr * 3.0f, a );
VectorScale( p2, tSqr * -6.0f, b );
VectorScale( p3, tSqr * 3.0f, c );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
// matrix row 3
VectorScale( p1, t * -3.0f, a );
VectorScale( p3, t * 3.0f, c );
// p4 unchanged
VectorAdd( a, output, output );
VectorAdd( c, output, output );
// matrix row 4
// p1 and p3 scaled by 1.0f, so done below
VectorScale( p1, oneOver6, a );
VectorScale( p2, 4.0f * oneOver6, b );
VectorScale( p3, oneOver6, c );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
}
void BSpline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Vector p1n, p4n;
Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
BSpline( p1n, p2, p3, p4n, t, output );
}
void Parabolic_Spline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Assert( s_bMathlibInitialized );
float tSqr = t*t*0.5f;
t *= 0.5f;
Assert( &output != &p1 );
Assert( &output != &p2 );
Assert( &output != &p3 );
Assert( &output != &p4 );
output.Init();
Vector a, b, c, d;
// matrix row 1
// no influence from t cubed
// matrix row 2
VectorScale( p1, tSqr, a );
VectorScale( p2, tSqr * -2.0f, b );
VectorScale( p3, tSqr, c );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
VectorAdd( c, output, output );
// matrix row 3
VectorScale( p1, t * -2.0f, a );
VectorScale( p2, t * 2.0f, b );
// p4 unchanged
VectorAdd( a, output, output );
VectorAdd( b, output, output );
// matrix row 4
VectorScale( p1, 0.5f, a );
VectorScale( p2, 0.5f, b );
VectorAdd( a, output, output );
VectorAdd( b, output, output );
}
void Parabolic_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output )
{
Vector p1n, p4n;
Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
Parabolic_Spline( p1n, p2, p3, p4n, t, output );
}
//-----------------------------------------------------------------------------
// Cubic Bernstein basis functions
// http://mathworld.wolfram.com/BernsteinPolynomial.html
//
// Purpose: Evaluate the cubic Bernstein basis for the input parametric coordinate.
// Output is the coefficient for that basis polynomial.
//-----------------------------------------------------------------------------
float CubicBasis0( float t )
{
float invT = 1.0f-t;
return invT*invT*invT;
}
float CubicBasis1( float t )
{
float invT = 1.0f-t;
return 3.0f*t*invT*invT;
}
float CubicBasis2( float t )
{
float invT = 1.0f-t;
return 3.0f*t*t*invT;
}
float CubicBasis3( float t )
{
return t*t*t;
}
//-----------------------------------------------------------------------------
// Purpose: Compress the input values for a ranged result such that from 75% to 200% smoothly of the range maps
//-----------------------------------------------------------------------------
float RangeCompressor( float flValue, float flMin, float flMax, float flBase )
{
// clamp base
if (flBase < flMin)
flBase = flMin;
if (flBase > flMax)
flBase = flMax;
flValue += flBase;
// convert to 0 to 1 value
float flMid = (flValue - flMin) / (flMax - flMin);
// convert to -1 to 1 value
float flTarget = flMid * 2 - 1;
if (fabs(flTarget) > 0.75)
{
float t = (fabs(flTarget) - 0.75) / (1.25);
if (t < 1.0)
{
if (flTarget > 0)
{
flTarget = Hermite_Spline( 0.75, 1, 0.75, 0, t );
}
else
{
flTarget = -Hermite_Spline( 0.75, 1, 0.75, 0, t );
}
}
else
{
flTarget = (flTarget > 0) ? 1.0f : -1.0f;
}
}
flMid = (flTarget + 1 ) / 2.0;
flValue = flMin * (1 - flMid) + flMax * flMid;
flValue -= flBase;
return flValue;
}
//#pragma optimize( "", on )
//-----------------------------------------------------------------------------
// Transforms a AABB into another space; which will inherently grow the box.
//-----------------------------------------------------------------------------
void TransformAABB( const matrix3x4_t& transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
Vector localCenter;
VectorAdd( vecMinsIn, vecMaxsIn, localCenter );
localCenter *= 0.5f;
Vector localExtents;
VectorSubtract( vecMaxsIn, localCenter, localExtents );
Vector worldCenter;
VectorTransform( localCenter, transform, worldCenter );
Vector worldExtents;
worldExtents.x = DotProductAbs( localExtents, transform[0] );
worldExtents.y = DotProductAbs( localExtents, transform[1] );
worldExtents.z = DotProductAbs( localExtents, transform[2] );
VectorSubtract( worldCenter, worldExtents, vecMinsOut );
VectorAdd( worldCenter, worldExtents, vecMaxsOut );
// sanity chec
Assert( vecMinsOut.LengthSqr() + vecMaxsOut.LengthSqr() < 1e+12 );
}
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void ITransformAABB( const matrix3x4_t& transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
Vector worldCenter;
VectorAdd( vecMinsIn, vecMaxsIn, worldCenter );
worldCenter *= 0.5f;
Vector worldExtents;
VectorSubtract( vecMaxsIn, worldCenter, worldExtents );
Vector localCenter;
VectorITransform( worldCenter, transform, localCenter );
Vector localExtents;
localExtents.x = FloatMakePositive( worldExtents.x * transform[0][0] ) +
FloatMakePositive( worldExtents.y * transform[1][0] ) +
FloatMakePositive( worldExtents.z * transform[2][0] );
localExtents.y = FloatMakePositive( worldExtents.x * transform[0][1] ) +
FloatMakePositive( worldExtents.y * transform[1][1] ) +
FloatMakePositive( worldExtents.z * transform[2][1] );
localExtents.z = FloatMakePositive( worldExtents.x * transform[0][2] ) +
FloatMakePositive( worldExtents.y * transform[1][2] ) +
FloatMakePositive( worldExtents.z * transform[2][2] );
VectorSubtract( localCenter, localExtents, vecMinsOut );
VectorAdd( localCenter, localExtents, vecMaxsOut );
}
//-----------------------------------------------------------------------------
// Rotates a AABB into another space; which will inherently grow the box.
// (same as TransformAABB, but doesn't take the translation into account)
//-----------------------------------------------------------------------------
void RotateAABB( const matrix3x4_t &transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
Vector localCenter;
VectorAdd( vecMinsIn, vecMaxsIn, localCenter );
localCenter *= 0.5f;
Vector localExtents;
VectorSubtract( vecMaxsIn, localCenter, localExtents );
Vector newCenter;
VectorRotate( localCenter, transform, newCenter );
Vector newExtents;
newExtents.x = DotProductAbs( localExtents, transform[0] );
newExtents.y = DotProductAbs( localExtents, transform[1] );
newExtents.z = DotProductAbs( localExtents, transform[2] );
VectorSubtract( newCenter, newExtents, vecMinsOut );
VectorAdd( newCenter, newExtents, vecMaxsOut );
}
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void IRotateAABB( const matrix3x4_t &transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
Vector oldCenter;
VectorAdd( vecMinsIn, vecMaxsIn, oldCenter );
oldCenter *= 0.5f;
Vector oldExtents;
VectorSubtract( vecMaxsIn, oldCenter, oldExtents );
Vector newCenter;
VectorIRotate( oldCenter, transform, newCenter );
Vector newExtents;
newExtents.x = FloatMakePositive( oldExtents.x * transform[0][0] ) +
FloatMakePositive( oldExtents.y * transform[1][0] ) +
FloatMakePositive( oldExtents.z * transform[2][0] );
newExtents.y = FloatMakePositive( oldExtents.x * transform[0][1] ) +
FloatMakePositive( oldExtents.y * transform[1][1] ) +
FloatMakePositive( oldExtents.z * transform[2][1] );
newExtents.z = FloatMakePositive( oldExtents.x * transform[0][2] ) +
FloatMakePositive( oldExtents.y * transform[1][2] ) +
FloatMakePositive( oldExtents.z * transform[2][2] );
VectorSubtract( newCenter, newExtents, vecMinsOut );
VectorAdd( newCenter, newExtents, vecMaxsOut );
}
float CalcSqrDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point )
{
float flDelta;
float flDistSqr = 0.0f;
if ( point.x < mins.x )
{
flDelta = (mins.x - point.x);
flDistSqr += flDelta * flDelta;
}
else if ( point.x > maxs.x )
{
flDelta = (point.x - maxs.x);
flDistSqr += flDelta * flDelta;
}
if ( point.y < mins.y )
{
flDelta = (mins.y - point.y);
flDistSqr += flDelta * flDelta;
}
else if ( point.y > maxs.y )
{
flDelta = (point.y - maxs.y);
flDistSqr += flDelta * flDelta;
}
if ( point.z < mins.z )
{
flDelta = (mins.z - point.z);
flDistSqr += flDelta * flDelta;
}
else if ( point.z > maxs.z )
{
flDelta = (point.z - maxs.z);
flDistSqr += flDelta * flDelta;
}
return flDistSqr;
}
void CalcClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut )
{
closestOut.x = clamp( point.x, mins.x, maxs.x );
closestOut.y = clamp( point.y, mins.y, maxs.y );
closestOut.z = clamp( point.z, mins.z, maxs.z );
}
void CalcSqrDistAndClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut, float &distSqrOut )
{
distSqrOut = 0.0f;
for ( int i = 0; i < 3; i++ )
{
if ( point[i] < mins[i] )
{
closestOut[i] = mins[i];
float flDelta = closestOut[i] - mins[i];
distSqrOut += flDelta * flDelta;
}
else if ( point[i] > maxs[i] )
{
closestOut[i] = maxs[i];
float flDelta = closestOut[i] - maxs[i];
distSqrOut += flDelta * flDelta;
}
else
{
closestOut[i] = point[i];
}
}
}
float CalcClosestPointToLineT( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vDir )
{
Assert( s_bMathlibInitialized );
VectorSubtract( vLineB, vLineA, vDir );
// D dot [P - (A + D*t)] = 0
// t = ( DP - DA) / DD
float div = vDir.Dot( vDir );
if( div < 0.00001f )
{
return 0;
}
else
{
return (vDir.Dot( P ) - vDir.Dot( vLineA )) / div;
}
}
void CalcClosestPointOnLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *outT )
{
Assert( s_bMathlibInitialized );
Vector vDir;
float t = CalcClosestPointToLineT( P, vLineA, vLineB, vDir );
if ( outT ) *outT = t;
vClosest.MulAdd( vLineA, vDir, t );
}
float CalcDistanceToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector vClosest;
CalcClosestPointOnLine( P, vLineA, vLineB, vClosest, outT );
return P.DistTo(vClosest);
}
float CalcDistanceSqrToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector vClosest;
CalcClosestPointOnLine( P, vLineA, vLineB, vClosest, outT );
return P.DistToSqr(vClosest);
}
void CalcClosestPointOnLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *outT )
{
Vector vDir;
float t = CalcClosestPointToLineT( P, vLineA, vLineB, vDir );
t = clamp( t, 0, 1 );
if ( outT )
{
*outT = t;
}
vClosest.MulAdd( vLineA, vDir, t );
}
float CalcDistanceToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector vClosest;
CalcClosestPointOnLineSegment( P, vLineA, vLineB, vClosest, outT );
return P.DistTo( vClosest );
}
float CalcDistanceSqrToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector vClosest;
CalcClosestPointOnLineSegment( P, vLineA, vLineB, vClosest, outT );
return P.DistToSqr(vClosest);
}
float CalcClosestPointToLineT2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vDir )
{
Assert( s_bMathlibInitialized );
Vector2DSubtract( vLineB, vLineA, vDir );
// D dot [P - (A + D*t)] = 0
// t = (DP - DA) / DD
float div = vDir.Dot( vDir );
if( div < 0.00001f )
{
return 0;
}
else
{
return (vDir.Dot( P ) - vDir.Dot( vLineA )) / div;
}
}
void CalcClosestPointOnLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vClosest, float *outT )
{
Assert( s_bMathlibInitialized );
Vector2D vDir;
float t = CalcClosestPointToLineT2D( P, vLineA, vLineB, vDir );
if ( outT ) *outT = t;
vClosest.MulAdd( vLineA, vDir, t );
}
float CalcDistanceToLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector2D vClosest;
CalcClosestPointOnLine2D( P, vLineA, vLineB, vClosest, outT );
return P.DistTo( vClosest );
}
float CalcDistanceSqrToLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector2D vClosest;
CalcClosestPointOnLine2D( P, vLineA, vLineB, vClosest, outT );
return P.DistToSqr(vClosest);
}
void CalcClosestPointOnLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vClosest, float *outT )
{
Vector2D vDir;
float t = CalcClosestPointToLineT2D( P, vLineA, vLineB, vDir );
t = clamp( t, 0, 1 );
if ( outT )
{
*outT = t;
}
vClosest.MulAdd( vLineA, vDir, t );
}
float CalcDistanceToLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector2D vClosest;
CalcClosestPointOnLineSegment2D( P, vLineA, vLineB, vClosest, outT );
return P.DistTo( vClosest );
}
float CalcDistanceSqrToLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
Assert( s_bMathlibInitialized );
Vector2D vClosest;
CalcClosestPointOnLineSegment2D( P, vLineA, vLineB, vClosest, outT );
return P.DistToSqr( vClosest );
}
// Do we have another epsilon we could use
#define LINE_EPS ( 0.000001f )
//-----------------------------------------------------------------------------
// Purpose: Given lines p1->p2 and p3->p4, computes a line segment (pa->pb) and returns the parameters 0->1 multipliers
// along each segment for the returned points
// Input : p1 -
// p2 -
// p3 -
// p4 -
// *s1 -
// *s2 -
// Output : Returns true on success, false on failure.
//-----------------------------------------------------------------------------
bool CalcLineToLineIntersectionSegment(
const Vector& p1,const Vector& p2,const Vector& p3,const Vector& p4,Vector *s1,Vector *s2,
float *t1, float *t2)
{
Vector p13,p43,p21;
float d1343,d4321,d1321,d4343,d2121;
float numer,denom;
p13.x = p1.x - p3.x;
p13.y = p1.y - p3.y;
p13.z = p1.z - p3.z;
p43.x = p4.x - p3.x;
p43.y = p4.y - p3.y;
p43.z = p4.z - p3.z;
if (fabs(p43.x) < LINE_EPS && fabs(p43.y) < LINE_EPS && fabs(p43.z) < LINE_EPS)
return false;
p21.x = p2.x - p1.x;
p21.y = p2.y - p1.y;
p21.z = p2.z - p1.z;
if (fabs(p21.x) < LINE_EPS && fabs(p21.y) < LINE_EPS && fabs(p21.z) < LINE_EPS)
return false;
d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;
denom = d2121 * d4343 - d4321 * d4321;
if (fabs(denom) < LINE_EPS)
return false;
numer = d1343 * d4321 - d1321 * d4343;
*t1 = numer / denom;
*t2 = (d1343 + d4321 * (*t1)) / d4343;
if ( s1 != NULL && s2 != NULL )
{
s1->x = p1.x + *t1 * p21.x;
s1->y = p1.y + *t1 * p21.y;
s1->z = p1.z + *t1 * p21.z;
s2->x = p3.x + *t2 * p43.x;
s2->y = p3.y + *t2 * p43.y;
s2->z = p3.z + *t2 * p43.z;
}
return true;
}
#pragma optimize( "", off )
#ifndef EXCEPTION_EXECUTE_HANDLER
#define EXCEPTION_EXECUTE_HANDLER 1
#endif
#pragma optimize( "", on )
#ifndef NDEBUG
volatile static char const *pDebugString;
#endif
void MathLib_Init( float gamma, float texGamma, float brightness, int overbright, bool bAllow3DNow, bool bAllowSSE, bool bAllowSSE2, bool bAllowMMX )
{
if ( s_bMathlibInitialized )
return;
#ifdef _WIN32
Assert( _rotl( 0xC7654321, 1 ) == 0x8ECA8643 );
Assert( _rotl64( 0xC7654321ABCDEF00ull, 1 ) == 0x8ECA8643579BDE01ull );
#endif
#ifndef NDEBUG
pDebugString = "mathlib.lib built debug!";
#endif
// FIXME: Hook SSE into VectorAligned + Vector4DAligned
#if !defined( _GAMECONSOLE )
// Grab the processor information:
const CPUInformation& pi = GetCPUInformation();
if ( ! ( pi.m_bSSE && pi.m_bSSE2 ) )
{
Assert( 0 );
Error( "SSE and SSE2 are required." );
}
#endif //!360
s_bMathlibInitialized = true;
InitSinCosTable();
BuildGammaTable( gamma, texGamma, brightness, overbright );
SeedRandSIMD( 0x31415926 );
}
bool MathLib_MMXEnabled( void )
{
Assert( s_bMathlibInitialized );
return true;
}
bool MathLib_SSEEnabled( void )
{
Assert( s_bMathlibInitialized );
return true;
}
bool MathLib_SSE2Enabled( void )
{
Assert( s_bMathlibInitialized );
return true;
}
// BUGBUG: Why doesn't this call angle diff?!?!?
float ApproachAngle( float target, float value, float speed )
{
target = anglemod( target );
value = anglemod( value );
float delta = target - value;
// Speed is assumed to be positive
if ( speed < 0 )
speed = -speed;
if ( delta < -180 )
delta += 360;
else if ( delta > 180 )
delta -= 360;
if ( delta > speed )
value += speed;
else if ( delta < -speed )
value -= speed;
else
value = target;
return value;
}
// BUGBUG: Why do we need both of these?
float AngleDiff( float destAngle, float srcAngle )
{
float delta;
delta = fmodf(destAngle - srcAngle, 360.0f);
if ( destAngle > srcAngle )
{
if ( delta >= 180 )
delta -= 360;
}
else
{
if ( delta <= -180 )
delta += 360;
}
return delta;
}
float AngleDistance( float next, float cur )
{
float delta = next - cur;
if ( delta < -180 )
delta += 360;
else if ( delta > 180 )
delta -= 360;
return delta;
}
float AngleNormalize( float angle )
{
angle = fmodf(angle, 360.0f);
if (angle > 180)
{
angle -= 360;
}
if (angle < -180)
{
angle += 360;
}
return angle;
}
//--------------------------------------------------------------------------------------------------------------
// ensure that 0 <= angle <= 360
float AngleNormalizePositive( float angle )
{
angle = fmodf( angle, 360.0f );
if (angle < 0.0f)
{
angle += 360.0f;
}
return angle;
}
//--------------------------------------------------------------------------------------------------------------
bool AnglesAreEqual( float a, float b, float tolerance )
{
return (fabs( AngleDiff( a, b ) ) < tolerance);
}
void RotationDeltaAxisAngle( const QAngle &srcAngles, const QAngle &destAngles, Vector &deltaAxis, float &deltaAngle )
{
Quaternion srcQuat, destQuat, srcQuatInv, out;
AngleQuaternion( srcAngles, srcQuat );
AngleQuaternion( destAngles, destQuat );
QuaternionScale( srcQuat, -1, srcQuatInv );
QuaternionMult( destQuat, srcQuatInv, out );
QuaternionNormalize( out );
QuaternionAxisAngle( out, deltaAxis, deltaAngle );
}
void RotationDelta( const QAngle &srcAngles, const QAngle &destAngles, QAngle *out )
{
matrix3x4_t src, srcInv;
matrix3x4_t dest;
AngleMatrix( srcAngles, src );
AngleMatrix( destAngles, dest );
// xform = src(-1) * dest
MatrixInvert( src, srcInv );
matrix3x4_t xform;
ConcatTransforms( dest, srcInv, xform );
QAngle xformAngles;
MatrixAngles( xform, xformAngles );
if ( out )
{
*out = xformAngles;
}
}
void ClipLineSegmentToPlane( const Vector &vNormal, const Vector &vPlanePoint, Vector *p1, Vector *p2, float flBias )
{
float flDot1, flDot2;
flDot1 = ( *p1 - vPlanePoint ).Dot( vNormal ) + flBias;
flDot2 = ( *p2 - vPlanePoint ).Dot( vNormal ) + flBias;
if ( flDot1 >= 0 && flDot2 >= 0 )
{
return;
}
if ( flDot1 >= 0 )
{
Vector vRay = *p2 - *p1;
*p2 = *p1 + vRay * flDot1 / ( flDot1 - flDot2 );
}
else if ( flDot2 >= 0 )
{
Vector vRay = *p1 - *p2;
*p1 = *p2 + vRay * flDot2 / ( flDot2 - flDot1 );
}
else
{
*p1 = vec3_invalid;
*p2 = vec3_invalid;
}
}
//-----------------------------------------------------------------------------
// Purpose: Computes a triangle normal
//-----------------------------------------------------------------------------
void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept )
{
Vector e1, e2;
VectorSubtract( v2, v1, e1 );
VectorSubtract( v3, v1, e2 );
CrossProduct( e1, e2, normal );
VectorNormalize( normal );
intercept = DotProduct( normal, v1 );
}
//-----------------------------------------------------------------------------
// Purpose: Calculate the volume of a tetrahedron with these vertices
// Input : p0 - points of tetrahedron
// p1 -
// p2 -
// p3 -
// Output : float (volume in units^3)
//-----------------------------------------------------------------------------
float TetrahedronVolume( const Vector &p0, const Vector &p1, const Vector &p2, const Vector &p3 )
{
Vector a, b, c, cross;
float volume = 1.0f / 6.0f;
a = p1 - p0;
b = p2 - p0;
c = p3 - p0;
cross = CrossProduct( b, c );
volume *= DotProduct( a, cross );
if ( volume < 0 )
return -volume;
return volume;
}
// computes the area of a triangle given three verts
float TriangleArea( const Vector &v0, const Vector &v1, const Vector &v2 )
{
Vector vecEdge0, vecEdge1, vecCross;
VectorSubtract( v1, v0, vecEdge0 );
VectorSubtract( v2, v0, vecEdge1 );
CrossProduct( vecEdge0, vecEdge1, vecCross );
return ( VectorLength( vecCross ) * 0.5f );
}
//-----------------------------------------------------------------------------
// Purpose: This is a clone of BaseWindingForPlane()
// Input : *pOutVerts - an array of preallocated verts to build the polygon in
// normal - the plane normal
// dist - the plane constant
// Output : int - vert count (always 4)
//-----------------------------------------------------------------------------
int PolyFromPlane( Vector *pOutVerts, const Vector& normal, float dist, float fHalfScale )
{
int i, x;
vec_t max, v;
Vector org, vright, vup;
// find the major axis
max = -16384; //MAX_COORD_INTEGER
x = -1;
for (i=0 ; i<3; i++)
{
v = fabs(normal[i]);
if (v > max)
{
x = i;
max = v;
}
}
if (x==-1)
return 0;
// Build a unit vector along something other than the major axis
VectorCopy (vec3_origin, vup);
switch (x)
{
case 0:
case 1:
vup[2] = 1;
break;
case 2:
vup[0] = 1;
break;
}
// Remove the component of this vector along the normal
v = DotProduct (vup, normal);
VectorMA (vup, -v, normal, vup);
// Make it a unit (perpendicular)
VectorNormalize (vup);
// Center of the poly is at normal * dist
VectorScale (normal, dist, org);
// Calculate the third orthonormal basis vector for our plane space (this one and vup are in the plane)
CrossProduct (vup, normal, vright);
// Make the plane's basis vectors big (these are the half-sides of the polygon we're making)
VectorScale (vup, fHalfScale, vup);
VectorScale (vright, fHalfScale, vright);
// Move diagonally away from org to create the corner verts
VectorSubtract (org, vright, pOutVerts[0]); // left
VectorAdd (pOutVerts[0], vup, pOutVerts[0]); // up
VectorAdd (org, vright, pOutVerts[1]); // right
VectorAdd (pOutVerts[1], vup, pOutVerts[1]); // up
VectorAdd (org, vright, pOutVerts[2]); // right
VectorSubtract (pOutVerts[2], vup, pOutVerts[2]); // down
VectorSubtract (org, vright, pOutVerts[3]); // left
VectorSubtract (pOutVerts[3], vup, pOutVerts[3]); // down
// The four corners form a planar quadrilateral normal to "normal"
return 4;
}
// Returns void as it was impossible for the function to returns anything other than 4.
// Any absolute of a floating value will always return a number greater than -16384. That test seemed bogus.
void PolyFromPlane_SIMD( fltx4 *pOutVerts, const fltx4 & plane, float fHalfScale )
{
// So we need to find the biggest component of all three,
// And depending of the value, we need to build a unit vector along something that is not the major axis.
fltx4 f4Abs = AbsSIMD( plane );
fltx4 x = SplatXSIMD( f4Abs );
fltx4 y = SplatYSIMD( f4Abs );
fltx4 z = SplatZSIMD( f4Abs );
fltx4 max = MaxSIMD( x, y );
max = MaxSIMD( max, z );
// Simplify the code, if Z is the biggest component, we will use 1 0 0.
// If X or Y are the biggest, we will use 0 0 1.
bi32x4 fIsMax = CmpEqSIMD( max, f4Abs ); // isMax will be set for the components that are the max
fltx4 fIsZMax = SplatZSIMD( (fltx4)fIsMax ); // 0 if Z is not the max, 0xffffffff is Z is the max
// And depending if Z is max or not, we are going to select one unit vector or the other
fltx4 vup = MaskedAssign( (bi32x4)fIsZMax, g_SIMD_Identity[0], g_SIMD_Identity[2] );
fltx4 normal = SetWToZeroSIMD( plane );
fltx4 dist = SplatWSIMD( plane );
// Remove the component of this vector along the normal
fltx4 v = Dot3SIMD( vup, normal );
vup = MaddSIMD( -v, normal, vup);
// Make it a unit (perpendicular)
vup = Normalized3SIMD( vup );
// Center of the poly is at normal * dist
fltx4 org = MulSIMD( dist, normal );
// Calculate the third orthonormal basis vector for our plane space (this one and vup are in the plane)
fltx4 vright = CrossProductSIMD( vup, normal);
// Make the plane's basis vectors big (these are the half-sides of the polygon we're making)
fltx4 f4HalfScale = ReplicateX4( fHalfScale );
vup = MulSIMD( f4HalfScale, vup );
vright = MulSIMD( f4HalfScale, vright );
// Move diagonally away from org to create the corner verts
fltx4 vleft = SubSIMD( org, vright );
vright = AddSIMD( org, vright );
pOutVerts[0] = AddSIMD( vleft, vup ); // left + up
pOutVerts[1] = AddSIMD( vright, vup ); // right + up
pOutVerts[2] = SubSIMD( vright, vup ); // right + down
pOutVerts[3] = SubSIMD( vleft, vup ); // left + down
}
//-----------------------------------------------------------------------------
// Purpose: clip a poly to the plane and return the poly on the front side of the plane
// Input : *inVerts - input polygon
// vertCount - # verts in input poly
// *outVerts - destination poly
// normal - plane normal
// dist - plane constant
// Output : int - # verts in output poly
//-----------------------------------------------------------------------------
int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& normal, float dist, float fOnPlaneEpsilon )
{
vec_t *dists = (vec_t *)stackalloc( sizeof(vec_t) * vertCount * 4 ); //4x vertcount should cover all cases
int *sides = (int *)stackalloc( sizeof(vec_t) * vertCount * 4 );
int counts[3];
vec_t dot;
int i, j;
Vector mid = vec3_origin;
int outCount;
counts[0] = counts[1] = counts[2] = 0;
// determine sides for each point
for ( i = 0; i < vertCount; i++ )
{
dot = DotProduct( inVerts[i], normal) - dist;
dists[i] = dot;
if ( dot > fOnPlaneEpsilon )
{
sides[i] = SIDE_FRONT;
}
else if ( dot < -fOnPlaneEpsilon )
{
sides[i] = SIDE_BACK;
}
else
{
sides[i] = SIDE_ON;
}
counts[sides[i]]++;
}
sides[i] = sides[0];
dists[i] = dists[0];
if (!counts[0])
return 0;
if (!counts[1])
{
// Copy to output verts
for ( i = 0; i < vertCount; i++ )
{
VectorCopy( inVerts[i], outVerts[i] );
}
return vertCount;
}
outCount = 0;
for ( i = 0; i < vertCount; i++ )
{
Vector& p1 = inVerts[i];
if (sides[i] == SIDE_ON)
{
VectorCopy( p1, outVerts[outCount]);
outCount++;
continue;
}
if (sides[i] == SIDE_FRONT)
{
VectorCopy( p1, outVerts[outCount]);
outCount++;
}
if (sides[i+1] == SIDE_ON || sides[i+1] == sides[i])
continue;
// generate a split point
Vector& p2 = inVerts[(i+1)%vertCount];
dot = dists[i] / (dists[i]-dists[i+1]);
for (j=0 ; j<3 ; j++)
{ // avoid round off error when possible
if (normal[j] == 1)
mid[j] = dist;
else if (normal[j] == -1)
mid[j] = -dist;
else
mid[j] = p1[j] + dot*(p2[j]-p1[j]);
}
VectorCopy (mid, outVerts[outCount]);
outCount++;
}
return outCount;
}
int ClipPolyToPlane_SIMD( fltx4 *pInVerts, int nVertCount, fltx4 *pOutVerts, const fltx4& plane, float fOnPlaneEpsilon )
{
vec_t *dists = (vec_t *)stackalloc( sizeof(vec_t) * nVertCount * 4 ); //4* nVertCount should cover all cases
uint8 *sides = (uint8 *)stackalloc( sizeof(uint8) * nVertCount * 4 );
int i;
/*
* It seems something could be done here... Especially in relation with the code below i, i + 1, etc...
fltx4 f4OnPlaneEpsilonP = ReplicateX4( fOnPlaneEpsilon );
fltx4 f4OnPlaneEpsilonM = -f4OnPlaneEpsilonP;
Also we could store the full fltx4 instead of a single float. It would avoid doing a SubFloat() here,
and a ReplicateX4() later. Trading off potential LHS against L2 cache misses?
*/
// determine sides for each point
int nAllSides = 0;
fltx4 f4Dist = SplatWSIMD( plane );
for ( i = 0; i < nVertCount; i++ )
{
// dot = DotProduct( pInVerts[i], normal) - dist;
fltx4 dot = Dot3SIMD( pInVerts[i], plane );
dot = SubSIMD( dot, f4Dist );
float fDot = SubFloat( dot, 0 );
dists[i] = fDot;
// Look how to update sides with a branch-less version
int nSide = OR_SIDE_ON;
if ( fDot > fOnPlaneEpsilon )
{
nSide = OR_SIDE_FRONT;
}
else if ( fDot < -fOnPlaneEpsilon )
{
nSide = OR_SIDE_BACK;
}
sides[i] = nSide;
nAllSides |= nSide;
}
sides[i] = sides[0];
dists[i] = dists[0];
// Shortcuts (either completely clipped or not clipped at all)
if ( ( nAllSides & OR_SIDE_FRONT ) == 0 )
{
return 0; // Completely clipped
}
if ( ( nAllSides & OR_SIDE_BACK ) == 0 )
{
// Not clipped at all, copy to output verts
Assert ( i == nVertCount );
int nIndex = 0;
while ( i >= 4 )
{
pOutVerts[nIndex] = pInVerts[nIndex];
pOutVerts[nIndex + 1] = pInVerts[nIndex + 1];
pOutVerts[nIndex + 2] = pInVerts[nIndex + 2];
pOutVerts[nIndex + 3] = pInVerts[nIndex + 3];
nIndex += 4;
i -= 4;
}
while ( i > 0 )
{
pOutVerts[nIndex] = pInVerts[nIndex];
++nIndex;
--i;
}
return nVertCount;
}
fltx4 f4one = Four_Ones;
fltx4 f4MOne = -f4one;
fltx4 f4OneMask = (fltx4)CmpEqSIMD( plane, f4one );
fltx4 f4mOneMask = (fltx4)CmpEqSIMD( plane, f4MOne );
fltx4 f4AllMask = OrSIMD( f4OneMask, f4mOneMask ); // 0xffffffff where normal was 1 or -1, 0 otherwise
f4OneMask = AndSIMD( f4OneMask, f4Dist ); // Dist where normal.* was 1
f4mOneMask = AndSIMD( f4mOneMask, -f4Dist ); // -Dist where normal.* was -1
fltx4 f4AllValue = OrSIMD( f4OneMask, f4mOneMask ); // Dist and -Dist where normal.* was 1 and -1
// f4AllMask and f4AllValue will be used together (to override the default calculation).
int nOutCount = 0;
for ( i = 0; i < nVertCount; i++ )
{
const fltx4& p1 = pInVerts[i];
if (sides[i] == OR_SIDE_ON)
{
pOutVerts[nOutCount++] = p1;
continue;
}
if (sides[i] == OR_SIDE_FRONT)
{
pOutVerts[nOutCount++] = p1;
}
if (sides[i+1] == OR_SIDE_ON || sides[i+1] == sides[i])
continue;
// generate a split point
fltx4& p2 = pInVerts[(i+1)%nVertCount];
float fDot = dists[i] / (dists[i]-dists[i+1]);
fltx4 f4Dot = ReplicateX4( fDot );
// mid[j] = v1[j] + dot*(v2[j]-v1[j]); - For j=0...2
fltx4 f4Result = MaddSIMD( f4Dot, SubSIMD( p2, p1) , p1);
// If normal.* is 1, it should be dist, if -1, it should be -dist, otherwise it should be mid[j] = v1[j] + dot*(v2[j]-v1[j]);
fltx4 mid = MaskedAssign( (bi32x4)f4AllMask, f4AllValue, f4Result );
pOutVerts[nOutCount++] = mid;
}
return nOutCount;
}
int ClipPolyToPlane_Precise( double *inVerts, int vertCount, double *outVerts, const double *normal, double dist, double fOnPlaneEpsilon )
{
double *dists = (double *)stackalloc( sizeof(double) * vertCount * 4 ); //4x vertcount should cover all cases
int *sides = (int *)stackalloc( sizeof(double) * vertCount * 4 );
int counts[3];
double dot;
int i, j;
//Vector mid = vec3_origin;
double mid[3];
mid[0] = 0.0;
mid[1] = 0.0;
mid[2] = 0.0;
int outCount;
counts[0] = counts[1] = counts[2] = 0;
// determine sides for each point
for ( i = 0; i < vertCount; i++ )
{
//dot = DotProduct( inVerts[i], normal) - dist;
dot = ((inVerts[i*3 + 0] * normal[0]) + (inVerts[i*3 + 1] * normal[1]) + (inVerts[i*3 + 2] * normal[2])) - dist;
dists[i] = dot;
if ( dot > fOnPlaneEpsilon )
{
sides[i] = SIDE_FRONT;
}
else if ( dot < -fOnPlaneEpsilon )
{
sides[i] = SIDE_BACK;
}
else
{
sides[i] = SIDE_ON;
}
counts[sides[i]]++;
}
sides[i] = sides[0];
dists[i] = dists[0];
if (!counts[0])
return 0;
if (!counts[1])
{
// Copy to output verts
//for ( i = 0; i < vertCount; i++ )
for ( i = 0; i < vertCount * 3; i++ )
{
//VectorCopy( inVerts[i], outVerts[i] );
outVerts[i] = inVerts[i];
}
return vertCount;
}
outCount = 0;
for ( i = 0; i < vertCount; i++ )
{
//Vector& p1 = inVerts[i];
double *p1 = &inVerts[i*3];
//p1[0] = inVerts[i*3 + 0];
//p1[1] = inVerts[i*3 + 1];
//p1[2] = inVerts[i*3 + 2];
if (sides[i] == SIDE_ON)
{
//VectorCopy( p1, outVerts[outCount]);
outVerts[outCount*3 + 0] = p1[0];
outVerts[outCount*3 + 1] = p1[1];
outVerts[outCount*3 + 2] = p1[2];
outCount++;
continue;
}
if (sides[i] == SIDE_FRONT)
{
//VectorCopy( p1, outVerts[outCount]);
outVerts[outCount*3 + 0] = p1[0];
outVerts[outCount*3 + 1] = p1[1];
outVerts[outCount*3 + 2] = p1[2];
outCount++;
}
if (sides[i+1] == SIDE_ON || sides[i+1] == sides[i])
continue;
// generate a split point
//Vector& p2 = inVerts[(i+1)%vertCount];
int wrappedindex = (i+1)%vertCount;
double *p2 = &inVerts[wrappedindex*3];
//p2[0] = inVerts[wrappedindex*3 + 0];
//p2[1] = inVerts[wrappedindex*3 + 1];
//p2[2] = inVerts[wrappedindex*3 + 2];
dot = dists[i] / (dists[i]-dists[i+1]);
for (j=0 ; j<3 ; j++)
{
mid[j] = (double)p1[j] + dot*((double)p2[j]-(double)p1[j]);
}
//VectorCopy (mid, outVerts[outCount]);
outVerts[outCount*3 + 0] = mid[0];
outVerts[outCount*3 + 1] = mid[1];
outVerts[outCount*3 + 2] = mid[2];
outCount++;
}
return outCount;
}
int CeilPow2( int in )
{
int retval;
retval = 1;
while( retval < in )
retval <<= 1;
return retval;
}
int FloorPow2( int in )
{
int retval;
retval = 1;
while( retval < in )
retval <<= 1;
return retval >> 1;
}
//-----------------------------------------------------------------------------
// Computes Y fov from an X fov and a screen aspect ratio
//-----------------------------------------------------------------------------
float CalcFovY( float flFovX, float flAspect )
{
if ( flFovX < 1 || flFovX > 179)
{
flFovX = 90; // error, set to 90
}
// The long, but illustrative version (more closely matches CShaderAPIDX8::PerspectiveX, which
// is what it's based on).
//
//float width = 2 * zNear * tan( DEG2RAD( fov_x / 2.0 ) );
//float height = width / screenaspect;
//float yRadians = atan( (height/2.0) / zNear );
//return RAD2DEG( yRadians ) * 2;
// The short and sweet version.
float val = atan( tan( DEG2RAD( flFovX ) * 0.5f ) / flAspect );
val = RAD2DEG( val ) * 2.0f;
return val;
}
float CalcFovX( float flFovY, float flAspect )
{
return RAD2DEG( atan( tan( DEG2RAD( flFovY ) * 0.5f ) * flAspect ) ) * 2.0f;
}
#endif // !defined(__SPU__)
#if !defined(__SPU__)
//-----------------------------------------------------------------------------
// Generate a frustum based on perspective view parameters
//-----------------------------------------------------------------------------
void GeneratePerspectiveFrustum( const Vector& origin, const Vector &forward,
const Vector &right, const Vector &up, float flZNear, float flZFar,
float flFovX, float flFovY, VPlane *pPlanesOut )
{
float flIntercept = DotProduct( origin, forward );
// Setup the near and far planes.
pPlanesOut[FRUSTUM_FARZ].Init( -forward, -flZFar - flIntercept );
pPlanesOut[FRUSTUM_NEARZ].Init( forward, flZNear + flIntercept );
flFovX *= 0.5f;
flFovY *= 0.5f;
float flTanX = tan( DEG2RAD( flFovX ) );
float flTanY = tan( DEG2RAD( flFovY ) );
// OPTIMIZE: Normalizing these planes is not necessary for culling
Vector normalPos, normalNeg;
VectorMA( right, flTanX, forward, normalPos );
VectorMA( normalPos, -2.0f, right, normalNeg );
VectorNormalize( normalPos );
VectorNormalize( normalNeg );
pPlanesOut[FRUSTUM_LEFT].Init( normalPos, normalPos.Dot( origin ) );
pPlanesOut[FRUSTUM_RIGHT].Init( normalNeg, normalNeg.Dot( origin ) );
VectorMA( up, flTanY, forward, normalPos );
VectorMA( normalPos, -2.0f, up, normalNeg );
VectorNormalize( normalPos );
VectorNormalize( normalNeg );
pPlanesOut[FRUSTUM_BOTTOM].Init( normalPos, normalPos.Dot( origin ) );
pPlanesOut[FRUSTUM_TOP].Init( normalNeg, normalNeg.Dot( origin ) );
}
//-----------------------------------------------------------------------------
// Generate a frustum based on orthographic parameters
//-----------------------------------------------------------------------------
void GenerateOrthoFrustum( const Vector &origin, const Vector &forward, const Vector &right, const Vector &up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar, VPlane *pPlanesOut )
{
float flIntercept = DotProduct( origin, forward );
pPlanesOut[FRUSTUM_NEARZ].Init( forward, flZNear + flIntercept );
pPlanesOut[FRUSTUM_FARZ].Init( -forward, -flZFar - flIntercept );
flIntercept = DotProduct( origin, right );
pPlanesOut[FRUSTUM_RIGHT].Init( -right, -flRight - flIntercept );
pPlanesOut[FRUSTUM_LEFT].Init( right, flLeft + flIntercept );
flIntercept = DotProduct( origin, up );
pPlanesOut[FRUSTUM_BOTTOM].Init( up, flBottom + flIntercept );
pPlanesOut[FRUSTUM_TOP].Init( -up, -flTop - flIntercept );
}
//-----------------------------------------------------------------------------
// Version that accepts angles instead of vectors
//-----------------------------------------------------------------------------
void GeneratePerspectiveFrustum( const Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t &frustum )
{
VPlane planes[FRUSTUM_NUMPLANES];
Vector vecForward, vecRight, vecUp;
AngleVectors( angles, &vecForward, &vecRight, &vecUp );
float flFovY = CalcFovY( flFovX, flAspectRatio );
GeneratePerspectiveFrustum( origin, vecForward, vecRight, vecUp, flZNear, flZFar, flFovX, flFovY, planes );
frustum.SetPlanes( planes );
}
void fourplanes_t::ComputeSignbits()
{
xSign = CmpLtSIMD( nX, Four_Zeros );
ySign = CmpLtSIMD( nY, Four_Zeros );
zSign = CmpLtSIMD( nZ, Four_Zeros );
nXAbs = fabs(nX);
nYAbs = fabs(nY);
nZAbs = fabs(nZ);
}
void fourplanes_t::GetPlane( int index, Vector *pNormalOut, float *pDistOut ) const
{
pNormalOut->x = SubFloat(nX,index);
pNormalOut->y = SubFloat(nY,index);
pNormalOut->z = SubFloat(nZ,index);
*pDistOut = SubFloat(dist,index);
}
void fourplanes_t::SetPlane( int index, const Vector &vecNormal, float planeDist )
{
SubFloat(nX,index) = vecNormal.x;
SubFloat(nY,index) = vecNormal.y;
SubFloat(nZ,index) = vecNormal.z;
SubFloat(dist,index) = planeDist;
ComputeSignbits();
}
void fourplanes_t::Set4Planes( const VPlane *pPlanes )
{
nX = LoadUnalignedSIMD( &pPlanes[0].m_Normal.x );
nY = LoadUnalignedSIMD( &pPlanes[1].m_Normal.x );
nZ = LoadUnalignedSIMD( &pPlanes[2].m_Normal.x );
dist = LoadUnalignedSIMD( &pPlanes[3].m_Normal.x );
TransposeSIMD(nX, nY, nZ, dist);
ComputeSignbits();
}
void fourplanes_t::Set2Planes( const VPlane *pPlanes )
{
nX = LoadUnalignedSIMD( &pPlanes[0].m_Normal.x );
nY = LoadUnalignedSIMD( &pPlanes[1].m_Normal.x );
nZ = Four_Zeros;
dist = Four_Zeros;
TransposeSIMD(nX, nY, nZ, dist);
ComputeSignbits();
}
void fourplanes_t::Get4Planes( VPlane *pPlanesOut ) const
{
fltx4 p0 = nX;
fltx4 p1 = nY;
fltx4 p2 = nZ;
fltx4 p3 = dist;
TransposeSIMD(p0, p1, p2, p3);
StoreUnalignedSIMD( &pPlanesOut[0].m_Normal.x, p0 );
StoreUnalignedSIMD( &pPlanesOut[1].m_Normal.x, p1 );
StoreUnalignedSIMD( &pPlanesOut[2].m_Normal.x, p2 );
StoreUnalignedSIMD( &pPlanesOut[3].m_Normal.x, p3 );
}
void fourplanes_t::Get2Planes( VPlane *pPlanesOut ) const
{
fltx4 p0 = nX;
fltx4 p1 = nY;
fltx4 p2 = nZ;
fltx4 p3 = dist;
TransposeSIMD(p0, p1, p2, p3);
StoreUnalignedSIMD( &pPlanesOut[0].m_Normal.x, p0 );
StoreUnalignedSIMD( &pPlanesOut[1].m_Normal.x, p1 );
}
Frustum_t::Frustum_t()
{
memset(this, 0, sizeof(*this));
}
void Frustum_t::SetPlane( int i, const Vector &vecNormal, float dist )
{
if ( i < 4 )
{
planes[0].SetPlane( i, vecNormal, dist );
}
else
{
planes[1].SetPlane( i-4, vecNormal, dist );
}
}
void Frustum_t::GetPlane( int i, Vector *pNormalOut, float *pDistOut ) const
{
if ( i < 4 )
{
planes[0].GetPlane( i, pNormalOut, pDistOut );
}
else
{
planes[1].GetPlane( i-4, pNormalOut, pDistOut );
}
}
void Frustum_t::SetPlanes( const VPlane *pPlanes )
{
planes[0].Set4Planes(pPlanes);
planes[1].Set2Planes(pPlanes+4);
}
void Frustum_t::GetPlanes( VPlane *pPlanesOut ) const
{
planes[0].Get4Planes(pPlanesOut);
planes[1].Get2Planes(pPlanesOut+4);
}
bool Frustum_t::CullBox( const Vector &mins, const Vector &maxs ) const
{
fltx4 mins4 = LoadUnalignedSIMD( &mins.x );
fltx4 minx = SplatXSIMD(mins4);
fltx4 miny = SplatYSIMD(mins4);
fltx4 minz = SplatZSIMD(mins4);
fltx4 maxs4 = LoadUnalignedSIMD( &maxs.x );
fltx4 maxx = SplatXSIMD(maxs4);
fltx4 maxy = SplatYSIMD(maxs4);
fltx4 maxz = SplatZSIMD(maxs4);
// compute the dot product of the normal and the farthest corner
// dotBack0 = DotProduct( normal, normals.x < 0 ? mins.x : maxs.x );
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = MulSIMD( planes[i].nX, MaskedAssign( planes[i].xSign, minx, maxx ) );
fltx4 yTotalBack = MulSIMD( planes[i].nY, MaskedAssign( planes[i].ySign, miny, maxy ) );
fltx4 zTotalBack = MulSIMD( planes[i].nZ, MaskedAssign( planes[i].zSign, minz, maxz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
if ( IsVector4LessThan( dotBack, planes[i].dist ) )
return true;
}
return false;
}
bool Frustum_t::CullBox( const fltx4 &mins4, const fltx4 &maxs4 ) const
{
fltx4 minx = SplatXSIMD(mins4);
fltx4 miny = SplatYSIMD(mins4);
fltx4 minz = SplatZSIMD(mins4);
fltx4 maxx = SplatXSIMD(maxs4);
fltx4 maxy = SplatYSIMD(maxs4);
fltx4 maxz = SplatZSIMD(maxs4);
// compute the dot product of the normal and the farthest corner
// dotBack0 = DotProduct( normal, normals.x < 0 ? mins.x : maxs.x );
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = MulSIMD( planes[i].nX, MaskedAssign( planes[i].xSign, minx, maxx ) );
fltx4 yTotalBack = MulSIMD( planes[i].nY, MaskedAssign( planes[i].ySign, miny, maxy ) );
fltx4 zTotalBack = MulSIMD( planes[i].nZ, MaskedAssign( planes[i].zSign, minz, maxz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
if ( IsVector4LessThan( dotBack, planes[i].dist ) )
return true;
}
return false;
}
bool Frustum_t::CullBoxCenterExtents( const Vector &center, const Vector &extents ) const
{
fltx4 center4 = LoadUnalignedSIMD( &center.x );
fltx4 centerx = SplatXSIMD(center4);
fltx4 centery = SplatYSIMD(center4);
fltx4 centerz = SplatZSIMD(center4);
fltx4 extents4 = LoadUnalignedSIMD( &extents.x );
fltx4 extx = SplatXSIMD(extents4);
fltx4 exty = SplatYSIMD(extents4);
fltx4 extz = SplatZSIMD(extents4);
// compute the dot product of the normal and the farthest corner
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = AddSIMD( MulSIMD( planes[i].nX, centerx ), MulSIMD(planes[i].nXAbs, extx ) );
fltx4 yTotalBack = AddSIMD( MulSIMD( planes[i].nY, centery ), MulSIMD(planes[i].nYAbs, exty ) );
fltx4 zTotalBack = AddSIMD( MulSIMD( planes[i].nZ, centerz ), MulSIMD(planes[i].nZAbs, extz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
if ( IsVector4LessThan( dotBack, planes[i].dist ) )
return true;
}
return false;
}
bool Frustum_t::CullBoxCenterExtents( const fltx4 &fl4Center, const fltx4 &fl4Extents ) const
{
fltx4 centerx = SplatXSIMD(fl4Center);
fltx4 centery = SplatYSIMD(fl4Center);
fltx4 centerz = SplatZSIMD(fl4Center);
fltx4 extx = SplatXSIMD(fl4Extents);
fltx4 exty = SplatYSIMD(fl4Extents);
fltx4 extz = SplatZSIMD(fl4Extents);
// compute the dot product of the normal and the farthest corner
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = AddSIMD( MulSIMD( planes[i].nX, centerx ), MulSIMD(planes[i].nXAbs, extx ) );
fltx4 yTotalBack = AddSIMD( MulSIMD( planes[i].nY, centery ), MulSIMD(planes[i].nYAbs, exty ) );
fltx4 zTotalBack = AddSIMD( MulSIMD( planes[i].nZ, centerz ), MulSIMD(planes[i].nZAbs, extz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
if ( IsVector4LessThan( dotBack, planes[i].dist ) )
return true;
}
return false;
}
// Return true if this bounding volume is contained in the frustum, false if it is not
// TODO SIMDIFY
bool Frustum_t::Contains( const Vector &mins, const Vector &maxs ) const
{
// Get box corners
Vector vCorners[8];
vCorners[0] = mins;
vCorners[1] = Vector( mins.x, mins.y, maxs.z );
vCorners[2] = Vector( mins.x, maxs.y, mins.z );
vCorners[3] = Vector( mins.x, maxs.y, maxs.z );
vCorners[4] = Vector( maxs.x, mins.y, mins.z );
vCorners[5] = Vector( maxs.x, mins.y, maxs.z );
vCorners[6] = Vector( maxs.x, maxs.y, mins.z );
vCorners[7] = maxs;
// if we are in with all points, then we are fully in
for ( int j = 0; j < FRUSTUM_NUMPLANES; ++j )
{
for( int i = 0; i < 8; ++i )
{
// compute the dot product of the normal and the corner
Vector vNormal;
float dist;
GetPlane( i, &vNormal, &dist );
if ( DotProduct( vCorners[j], vNormal ) <= 0 )
{
return false;
}
}
}
return true; // all pts were inside
}
// Brute force SAT frustum intersection between two frustums
bool Frustum_t::Intersects( Frustum_t &otherFrustum ) const
{
Vector pPointsA[8];
bool bResult = false;
bResult = GetCorners( pPointsA );
Assert( bResult );
VPlane pPlanesA[FRUSTUM_NUMPLANES];
GetPlanes( pPlanesA );
Vector pPointsB[8];
bResult = otherFrustum.GetCorners( pPointsB );
Assert( bResult );
VPlane pPlanesB[FRUSTUM_NUMPLANES];
otherFrustum.GetPlanes( pPlanesB );
// See if all points in B are on one side of any plane in A
for ( int p=0; p<6; ++p )
{
bool bPointsOnOutside = true;
for ( int i=0; i<8; ++i )
{
float flDist = pPlanesA[ p ].DistTo( pPointsB[ i ] );
// If dist is pos, we are not on the outside
if ( flDist > 0 )
{
bPointsOnOutside = false;
break;
}
}
// We never hit a negative case, we have a separating axis
if ( bPointsOnOutside )
{
return false;
}
}
// See if all points in A are on one side of any plane in B
for ( int p=0; p<6; ++p )
{
bool bPointsOnOutside = true;
for ( int i=0; i<8; ++i )
{
float flDist = pPlanesB[ p ].DistTo( pPointsA[ i ] );
// If dist is pos, we are not on the outside
if ( flDist > 0 )
{
bPointsOnOutside = false;
break;
}
}
// We never hit a negative case, we have a separating axis
if ( bPointsOnOutside )
{
return false;
}
}
// They intersect
return true;
}
// Return true if this bounding volume intersects the frustum, false if it is outside
bool Frustum_t::Intersects( const Vector &mins, const Vector &maxs ) const
{
fltx4 mins4 = LoadUnalignedSIMD( &mins.x );
fltx4 minx = SplatXSIMD(mins4);
fltx4 miny = SplatYSIMD(mins4);
fltx4 minz = SplatZSIMD(mins4);
fltx4 maxs4 = LoadUnalignedSIMD( &maxs.x );
fltx4 maxx = SplatXSIMD(maxs4);
fltx4 maxy = SplatYSIMD(maxs4);
fltx4 maxz = SplatZSIMD(maxs4);
// compute the dot product of the normal and the farthest corner
// dotBack0 = DotProduct( normal, normals.x < 0 ? mins.x : maxs.x );
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = MulSIMD( planes[i].nX, MaskedAssign( planes[i].xSign, minx, maxx ) );
fltx4 yTotalBack = MulSIMD( planes[i].nY, MaskedAssign( planes[i].ySign, miny, maxy ) );
fltx4 zTotalBack = MulSIMD( planes[i].nZ, MaskedAssign( planes[i].zSign, minz, maxz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
#if _X360
if ( !XMVector3GreaterOrEqual( dotBack, planes[i].dist ) )
return false;
#elif defined( _PS3 )
bi32x4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#else
fltx4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#endif
}
return true;
}
bool Frustum_t::Intersects( const fltx4 &mins4, const fltx4 &maxs4 ) const
{
fltx4 minx = SplatXSIMD(mins4);
fltx4 miny = SplatYSIMD(mins4);
fltx4 minz = SplatZSIMD(mins4);
fltx4 maxx = SplatXSIMD(maxs4);
fltx4 maxy = SplatYSIMD(maxs4);
fltx4 maxz = SplatZSIMD(maxs4);
// compute the dot product of the normal and the farthest corner
// dotBack0 = DotProduct( normal, normals.x < 0 ? mins.x : maxs.x );
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = MulSIMD( planes[i].nX, MaskedAssign( planes[i].xSign, minx, maxx ) );
fltx4 yTotalBack = MulSIMD( planes[i].nY, MaskedAssign( planes[i].ySign, miny, maxy ) );
fltx4 zTotalBack = MulSIMD( planes[i].nZ, MaskedAssign( planes[i].zSign, minz, maxz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
#if _X360
if ( !XMVector4GreaterOrEqual( dotBack, planes[i].dist ) )
return false;
#elif defined( _PS3 )
bi32x4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#else
fltx4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#endif
}
return true;
}
bool Frustum_t::IntersectsCenterExtents( const Vector &center, const Vector &extents ) const
{
fltx4 center4 = LoadUnalignedSIMD( &center.x );
fltx4 centerx = SplatXSIMD(center4);
fltx4 centery = SplatYSIMD(center4);
fltx4 centerz = SplatZSIMD(center4);
fltx4 extents4 = LoadUnalignedSIMD( &extents.x );
fltx4 extx = SplatXSIMD(extents4);
fltx4 exty = SplatYSIMD(extents4);
fltx4 extz = SplatZSIMD(extents4);
// compute the dot product of the normal and the farthest corner
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = AddSIMD( MulSIMD( planes[i].nX, centerx ), MulSIMD(planes[i].nXAbs, extx ) );
fltx4 yTotalBack = AddSIMD( MulSIMD( planes[i].nY, centery ), MulSIMD(planes[i].nYAbs, exty ) );
fltx4 zTotalBack = AddSIMD( MulSIMD( planes[i].nZ, centerz ), MulSIMD(planes[i].nZAbs, extz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
#if _X360
if ( !XMVector4GreaterOrEqual( dotBack, planes[i].dist ) )
return false;
#elif defined( _PS3 )
bi32x4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#else
fltx4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#endif
}
return true;
}
bool Frustum_t::IntersectsCenterExtents( const fltx4 &fl4Center, const fltx4 &fl4Extents ) const
{
fltx4 centerx = SplatXSIMD(fl4Center);
fltx4 centery = SplatYSIMD(fl4Center);
fltx4 centerz = SplatZSIMD(fl4Center);
fltx4 extx = SplatXSIMD(fl4Extents);
fltx4 exty = SplatYSIMD(fl4Extents);
fltx4 extz = SplatZSIMD(fl4Extents);
// compute the dot product of the normal and the farthest corner
for ( int i = 0; i < 2; i++ )
{
fltx4 xTotalBack = AddSIMD( MulSIMD( planes[i].nX, centerx ), MulSIMD(planes[i].nXAbs, extx ) );
fltx4 yTotalBack = AddSIMD( MulSIMD( planes[i].nY, centery ), MulSIMD(planes[i].nYAbs, exty ) );
fltx4 zTotalBack = AddSIMD( MulSIMD( planes[i].nZ, centerz ), MulSIMD(planes[i].nZAbs, extz ) );
fltx4 dotBack = AddSIMD( xTotalBack, AddSIMD(yTotalBack, zTotalBack) );
// if plane of the farthest corner is behind the plane, then the box is completely outside this plane
#if _X360
if ( !XMVector3GreaterOrEqual( dotBack, planes[i].dist ) )
return false;
#elif defined( _PS3 )
bi32x4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#else
fltx4 isOut = CmpLtSIMD( dotBack, planes[i].dist );
if ( IsAnyNegative(isOut) )
return false;
#endif
}
return true;
}
//-----------------------------------------------------------------------------
// Generate a frustum based on orthographic parameters
//-----------------------------------------------------------------------------
void GenerateOrthoFrustumFLU( const Vector &origin, const Vector &forward, const Vector &vLeft, const Vector &up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar, VPlane *pPlanesOut )
{
// YUP_ACTIVE: FIXME : This is actually producing incorrect planes (see the VectorMA below)
Vector vRight = vLeft;
vRight *= -1.0f;
float flIntercept = DotProduct( origin, forward );
pPlanesOut[FRUSTUM_NEARZ].Init( forward, flZNear + flIntercept );
pPlanesOut[FRUSTUM_FARZ].Init( -forward, -flZFar - flIntercept );
flIntercept = DotProduct( origin, vRight );
pPlanesOut[FRUSTUM_RIGHT].Init( -vRight, -flRight - flIntercept );
pPlanesOut[FRUSTUM_LEFT].Init( vRight, flLeft + flIntercept );
flIntercept = DotProduct( origin, up );
pPlanesOut[FRUSTUM_BOTTOM].Init( up, flBottom + flIntercept );
pPlanesOut[FRUSTUM_TOP].Init( -up, -flTop - flIntercept );
}
//-----------------------------------------------------------------------------
// Generate a frustum based on perspective view parameters
//-----------------------------------------------------------------------------
void GeneratePerspectiveFrustumFLU( const Vector& origin, const Vector &forward,
const Vector &vLeft, const Vector &up, float flZNear, float flZFar,
float flFovX, float flAspect, VPlane *pPlanesOut )
{
// YUP_ACTIVE: FIXME : This is actually producing incorrect planes (see the VectorMA below)
Vector vRight = vLeft;
vRight *= -1.0f;
float flIntercept = DotProduct( origin, forward );
// Setup the near and far planes.
pPlanesOut[FRUSTUM_FARZ].Init( -forward, -flZFar - flIntercept );
pPlanesOut[FRUSTUM_NEARZ].Init( forward, flZNear + flIntercept );
flFovX *= 0.5f;
float flTanX = tan( DEG2RAD( flFovX ) );
float flTanY = flTanX / flAspect;
// OPTIMIZE: Normalizing these planes is not necessary for culling
Vector normalPos, normalNeg;
// NOTE: This should be using left and not right to produce correct planes, not changing it quite yet
// because I'm not able to test whether fixing this breaks anything.
VectorMA( vRight, flTanX, forward, normalPos );
VectorMA( normalPos, -2.0f, vRight, normalNeg );
VectorNormalize( normalPos );
VectorNormalize( normalNeg );
pPlanesOut[FRUSTUM_LEFT].Init( normalPos, normalPos.Dot( origin ) );
pPlanesOut[FRUSTUM_RIGHT].Init( normalNeg, normalNeg.Dot( origin ) );
VectorMA( up, flTanY, forward, normalPos );
VectorMA( normalPos, -2.0f, up, normalNeg );
VectorNormalize( normalPos );
VectorNormalize( normalNeg );
pPlanesOut[FRUSTUM_BOTTOM].Init( normalPos, normalPos.Dot( origin ) );
pPlanesOut[FRUSTUM_TOP].Init( normalNeg, normalNeg.Dot( origin ) );
}
// Generate a frustum based on perspective view parameters
void Frustum_t::CreatePerspectiveFrustumFLU( const Vector &vOrigin, const Vector &vForward,
const Vector &vLeft, const Vector &vUp, float flZNear, float flZFar,
float flFovX, float flAspect )
{
VPlane planes[FRUSTUM_NUMPLANES];
GeneratePerspectiveFrustumFLU( vOrigin, vForward, vLeft, vUp, flZNear, flZFar, flFovX, flAspect, planes );
SetPlanes( planes );
}
//#ifndef YUP_ACTIVE
void Frustum_t::CreatePerspectiveFrustum( const Vector& origin, const Vector &forward,
const Vector &right, const Vector &up, float flZNear, float flZFar,
float flFovX, float flAspect )
{
Vector vLeft = right;
vLeft *= -1.0f;
CreatePerspectiveFrustumFLU( origin, forward, vLeft, up, flZNear, flZFar, flFovX, flAspect );
}
//#endif
// Version that accepts angles instead of vectors
void Frustum_t::CreatePerspectiveFrustum( const Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio )
{
VPlane planes[FRUSTUM_NUMPLANES];
Vector vecForward, vecLeft, vecUp;
AngleVectorsFLU( angles, &vecForward, &vecLeft, &vecUp );
GeneratePerspectiveFrustumFLU( origin, vecForward, vecLeft, vecUp, flZNear, flZFar, flFovX, flAspectRatio, planes );
SetPlanes( planes );
}
// Generate a frustum based on orthographic parameters
void Frustum_t::CreateOrthoFrustumFLU( const Vector &origin, const Vector &forward, const Vector &vLeft, const Vector &up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar )
{
VPlane planes[FRUSTUM_NUMPLANES];
GenerateOrthoFrustumFLU( origin, forward, vLeft, up, flLeft, flRight, flBottom, flTop, flZNear, flZFar, planes );
SetPlanes( planes );
}
//#ifndef YUP_ACTIVE
void Frustum_t::CreateOrthoFrustum( const Vector &origin, const Vector &forward, const Vector &right, const Vector &up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar )
{
Vector vLeft = right;
vLeft *= -1.0f;
CreateOrthoFrustumFLU( origin, forward, vLeft, up, flLeft, flRight, flBottom, flTop, flZNear, flZFar );
}
// The points returned correspond to the corners of the frustum faces
// Points 0 to 3 correspond to the near face
// Points 4 to 7 correspond to the far face
// Returns points in a face in this order:
// 2--3
// | |
// 0--1
bool Frustum_t::GetCorners( Vector *pPoints ) const
{
VPlane planes[FRUSTUM_NUMPLANES];
GetPlanes( planes );
// Near face
// Bottom Left
if ( !PlaneIntersection( planes[FRUSTUM_NEARZ], planes[FRUSTUM_LEFT], planes[FRUSTUM_BOTTOM], pPoints[0] ) )
return false;
// Bottom right
if ( !PlaneIntersection( planes[FRUSTUM_NEARZ], planes[FRUSTUM_RIGHT], planes[FRUSTUM_BOTTOM], pPoints[1] ) )
return false;
// Upper Left
if ( !PlaneIntersection( planes[FRUSTUM_NEARZ], planes[FRUSTUM_LEFT], planes[FRUSTUM_TOP], pPoints[2] ) )
return false;
// Upper right
if ( !PlaneIntersection( planes[FRUSTUM_NEARZ], planes[FRUSTUM_RIGHT], planes[FRUSTUM_TOP], pPoints[3] ) )
return false;
// Far face
// Bottom Left
if ( !PlaneIntersection( planes[FRUSTUM_FARZ], planes[FRUSTUM_LEFT], planes[FRUSTUM_BOTTOM], pPoints[4] ) )
return false;
// Bottom right
if ( !PlaneIntersection( planes[FRUSTUM_FARZ], planes[FRUSTUM_RIGHT], planes[FRUSTUM_BOTTOM], pPoints[5] ) )
return false;
// Upper Left
if ( !PlaneIntersection( planes[FRUSTUM_FARZ], planes[FRUSTUM_LEFT], planes[FRUSTUM_TOP], pPoints[6] ) )
return false;
// Upper right
if ( !PlaneIntersection( planes[FRUSTUM_FARZ], planes[FRUSTUM_RIGHT], planes[FRUSTUM_TOP], pPoints[7] ) )
return false;
return true;
}
// NOTE: This routine was taken (and modified) from NVidia's BlinnReflection demo
// Creates basis vectors, based on a vertex and index list.
// See the NVidia white paper 'GDC2K PerPixel Lighting' for a description
// of how this computation works
#define SMALL_FLOAT 1e-12
void CalcTriangleTangentSpace( const Vector &p0, const Vector &p1, const Vector &p2,
const Vector2D &t0, const Vector2D &t1, const Vector2D& t2,
Vector &sVect, Vector &tVect )
{
/* Compute the partial derivatives of X, Y, and Z with respect to S and T. */
sVect.Init( 0.0f, 0.0f, 0.0f );
tVect.Init( 0.0f, 0.0f, 0.0f );
// x, s, t
Vector edge01( p1.x - p0.x, t1.x - t0.x, t1.y - t0.y );
Vector edge02( p2.x - p0.x, t2.x - t0.x, t2.y - t0.y );
Vector cross;
CrossProduct( edge01, edge02, cross );
if ( fabs( cross.x ) > SMALL_FLOAT )
{
sVect.x += -cross.y / cross.x;
tVect.x += -cross.z / cross.x;
}
// y, s, t
edge01.Init( p1.y - p0.y, t1.x - t0.x, t1.y - t0.y );
edge02.Init( p2.y - p0.y, t2.x - t0.x, t2.y - t0.y );
CrossProduct( edge01, edge02, cross );
if ( fabs( cross.x ) > SMALL_FLOAT )
{
sVect.y += -cross.y / cross.x;
tVect.y += -cross.z / cross.x;
}
// z, s, t
edge01.Init( p1.z - p0.z, t1.x - t0.x, t1.y - t0.y );
edge02.Init( p2.z - p0.z, t2.x - t0.x, t2.y - t0.y );
CrossProduct( edge01, edge02, cross );
if( fabs( cross.x ) > SMALL_FLOAT )
{
sVect.z += -cross.y / cross.x;
tVect.z += -cross.z / cross.x;
}
// Normalize sVect and tVect
VectorNormalize( sVect );
VectorNormalize( tVect );
}
//-----------------------------------------------------------------------------
// Convert RGB to HSV
//-----------------------------------------------------------------------------
void RGBtoHSV( const Vector &rgb, Vector &hsv )
{
float flMax = MAX( rgb.x, rgb.y );
flMax = MAX( flMax, rgb.z );
float flMin = MIN( rgb.x, rgb.y );
flMin = MIN( flMin, rgb.z );
// hsv.z is the value
hsv.z = flMax;
// hsv.y is the saturation
if (flMax != 0.0F)
{
hsv.y = (flMax - flMin) / flMax;
}
else
{
hsv.y = 0.0F;
}
// hsv.x is the hue
if (hsv.y == 0.0F)
{
hsv.x = -1.0f;
}
else
{
float32 d = flMax - flMin;
if (rgb.x == flMax)
{
hsv.x = (rgb.y - rgb.z) / d;
}
else if (rgb.y == flMax)
{
hsv.x = 2.0F + (rgb.z - rgb.x) / d;
}
else
{
hsv.x = 4.0F + (rgb.x - rgb.y) / d;
}
hsv.x *= 60.0F;
if ( hsv.x < 0.0F )
{
hsv.x += 360.0F;
}
}
}
//-----------------------------------------------------------------------------
// Convert HSV to RGB
//-----------------------------------------------------------------------------
void HSVtoRGB( const Vector &hsv, Vector &rgb )
{
if ( hsv.y == 0.0F )
{
rgb.Init( hsv.z, hsv.z, hsv.z );
return;
}
float32 hue = hsv.x;
if (hue == 360.0F)
{
hue = 0.0F;
}
hue /= 60.0F;
int i = Float2Int( hue ); // integer part
float32 f = hue - i; // fractional part
float32 p = hsv.z * (1.0F - hsv.y);
float32 q = hsv.z * (1.0F - hsv.y * f);
float32 t = hsv.z * (1.0F - hsv.y * (1.0F - f));
switch(i)
{
case 0: rgb.Init( hsv.z, t, p ); break;
case 1: rgb.Init( q, hsv.z, p ); break;
case 2: rgb.Init( p, hsv.z, t ); break;
case 3: rgb.Init( p, q, hsv.z ); break;
case 4: rgb.Init( t, p, hsv.z ); break;
case 5: rgb.Init( hsv.z, p, q ); break;
}
}
void GetInterpolationData( float const *pKnotPositions,
float const *pKnotValues,
int nNumValuesinList,
int nInterpolationRange,
float flPositionToInterpolateAt,
bool bWrap,
float *pValueA,
float *pValueB,
float *pInterpolationValue)
{
// first, find the bracketting knots by looking for the first knot >= our index
int idx;
for(idx = 0; idx < nNumValuesinList; idx++ )
{
if ( pKnotPositions[idx] >= flPositionToInterpolateAt )
break;
}
int nKnot1, nKnot2;
float flOffsetFromStartOfGap, flSizeOfGap;
if ( idx == 0)
{
if ( bWrap )
{
nKnot1 = nNumValuesinList-1;
nKnot2 = 0;
flSizeOfGap =
( pKnotPositions[nKnot2] + ( nInterpolationRange-pKnotPositions[nKnot1] ) );
flOffsetFromStartOfGap =
flPositionToInterpolateAt + ( nInterpolationRange-pKnotPositions[nKnot1] );
}
else
{
*pValueA = *pValueB = pKnotValues[0];
*pInterpolationValue = 1.0;
return;
}
}
else if ( idx == nNumValuesinList ) // ran out of values
{
if ( bWrap )
{
nKnot1 = nNumValuesinList -1;
nKnot2 = 0;
flSizeOfGap = ( pKnotPositions[nKnot2] +
( nInterpolationRange-pKnotPositions[nKnot1] ) );
flOffsetFromStartOfGap = flPositionToInterpolateAt - pKnotPositions[nKnot1];
}
else
{
*pValueA = *pValueB = pKnotValues[nNumValuesinList-1];
*pInterpolationValue = 1.0;
return;
}
}
else
{
nKnot1 = idx-1;
nKnot2 = idx;
flSizeOfGap = pKnotPositions[nKnot2]-pKnotPositions[nKnot1];
flOffsetFromStartOfGap = flPositionToInterpolateAt-pKnotPositions[nKnot1];
}
*pValueA = pKnotValues[nKnot1];
*pValueB = pKnotValues[nKnot2];
*pInterpolationValue = FLerp( 0, 1, 0, flSizeOfGap, flOffsetFromStartOfGap );
return;
}
static Vector RandomVectorOnUnitSphere( float u, float v )
{
float flPhi = acos( 1 - 2 * u );
float flTheta = 2 * M_PI * v;
float flSinPhi, flCosPhi;
float flSinTheta, flCosTheta;
SinCos( flPhi, &flSinPhi, &flCosPhi );
SinCos( flTheta, &flSinTheta, &flCosTheta );
return Vector( flSinPhi * flCosTheta, flSinPhi * flSinTheta, flCosPhi );
}
Vector RandomVectorOnUnitSphere()
{
// Guarantee uniform random distribution on a sphere
// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
float u = RandomFloat( 0., 1. );
float v = RandomFloat( 0., 1. );
return RandomVectorOnUnitSphere( u, v );
}
Vector RandomVectorOnUnitSphere( IUniformRandomStream *pRnd )
{
return RandomVectorOnUnitSphere( pRnd->RandomFloat(), pRnd->RandomFloat() );
}
float RandomVectorInUnitSphere( Vector *pVector )
{
// Guarantee uniform random distribution within a sphere
// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
float u = ((float)rand() / VALVE_RAND_MAX);
float v = ((float)rand() / VALVE_RAND_MAX);
float w = ((float)rand() / VALVE_RAND_MAX);
float flPhi = acos( 1 - 2 * u );
float flTheta = 2 * M_PI * v;
float flRadius = powf( w, 1.0f / 3.0f );
float flSinPhi, flCosPhi;
float flSinTheta, flCosTheta;
SinCos( flPhi, &flSinPhi, &flCosPhi );
SinCos( flTheta, &flSinTheta, &flCosTheta );
pVector->x = flRadius * flSinPhi * flCosTheta;
pVector->y = flRadius * flSinPhi * flSinTheta;
pVector->z = flRadius * flCosPhi;
return flRadius;
}
Vector RandomVectorInUnitSphere()
{
Vector vOut;
RandomVectorInUnitSphere( &vOut );
return vOut;
}
Vector RandomVectorInUnitSphere( IUniformRandomStream *pRnd )
{
float w = pRnd->RandomFloat();
float flRadius = powf( w, 1.0f / 3.0f );
Vector v = RandomVectorOnUnitSphere( pRnd ) * flRadius;
return v;
}
float RandomVectorInUnitCircle( Vector2D *pVector )
{
// Guarantee uniform random distribution within a sphere
// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
float u = ((float)rand() / VALVE_RAND_MAX);
float v = ((float)rand() / VALVE_RAND_MAX);
float flTheta = 2 * M_PI * v;
float flRadius = powf( u, 1.0f / 2.0f );
float flSinTheta, flCosTheta;
SinCos( flTheta, &flSinTheta, &flCosTheta );
pVector->x = flRadius * flCosTheta;
pVector->y = flRadius * flSinTheta;
return flRadius;
}
const Quaternion RandomQuaternion()
{
// Guarantee uniform distribution within S^3. Found on the internet, looked through the proof very briefly, looks sound enough to tentatively trust it before testing or checking the proof for real.
// http://mathproofs.blogspot.com/2005/05/uniformly-distributed-random-unit.html
float u = RandomFloat( 0, 2 * M_PI ), flSinU = sinf( u );
float v = acosf( RandomFloat( -1, 1 ) ), flSinV = sinf( v );
float w = 0.5f * ( RandomFloat( 0, M_PI ) + acosf( RandomFloat( 0, 1 ) ) + M_PI / 2 ), flSinW = sinf( w );
return Quaternion( cosf( u ), flSinU * cosf( v ), flSinU * flSinV * cosf( w ), flSinU * flSinV * flSinW );
}
const Quaternion RandomQuaternion( IUniformRandomStream *pRnd )
{
// Guarantee uniform distribution within S^3. Found on the internet, looked through the proof very briefly, looks sound enough to tentatively trust it before testing or checking the proof for real.
// http://mathproofs.blogspot.com/2005/05/uniformly-distributed-random-unit.html
float u = pRnd->RandomFloat( 0, 2 * M_PI ), flSinU = sinf( u );
float v = acosf( pRnd->RandomFloat( -1, 1 ) ), flSinV = sinf( v );
float w = 0.5f * ( pRnd->RandomFloat( 0, M_PI ) + acosf( pRnd->RandomFloat( 0, 1 ) ) + M_PI / 2 ), flSinW = sinf( w );
return Quaternion( cosf( u ), flSinU * cosf( v ), flSinU * flSinV * cosf( w ), flSinU * flSinV * flSinW );
}
// Originally from hammer_mathlib.cpp
//
// Generate the corner points of a box:
// +y _+z
// ^ /|
// | /
// | 3---7
// /| /|
// / | / |
// 2---6 |
// | 1|--5
// | / | /
// |/ |/
// 0---4 --> +x
//
void PointsFromBox( const Vector &mins, const Vector &maxs, Vector *points )
{
points[ 0 ][ 0 ] = mins[ 0 ];
points[ 0 ][ 1 ] = mins[ 1 ];
points[ 0 ][ 2 ] = mins[ 2 ];
points[ 1 ][ 0 ] = mins[ 0 ];
points[ 1 ][ 1 ] = mins[ 1 ];
points[ 1 ][ 2 ] = maxs[ 2 ];
points[ 2 ][ 0 ] = mins[ 0 ];
points[ 2 ][ 1 ] = maxs[ 1 ];
points[ 2 ][ 2 ] = mins[ 2 ];
points[ 3 ][ 0 ] = mins[ 0 ];
points[ 3 ][ 1 ] = maxs[ 1 ];
points[ 3 ][ 2 ] = maxs[ 2 ];
points[ 4 ][ 0 ] = maxs[ 0 ];
points[ 4 ][ 1 ] = mins[ 1 ];
points[ 4 ][ 2 ] = mins[ 2 ];
points[ 5 ][ 0 ] = maxs[ 0 ];
points[ 5 ][ 1 ] = mins[ 1 ];
points[ 5 ][ 2 ] = maxs[ 2 ];
points[ 6 ][ 0 ] = maxs[ 0 ];
points[ 6 ][ 1 ] = maxs[ 1 ];
points[ 6 ][ 2 ] = mins[ 2 ];
points[ 7 ][ 0 ] = maxs[ 0 ];
points[ 7 ][ 1 ] = maxs[ 1 ];
points[ 7 ][ 2 ] = maxs[ 2 ];
}
void BuildTransformedBox( Vector *v2, Vector const &bbmin, Vector const &bbmax, const matrix3x4_t& m )
{
Vector v[ 8 ];
PointsFromBox( bbmin, bbmax, v );
VectorTransform( v[ 0 ], m, v2[ 0 ] );
VectorTransform( v[ 1 ], m, v2[ 1 ] );
VectorTransform( v[ 2 ], m, v2[ 2 ] );
VectorTransform( v[ 3 ], m, v2[ 3 ] );
VectorTransform( v[ 4 ], m, v2[ 4 ] );
VectorTransform( v[ 5 ], m, v2[ 5 ] );
VectorTransform( v[ 6 ], m, v2[ 6 ] );
VectorTransform( v[ 7 ], m, v2[ 7 ] );
}
#endif // !defined(__SPU__)