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329 lines
11 KiB
329 lines
11 KiB
//-----------------------------------------------------------------------------
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// File: D3DMath.cpp
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//
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// Desc: Shortcut macros and functions for using DX objects
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//
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// Copyright (c) 1997-1999 Microsoft Corporation. All rights reserved
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//-----------------------------------------------------------------------------
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#define D3D_OVERLOADS
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#define STRICT
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#include "StdAfx.h"
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#include <math.h>
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#include "D3DMath.h"
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//-----------------------------------------------------------------------------
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// Name: D3DMath_MatrixMultiply()
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// Desc: Does the matrix operation: [Q] = [A] * [B]. Note that the order of
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// this operation was changed from the previous version of the DXSDK.
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//-----------------------------------------------------------------------------
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VOID D3DMath_MatrixMultiply(D3DMATRIX& q, D3DMATRIX& a, D3DMATRIX& b)
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{
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FLOAT* pA = (FLOAT*)&a;
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FLOAT* pB = (FLOAT*)&b;
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FLOAT pM[16];
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ZeroMemory(pM, sizeof(D3DMATRIX));
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for(WORD i=0; i<4; i++)
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for(WORD j=0; j<4; j++)
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for(WORD k=0; k<4; k++)
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pM[4*i+j] += pA[4*i+k] * pB[4*k+j];
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memcpy(&q, pM, sizeof(D3DMATRIX));
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_MatrixInvert()
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// Desc: Does the matrix operation: [Q] = inv[A]. Note: this function only
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// works for matrices with [0 0 0 1] for the 4th column.
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//-----------------------------------------------------------------------------
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HRESULT D3DMath_MatrixInvert(D3DMATRIX& q, D3DMATRIX& a)
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{
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if (fabs(a._44 - 1.0f) > .001f)
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return E_INVALIDARG;
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if (fabs(a._14) > .001f || fabs(a._24) > .001f || fabs(a._34) > .001f)
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return E_INVALIDARG;
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FLOAT fDetInv = 1.0f / (a._11 * (a._22 * a._33 - a._23 * a._32) -
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a._12 * (a._21 * a._33 - a._23 * a._31) +
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a._13 * (a._21 * a._32 - a._22 * a._31));
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q._11 = fDetInv * (a._22 * a._33 - a._23 * a._32);
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q._12 = -fDetInv * (a._12 * a._33 - a._13 * a._32);
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q._13 = fDetInv * (a._12 * a._23 - a._13 * a._22);
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q._14 = 0.0f;
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q._21 = -fDetInv * (a._21 * a._33 - a._23 * a._31);
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q._22 = fDetInv * (a._11 * a._33 - a._13 * a._31);
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q._23 = -fDetInv * (a._11 * a._23 - a._13 * a._21);
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q._24 = 0.0f;
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q._31 = fDetInv * (a._21 * a._32 - a._22 * a._31);
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q._32 = -fDetInv * (a._11 * a._32 - a._12 * a._31);
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q._33 = fDetInv * (a._11 * a._22 - a._12 * a._21);
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q._34 = 0.0f;
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q._41 = -(a._41 * q._11 + a._42 * q._21 + a._43 * q._31);
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q._42 = -(a._41 * q._12 + a._42 * q._22 + a._43 * q._32);
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q._43 = -(a._41 * q._13 + a._42 * q._23 + a._43 * q._33);
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q._44 = 1.0f;
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return S_OK;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_VectorMatrixMultiply()
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// Desc: Multiplies a vector by a matrix
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//-----------------------------------------------------------------------------
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HRESULT D3DMath_VectorMatrixMultiply(D3DVECTOR& vDest, D3DVECTOR& vSrc,
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D3DMATRIX& mat)
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{
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FLOAT x = vSrc.x*mat._11 + vSrc.y*mat._21 + vSrc.z* mat._31 + mat._41;
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FLOAT y = vSrc.x*mat._12 + vSrc.y*mat._22 + vSrc.z* mat._32 + mat._42;
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FLOAT z = vSrc.x*mat._13 + vSrc.y*mat._23 + vSrc.z* mat._33 + mat._43;
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FLOAT w = vSrc.x*mat._14 + vSrc.y*mat._24 + vSrc.z* mat._34 + mat._44;
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if (fabs(w) < g_EPSILON)
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return E_INVALIDARG;
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vDest.x = x/w;
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vDest.y = y/w;
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vDest.z = z/w;
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return S_OK;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_VertexMatrixMultiply()
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// Desc: Multiplies a vertex by a matrix
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//-----------------------------------------------------------------------------
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HRESULT D3DMath_VertexMatrixMultiply(D3DVERTEX& vDest, D3DVERTEX& vSrc,
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D3DMATRIX& mat)
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{
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HRESULT hr;
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D3DVECTOR* pSrcVec = (D3DVECTOR*)&vSrc.x;
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D3DVECTOR* pDestVec = (D3DVECTOR*)&vDest.x;
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if (SUCCEEDED(hr = D3DMath_VectorMatrixMultiply(*pDestVec, *pSrcVec,
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mat)))
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{
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pSrcVec = (D3DVECTOR*)&vSrc.nx;
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pDestVec = (D3DVECTOR*)&vDest.nx;
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hr = D3DMath_VectorMatrixMultiply(*pDestVec, *pSrcVec, mat);
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}
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return hr;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_QuaternionFromRotation()
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// Desc: Converts a normalized axis and angle to a unit quaternion.
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//-----------------------------------------------------------------------------
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VOID D3DMath_QuaternionFromRotation(FLOAT& x, FLOAT& y, FLOAT& z, FLOAT& w,
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D3DVECTOR& v, FLOAT fTheta)
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{
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x = sinf(fTheta/2.0f) * v.x;
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y = sinf(fTheta/2.0f) * v.y;
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z = sinf(fTheta/2.0f) * v.z;
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w = cosf(fTheta/2.0f);
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_RotationFromQuaternion()
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// Desc: Converts a normalized axis and angle to a unit quaternion.
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//-----------------------------------------------------------------------------
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VOID D3DMath_RotationFromQuaternion(D3DVECTOR& v, FLOAT& fTheta,
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FLOAT x, FLOAT y, FLOAT z, FLOAT w)
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{
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fTheta = acosf(w) * 2.0f;
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v.x = x / sinf(fTheta/2.0f);
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v.y = y / sinf(fTheta/2.0f);
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v.z = z / sinf(fTheta/2.0f);
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_QuaternionFromAngles()
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// Desc: Converts euler angles to a unit quaternion.
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//-----------------------------------------------------------------------------
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VOID D3DMath_QuaternionFromAngles(FLOAT& x, FLOAT& y, FLOAT& z, FLOAT& w,
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FLOAT fYaw, FLOAT fPitch, FLOAT fRoll)
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{
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FLOAT fSinYaw = sinf(fYaw/2.0f);
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FLOAT fSinPitch = sinf(fPitch/2.0f);
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FLOAT fSinRoll = sinf(fRoll/2.0f);
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FLOAT fCosYaw = cosf(fYaw/2.0f);
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FLOAT fCosPitch = cosf(fPitch/2.0f);
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FLOAT fCosRoll = cosf(fRoll/2.0f);
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x = fSinRoll * fCosPitch * fCosYaw - fCosRoll * fSinPitch * fSinYaw;
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y = fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw;
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z = fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw;
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w = fCosRoll * fCosPitch * fCosYaw + fSinRoll * fSinPitch * fSinYaw;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_MatrixFromQuaternion()
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// Desc: Converts a unit quaternion into a rotation matrix.
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//-----------------------------------------------------------------------------
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VOID D3DMath_MatrixFromQuaternion(D3DMATRIX& mat, FLOAT x, FLOAT y, FLOAT z,
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FLOAT w)
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{
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FLOAT xx = x*x; FLOAT yy = y*y; FLOAT zz = z*z;
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FLOAT xy = x*y; FLOAT xz = x*z; FLOAT yz = y*z;
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FLOAT wx = w*x; FLOAT wy = w*y; FLOAT wz = w*z;
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mat._11 = 1 - 2 * (yy + zz);
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mat._12 = 2 * (xy - wz);
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mat._13 = 2 * (xz + wy);
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mat._21 = 2 * (xy + wz);
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mat._22 = 1 - 2 * (xx + zz);
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mat._23 = 2 * (yz - wx);
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mat._31 = 2 * (xz - wy);
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mat._32 = 2 * (yz + wx);
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mat._33 = 1 - 2 * (xx + yy);
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mat._14 = mat._24 = mat._34 = 0.0f;
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mat._41 = mat._42 = mat._43 = 0.0f;
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mat._44 = 1.0f;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_QuaternionFromMatrix()
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// Desc: Converts a rotation matrix into a unit quaternion.
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//-----------------------------------------------------------------------------
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VOID D3DMath_QuaternionFromMatrix(FLOAT& x, FLOAT& y, FLOAT& z, FLOAT& w,
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D3DMATRIX& mat)
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{
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if (mat._11 + mat._22 + mat._33 > 0.0f)
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{
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FLOAT s = sqrtf(mat._11 + mat._22 + mat._33 + mat._44);
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x = (mat._23-mat._32) / (2*s);
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y = (mat._31-mat._13) / (2*s);
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z = (mat._12-mat._21) / (2*s);
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w = 0.5f * s;
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}
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else
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{
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}
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FLOAT xx = x*x; FLOAT yy = y*y; FLOAT zz = z*z;
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FLOAT xy = x*y; FLOAT xz = x*z; FLOAT yz = y*z;
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FLOAT wx = w*x; FLOAT wy = w*y; FLOAT wz = w*z;
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mat._11 = 1 - 2 * (yy + zz);
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mat._12 = 2 * (xy - wz);
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mat._13 = 2 * (xz + wy);
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mat._21 = 2 * (xy + wz);
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mat._22 = 1 - 2 * (xx + zz);
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mat._23 = 2 * (yz - wx);
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mat._31 = 2 * (xz - wy);
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mat._32 = 2 * (yz + wx);
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mat._33 = 1 - 2 * (xx + yy);
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mat._14 = mat._24 = mat._34 = 0.0f;
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mat._41 = mat._42 = mat._43 = 0.0f;
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mat._44 = 1.0f;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_QuaternionMultiply()
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// Desc: Mulitples two quaternions together as in {Q} = {A} * {B}.
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//-----------------------------------------------------------------------------
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VOID D3DMath_QuaternionMultiply(FLOAT& Qx, FLOAT& Qy, FLOAT& Qz, FLOAT& Qw,
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FLOAT Ax, FLOAT Ay, FLOAT Az, FLOAT Aw,
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FLOAT Bx, FLOAT By, FLOAT Bz, FLOAT Bw)
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{
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FLOAT Dx = Ax*Bw + Ay*Bz - Az*By + Aw*Bx;
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FLOAT Dy = -Ax*Bz + Ay*Bw + Az*Bx + Aw*By;
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FLOAT Dz = Ax*By - Ay*Bx + Az*Bw + Aw*Bz;
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FLOAT Dw = -Ax*Bx - Ay*By - Az*Bz + Aw*Bw;
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Qx = Dx; Qy = Dy; Qz = Dz; Qw = Dw;
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}
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//-----------------------------------------------------------------------------
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// Name: D3DMath_SlerpQuaternions()
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// Desc: Compute a quaternion which is the spherical linear interpolation
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// between two other quaternions by dvFraction.
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//-----------------------------------------------------------------------------
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VOID D3DMath_QuaternionSlerp(FLOAT& Qx, FLOAT& Qy, FLOAT& Qz, FLOAT& Qw,
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FLOAT Ax, FLOAT Ay, FLOAT Az, FLOAT Aw,
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FLOAT Bx, FLOAT By, FLOAT Bz, FLOAT Bw,
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FLOAT fAlpha)
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{
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// Compute dot product (equal to cosine of the angle between quaternions)
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FLOAT fCosTheta = Ax*Bx + Ay*By + Az*Bz + Aw*Bw;
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// Check angle to see if quaternions are in opposite hemispheres
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if (fCosTheta < 0.0f)
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{
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// If so, flip one of the quaterions
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fCosTheta = -fCosTheta;
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Bx = -Bx; By = -By; Bz = -Bz; Bw = -Bw;
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}
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// Set factors to do linear interpolation, as a special case where the
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// quaternions are close together.
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FLOAT fBeta = 1.0f - fAlpha;
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// If the quaternions aren't close, proceed with spherical interpolation
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if (1.0f - fCosTheta > 0.001f)
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{
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FLOAT fTheta = acosf(fCosTheta);
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fBeta = sinf(fTheta*fBeta) / sinf(fTheta);
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fAlpha = sinf(fTheta*fAlpha) / sinf(fTheta);
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}
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// Do the interpolation
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Qx = fBeta*Ax + fAlpha*Bx;
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Qy = fBeta*Ay + fAlpha*By;
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Qz = fBeta*Az + fAlpha*Bz;
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Qw = fBeta*Aw + fAlpha*Bw;
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}
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