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284 lines
8.2 KiB
284 lines
8.2 KiB
//========= Copyright Valve Corporation, All rights reserved. ============//
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//
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// Purpose:
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//
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// $NoKeywords: $
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//
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//=============================================================================//
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#ifndef _3D_UNITVEC_H
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#define _3D_UNITVEC_H
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#define UNITVEC_DECLARE_STATICS \
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float cUnitVector::mUVAdjustment[0x2000]; \
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Vector cUnitVector::mTmpVec;
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// upper 3 bits
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#define SIGN_MASK 0xe000
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#define XSIGN_MASK 0x8000
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#define YSIGN_MASK 0x4000
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#define ZSIGN_MASK 0x2000
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// middle 6 bits - xbits
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#define TOP_MASK 0x1f80
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// lower 7 bits - ybits
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#define BOTTOM_MASK 0x007f
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// unitcomp.cpp : A Unit Vector to 16-bit word conversion
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// algorithm based on work of Rafael Baptista ([email protected])
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// Accuracy improved by O.D. ([email protected])
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// Used with Permission.
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// a compressed unit vector. reasonable fidelty for unit
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// vectors in a 16 bit package. Good enough for surface normals
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// we hope.
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class cUnitVector // : public c3dMathObject
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{
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public:
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cUnitVector() { mVec = 0; }
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cUnitVector( const Vector& vec )
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{
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packVector( vec );
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}
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cUnitVector( unsigned short val ) { mVec = val; }
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cUnitVector& operator=( const Vector& vec )
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{ packVector( vec ); return *this; }
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operator Vector()
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{
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unpackVector( mTmpVec );
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return mTmpVec;
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}
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void packVector( const Vector& vec )
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{
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// convert from Vector to cUnitVector
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Assert( vec.IsValid());
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Vector tmp = vec;
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// input vector does not have to be unit length
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// Assert( tmp.length() <= 1.001f );
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mVec = 0;
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if ( tmp.x < 0 ) { mVec |= XSIGN_MASK; tmp.x = -tmp.x; }
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if ( tmp.y < 0 ) { mVec |= YSIGN_MASK; tmp.y = -tmp.y; }
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if ( tmp.z < 0 ) { mVec |= ZSIGN_MASK; tmp.z = -tmp.z; }
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// project the normal onto the plane that goes through
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// X0=(1,0,0),Y0=(0,1,0),Z0=(0,0,1).
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// on that plane we choose an (projective!) coordinate system
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// such that X0->(0,0), Y0->(126,0), Z0->(0,126),(0,0,0)->Infinity
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// a little slower... old pack was 4 multiplies and 2 adds.
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// This is 2 multiplies, 2 adds, and a divide....
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float w = 126.0f / ( tmp.x + tmp.y + tmp.z );
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long xbits = (long)( tmp.x * w );
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long ybits = (long)( tmp.y * w );
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Assert( xbits < 127 );
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Assert( xbits >= 0 );
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Assert( ybits < 127 );
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Assert( ybits >= 0 );
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// Now we can be sure that 0<=xp<=126, 0<=yp<=126, 0<=xp+yp<=126
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// however for the sampling we want to transform this triangle
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// into a rectangle.
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if ( xbits >= 64 )
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{
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xbits = 127 - xbits;
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ybits = 127 - ybits;
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}
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// now we that have xp in the range (0,127) and yp in
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// the range (0,63), we can pack all the bits together
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mVec |= ( xbits << 7 );
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mVec |= ybits;
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}
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void unpackVector( Vector& vec )
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{
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// if we do a straightforward backward transform
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// we will get points on the plane X0,Y0,Z0
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// however we need points on a sphere that goes through
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// these points. Therefore we need to adjust x,y,z so
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// that x^2+y^2+z^2=1 by normalizing the vector. We have
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// already precalculated the amount by which we need to
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// scale, so all we do is a table lookup and a
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// multiplication
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// get the x and y bits
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long xbits = (( mVec & TOP_MASK ) >> 7 );
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long ybits = ( mVec & BOTTOM_MASK );
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// map the numbers back to the triangle (0,0)-(0,126)-(126,0)
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if (( xbits + ybits ) >= 127 )
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{
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xbits = 127 - xbits;
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ybits = 127 - ybits;
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}
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// do the inverse transform and normalization
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// costs 3 extra multiplies and 2 subtracts. No big deal.
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float uvadj = mUVAdjustment[mVec & ~SIGN_MASK];
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vec.x = uvadj * (float) xbits;
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vec.y = uvadj * (float) ybits;
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vec.z = uvadj * (float)( 126 - xbits - ybits );
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// set all the sign bits
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if ( mVec & XSIGN_MASK ) vec.x = -vec.x;
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if ( mVec & YSIGN_MASK ) vec.y = -vec.y;
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if ( mVec & ZSIGN_MASK ) vec.z = -vec.z;
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Assert( vec.IsValid());
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}
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static void initializeStatics()
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{
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for ( int idx = 0; idx < 0x2000; idx++ )
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{
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long xbits = idx >> 7;
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long ybits = idx & BOTTOM_MASK;
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// map the numbers back to the triangle (0,0)-(0,127)-(127,0)
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if (( xbits + ybits ) >= 127 )
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{
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xbits = 127 - xbits;
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ybits = 127 - ybits;
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}
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// convert to 3D vectors
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float x = (float)xbits;
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float y = (float)ybits;
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float z = (float)( 126 - xbits - ybits );
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// calculate the amount of normalization required
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mUVAdjustment[idx] = 1.0f / sqrtf( y*y + z*z + x*x );
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Assert( _finite( mUVAdjustment[idx]));
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//cerr << mUVAdjustment[idx] << "\t";
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//if ( xbits == 0 ) cerr << "\n";
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}
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}
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#if 0
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void test()
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{
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#define TEST_RANGE 4
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#define TEST_RANDOM 100
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#define TEST_ANGERROR 1.0
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float maxError = 0;
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float avgError = 0;
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int numVecs = 0;
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{for ( int x = -TEST_RANGE; x < TEST_RANGE; x++ )
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{
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for ( int y = -TEST_RANGE; y < TEST_RANGE; y++ )
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{
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for ( int z = -TEST_RANGE; z < TEST_RANGE; z++ )
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{
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if (( x + y + z ) == 0 ) continue;
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Vector vec( (float)x, (float)y, (float)z );
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Vector vec2;
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vec.normalize();
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packVector( vec );
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unpackVector( vec2 );
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float ang = vec.dot( vec2 );
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ang = (( fabs( ang ) > 0.99999f ) ? 0 : (float)acos(ang));
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if (( ang > TEST_ANGERROR ) | ( !_finite( ang )))
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{
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cerr << "error: " << ang << endl;
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cerr << "orig vec: " << vec.x << ",\t"
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<< vec.y << ",\t" << vec.z << "\tmVec: "
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<< mVec << endl;
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cerr << "quantized vec2: " << vec2.x
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<< ",\t" << vec2.y << ",\t"
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<< vec2.z << endl << endl;
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}
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avgError += ang;
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numVecs++;
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if ( maxError < ang ) maxError = ang;
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}
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}
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}}
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for ( int w = 0; w < TEST_RANDOM; w++ )
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{
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Vector vec( genRandom(), genRandom(), genRandom());
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Vector vec2;
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vec.normalize();
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packVector( vec );
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unpackVector( vec2 );
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float ang =vec.dot( vec2 );
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ang = (( ang > 0.999f ) ? 0 : (float)acos(ang));
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if (( ang > TEST_ANGERROR ) | ( !_finite( ang )))
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{
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cerr << "error: " << ang << endl;
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cerr << "orig vec: " << vec.x << ",\t"
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<< vec.y << ",\t" << vec.z << "\tmVec: "
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<< mVec << endl;
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cerr << "quantized vec2: " << vec2.x << ",\t"
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<< vec2.y << ",\t"
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<< vec2.z << endl << endl;
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}
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avgError += ang;
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numVecs++;
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if ( maxError < ang ) maxError = ang;
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}
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{ for ( int x = 0; x < 50; x++ )
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{
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Vector vec( (float)x, 25.0f, 0.0f );
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Vector vec2;
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vec.normalize();
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packVector( vec );
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unpackVector( vec2 );
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float ang = vec.dot( vec2 );
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ang = (( fabs( ang ) > 0.999f ) ? 0 : (float)acos(ang));
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if (( ang > TEST_ANGERROR ) | ( !_finite( ang )))
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{
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cerr << "error: " << ang << endl;
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cerr << "orig vec: " << vec.x << ",\t"
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<< vec.y << ",\t" << vec.z << "\tmVec: "
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<< mVec << endl;
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cerr << " quantized vec2: " << vec2.x << ",\t"
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<< vec2.y << ",\t" << vec2.z << endl << endl;
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}
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avgError += ang;
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numVecs++;
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if ( maxError < ang ) maxError = ang;
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}}
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cerr << "max angle error: " << maxError
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<< ", average error: " << avgError / numVecs
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<< ", num tested vecs: " << numVecs << endl;
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}
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friend ostream& operator<< ( ostream& os, const cUnitVector& vec )
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{ os << vec.mVec; return os; }
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#endif
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//protected: // !!!!
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unsigned short mVec;
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static float mUVAdjustment[0x2000];
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static Vector mTmpVec;
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};
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#endif // _3D_VECTOR_H
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