//========= Copyright Valve Corporation, All rights reserved. ============// // // Purpose: Math primitives. // //===========================================================================// /// FIXME: As soon as all references to mathlib.c are gone, include it in here #include #include // Needed for FLT_EPSILON #include "tier0/basetypes.h" #include #include "tier0/dbg.h" #include "tier0/vprof.h" //#define _VPROF_MATHLIB #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" #include "mathlib/mathlib.h" #include "mathlib/vector.h" #if !defined( _X360 ) #include "mathlib/amd3dx.h" #ifndef OSX #include "3dnow.h" #endif #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 Vector vec3_invalid( FLT_MAX, FLT_MAX, FLT_MAX ); const int nanmask = 255<<23; //----------------------------------------------------------------------------- // 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 ); } float FASTCALL _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; } // 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; } //----------------------------------------------------------------------------- // Function pointers selecting the appropriate implementation //----------------------------------------------------------------------------- float (*pfSqrt)(float x) = _sqrtf; float (*pfRSqrt)(float x) = _rsqrtf; float (*pfRSqrtFast)(float x) = _rsqrtf; float (FASTCALL *pfVectorNormalize)(Vector& v) = _VectorNormalize; void (FASTCALL *pfVectorNormalizeFast)(Vector& v) = _VectorNormalizeFast; float (*pfInvRSquared)(const float* v) = _InvRSquared; void (*pfFastSinCos)(float x, float* s, float* c) = SinCos; float (*pfFastCos)(float x) = cosf; 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); } } qboolean VectorsEqual( const float *v1, const float *v2 ) { Assert( s_bMathlibInitialized ); return ( ( v1[0] == v2[0] ) && ( v1[1] == v2[1] ) && ( v1[2] == v2[2] ) ); } //----------------------------------------------------------------------------- // 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; } } // transform in1 by the matrix in2 void VectorTransform (const float *in1, const matrix3x4_t& in2, float *out) { Assert( s_bMathlibInitialized ); Assert( in1 != out ); out[0] = DotProduct(in1, in2[0]) + in2[0][3]; out[1] = DotProduct(in1, in2[1]) + in2[1][3]; out[2] = DotProduct(in1, in2[2]) + in2[2][3]; } // 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]; out[0] = in1t[0] * in2[0][0] + in1t[1] * in2[1][0] + in1t[2] * in2[2][0]; out[1] = in1t[0] * in2[0][1] + in1t[1] * in2[1][1] + in1t[2] * in2[2][1]; out[2] = in1t[0] * in2[0][2] + in1t[1] * in2[1][2] + in1t[2] * in2[2][2]; } // assume in2 is a rotation and rotate the input vector void VectorRotate( const float *in1, const matrix3x4_t& in2, float *out ) { Assert( s_bMathlibInitialized ); Assert( in1 != out ); out[0] = DotProduct( in1, in2[0] ); out[1] = DotProduct( in1, in2[1] ); out[2] = DotProduct( in1, in2[2] ); } // 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 ) { matrix3x4_t matRotate; QuaternionMatrix( in2, matRotate ); VectorRotate( in1, matRotate, out ); } // rotate by the inverse of the matrix void VectorIRotate( const float *in1, const matrix3x4_t& in2, float *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; } // 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; } void MatrixScaleBy ( const float flScale, matrix3x4_t &out ) { out[0][0] *= flScale; out[1][0] *= flScale; out[2][0] *= flScale; out[0][1] *= flScale; out[1][1] *= flScale; out[2][1] *= flScale; out[0][2] *= flScale; out[1][2] *= flScale; out[2][2] *= flScale; } void MatrixScaleByZero ( matrix3x4_t &out ) { out[0][0] = 0.0f; out[1][0] = 0.0f; out[2][0] = 0.0f; out[0][1] = 0.0f; out[1][1] = 0.0f; out[2][1] = 0.0f; out[0][2] = 0.0f; out[1][2] = 0.0f; out[2][2] = 0.0f; } 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]; } int Q_log2(int val) { int answer=0; while (val>>=1) answer++; return answer; } // 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 (forward[0] == 0 && forward[1] == 0) { // 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 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]; } void ConcatTransforms_Aligned( const matrix3x4_t &m0, const matrix3x4_t &m1, matrix3x4_t &out ) { Assert( (((size_t)&m0) % 16) == 0 ); Assert( (((size_t)&m1) % 16) == 0 ); Assert( (((size_t)&out) % 16) == 0 ); 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. ==================== */ 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 (&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<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; } } 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; } //----------------------------------------------------------------------------- // 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; } //----------------------------------------------------------------------------- // 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; float crcy = cr*cy; float crsy = cr*sy; float srcy = sr*cy; float srsy = sr*sy; matrix[0][1] = sp*srcy-crsy; matrix[1][1] = sp*srsy+crcy; matrix[2][1] = sr*cp; matrix[0][2] = (sp*crcy+srsy); matrix[1][2] = (sp*crsy-srcy); matrix[2][2] = cr*cp; matrix[0][3] = 0.0f; matrix[1][3] = 0.0f; matrix[2][3] = 0.0f; } 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 ); } //----------------------------------------------------------------------------- // Bounding box construction methods //----------------------------------------------------------------------------- void ClearBounds (Vector& mins, Vector& maxs) { Assert( s_bMathlibInitialized ); mins[0] = mins[1] = mins[2] = 99999; maxs[0] = maxs[1] = maxs[2] = -99999; } 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; } } // 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=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)) } float fRet = pow( x, lastExponent ); Assert ( !IS_NAN( fRet ) ); return fRet; } 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 ) { // Actual smooth curve. Visualization: // http://www.wolframalpha.com/input/?i=plot%5B+0.5+*+%281+-+cos%5B2+*+pi+*+x%5D%29+for+x+%3D+%280%2C+1%29+%5D return 0.5f * (1 - cos( 2.0f * M_PI * x ) ); } 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 ); } //----------------------------------------------------------------------------- // 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() ); } //----------------------------------------------------------------------------- // 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; } } //----------------------------------------------------------------------------- // 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; } void QuaternionMatrix( const Quaternion &q, const Vector &pos, matrix3x4_t& matrix ) { if ( !HushAsserts() ) { 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, matrix3x4_t& matrix ) { Assert( s_bMathlibInitialized ); if ( !HushAsserts() ) { 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 } //----------------------------------------------------------------------------- // 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() ); } //----------------------------------------------------------------------------- // 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; } //----------------------------------------------------------------------------- // 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) } //----------------------------------------------------------------------------- // 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) } //----------------------------------------------------------------------------- // 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 ); } //----------------------------------------------------------------------------- // 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() ); } //----------------------------------------------------------------------------- // 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 ); } } } //----------------------------------------------------------------------------- // 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 ); } //----------------------------------------------------------------------------- // 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 #pragma optimize( "g", off ) 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 ); } #pragma optimize( "", on ) 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 ); } // 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/%3CXns91B880592482seed7@povray.org%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 ); } //----------------------------------------------------------------------------- // 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 ); } //----------------------------------------------------------------------------- // 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.f, 1.f ); 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.f, 1.f ); 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; 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 ) static bool s_b3DNowEnabled = false; static bool s_bMMXEnabled = false; static bool s_bSSEEnabled = false; static bool s_bSSE2Enabled = false; void MathLib_Init( float gamma, float texGamma, float brightness, int overbright, bool bAllow3DNow, bool bAllowSSE, bool bAllowSSE2, bool bAllowMMX ) { if ( s_bMathlibInitialized ) return; // FIXME: Hook SSE into VectorAligned + Vector4DAligned #if !defined( _X360 ) // Grab the processor information: const CPUInformation& pi = *GetCPUInformation(); // Select the default generic routines. pfSqrt = _sqrtf; pfRSqrt = _rsqrtf; pfRSqrtFast = _rsqrtf; pfVectorNormalize = _VectorNormalize; pfVectorNormalizeFast = _VectorNormalizeFast; pfInvRSquared = _InvRSquared; pfFastSinCos = SinCos; pfFastCos = cosf; if ( bAllowMMX && pi.m_bMMX ) { // Select the MMX specific routines if available // (MMX routines were used by SW span fillers - not currently used for HW) s_bMMXEnabled = true; } else { s_bMMXEnabled = false; } // SSE Generally performs better than 3DNow when present, so this is placed // first to allow SSE to override these settings. #if !defined( OSX ) && !defined( PLATFORM_WINDOWS_PC64 ) && !defined(LINUX) if ( bAllow3DNow && pi.m_b3DNow ) { s_b3DNowEnabled = true; // Select the 3DNow specific routines if available; pfVectorNormalize = _3DNow_VectorNormalize; pfVectorNormalizeFast = _3DNow_VectorNormalizeFast; pfInvRSquared = _3DNow_InvRSquared; pfSqrt = _3DNow_Sqrt; pfRSqrt = _3DNow_RSqrt; pfRSqrtFast = _3DNow_RSqrt; } else #endif { s_b3DNowEnabled = false; } if ( bAllowSSE && pi.m_bSSE ) { s_bSSEEnabled = true; #ifndef PLATFORM_WINDOWS_PC64 // These are not yet available. // Select the SSE specific routines if available pfVectorNormalize = _VectorNormalize; pfVectorNormalizeFast = _SSE_VectorNormalizeFast; pfInvRSquared = _SSE_InvRSquared; pfSqrt = _SSE_Sqrt; pfRSqrt = _SSE_RSqrtAccurate; pfRSqrtFast = _SSE_RSqrtFast; #endif #ifdef PLATFORM_WINDOWS_PC32 pfFastSinCos = _SSE_SinCos; pfFastCos = _SSE_cos; #endif } else { s_bSSEEnabled = false; } if ( bAllowSSE2 && pi.m_bSSE2 ) { s_bSSE2Enabled = true; #ifdef PLATFORM_WINDOWS_PC32 pfFastSinCos = _SSE2_SinCos; pfFastCos = _SSE2_cos; #endif } else { s_bSSE2Enabled = false; } #endif // !_X360 s_bMathlibInitialized = true; InitSinCosTable(); BuildGammaTable( gamma, texGamma, brightness, overbright ); } bool MathLib_3DNowEnabled( void ) { Assert( s_bMathlibInitialized ); return s_b3DNowEnabled; } bool MathLib_MMXEnabled( void ) { Assert( s_bMathlibInitialized ); return s_bMMXEnabled; } bool MathLib_SSEEnabled( void ) { Assert( s_bMathlibInitialized ); return s_bSSEEnabled; } bool MathLib_SSE2Enabled( void ) { Assert( s_bMathlibInitialized ); return s_bSSE2Enabled; } float Approach( float target, float value, float speed ) { float delta = target - value; if ( delta > speed ) value += speed; else if ( delta < -speed ) value -= speed; else value = target; return value; } // 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; } } //----------------------------------------------------------------------------- // 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: This is a clone of BaseWindingForPlane() // Input : *outVerts - 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 *outVerts, 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, outVerts[0]); // left VectorAdd (outVerts[0], vup, outVerts[0]); // up VectorAdd (org, vright, outVerts[1]); // right VectorAdd (outVerts[1], vup, outVerts[1]); // up VectorAdd (org, vright, outVerts[2]); // right VectorSubtract (outVerts[2], vup, outVerts[2]); // down VectorSubtract (org, vright, outVerts[3]); // left VectorSubtract (outVerts[3], vup, outVerts[3]); // down // The four corners form a planar quadrilateral normal to "normal" return 4; } //----------------------------------------------------------------------------- // 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_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; } //----------------------------------------------------------------------------- // 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, Frustum_t &frustum ) { float flIntercept = DotProduct( origin, forward ); // Setup the near and far planes. frustum.SetPlane( FRUSTUM_FARZ, PLANE_ANYZ, -forward, -flZFar - flIntercept ); frustum.SetPlane( FRUSTUM_NEARZ, PLANE_ANYZ, 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 ); frustum.SetPlane( FRUSTUM_LEFT, PLANE_ANYZ, normalPos, normalPos.Dot( origin ) ); frustum.SetPlane( FRUSTUM_RIGHT, PLANE_ANYZ, normalNeg, normalNeg.Dot( origin ) ); VectorMA( up, flTanY, forward, normalPos ); VectorMA( normalPos, -2.0f, up, normalNeg ); VectorNormalize( normalPos ); VectorNormalize( normalNeg ); frustum.SetPlane( FRUSTUM_BOTTOM, PLANE_ANYZ, normalPos, normalPos.Dot( origin ) ); frustum.SetPlane( FRUSTUM_TOP, PLANE_ANYZ, normalNeg, normalNeg.Dot( origin ) ); } //----------------------------------------------------------------------------- // 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 ) { Vector vecForward, vecRight, vecUp; AngleVectors( angles, &vecForward, &vecRight, &vecUp ); float flFovY = CalcFovY( flFovX, flAspectRatio ); GeneratePerspectiveFrustum( origin, vecForward, vecRight, vecUp, flZNear, flZFar, flFovX, flFovY, frustum ); } bool R_CullBox( const Vector& mins, const Vector& maxs, const Frustum_t &frustum ) { return (( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_LEFT) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_TOP) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_NEARZ) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_FARZ) ) == 2 ) ); } bool R_CullBoxSkipNear( const Vector& mins, const Vector& maxs, const Frustum_t &frustum ) { return (( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_LEFT) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_TOP) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM) ) == 2 ) || ( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_FARZ) ) == 2 ) ); } // 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 = 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; } 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; } 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; } #ifdef FP_EXCEPTIONS_ENABLED #include // For _clearfp and _controlfp_s #endif // FPExceptionDisable and FPExceptionEnabler taken from my blog post // at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/ #ifdef FP_EXCEPTIONS_ENABLED // These functions are all inlined NOPs if FP_EXCEPTIONS_ENABLED is not defined. FPExceptionDisabler::FPExceptionDisabler() { // Retrieve the current state of the exception flags. This // must be done before changing them. _MCW_EM is a bit // mask representing all available exception masks. _controlfp_s(&mOldValues, 0, 0); // Set all of the exception flags, which suppresses FP // exceptions on the x87 and SSE units. _controlfp_s(0, _MCW_EM, _MCW_EM); } FPExceptionDisabler::~FPExceptionDisabler() { // Clear any pending FP exceptions. This must be done // prior to enabling FP exceptions since otherwise there // may be a 'deferred crash' as soon the exceptions are // enabled. _clearfp(); // Reset (possibly enabling) the exception status. _controlfp_s(0, mOldValues, _MCW_EM); } // Overflow, divide-by-zero, and invalid-operation are the FP // exceptions most frequently associated with bugs. FPExceptionEnabler::FPExceptionEnabler(unsigned int enableBits /*= _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID*/) { // Retrieve the current state of the exception flags. This // must be done before changing them. _MCW_EM is a bit // mask representing all available exception masks. _controlfp_s(&mOldValues, 0, 0); // Make sure no non-exception flags have been specified, // to avoid accidental changing of rounding modes, etc. enableBits &= _MCW_EM; // Clear any pending FP exceptions. This must be done // prior to enabling FP exceptions since otherwise there // may be a 'deferred crash' as soon the exceptions are // enabled. _clearfp(); // Zero out the specified bits, leaving other bits alone. _controlfp_s(0, ~enableBits, enableBits); } FPExceptionEnabler::~FPExceptionEnabler() { // Reset the exception state. _controlfp_s(0, mOldValues, _MCW_EM); } #endif