//========= Copyright Valve Corporation, All rights reserved. ============// // // Purpose: // //===========================================================================// #ifndef MATH_LIB_H #define MATH_LIB_H #include #include "minmax.h" #include "tier0/basetypes.h" #include "tier0/commonmacros.h" #include "mathlib/vector.h" #include "mathlib/vector2d.h" #include "tier0/dbg.h" #include "mathlib/math_pfns.h" #if defined(__i386__) || defined(_M_IX86) // For MMX intrinsics #include #endif // XXX remove me #undef clamp // Uncomment this to enable FP exceptions in parts of the code. // This can help track down FP bugs. However the code is not // FP exception clean so this not a turnkey operation. //#define FP_EXCEPTIONS_ENABLED #ifdef FP_EXCEPTIONS_ENABLED #include // For _clearfp and _controlfp_s #endif // FPExceptionDisabler and FPExceptionEnabler taken from my blog post // at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/ // Declare an object of this type in a scope in order to suppress // all floating-point exceptions temporarily. The old exception // state will be reset at the end. class FPExceptionDisabler { public: #ifdef FP_EXCEPTIONS_ENABLED FPExceptionDisabler(); ~FPExceptionDisabler(); private: unsigned int mOldValues; #else FPExceptionDisabler() {} ~FPExceptionDisabler() {} #endif private: // Make the copy constructor and assignment operator private // and unimplemented to prohibit copying. FPExceptionDisabler(const FPExceptionDisabler&); FPExceptionDisabler& operator=(const FPExceptionDisabler&); }; // Declare an object of this type in a scope in order to enable a // specified set of floating-point exceptions temporarily. The old // exception state will be reset at the end. // This class can be nested. class FPExceptionEnabler { public: // Overflow, divide-by-zero, and invalid-operation are the FP // exceptions most frequently associated with bugs. #ifdef FP_EXCEPTIONS_ENABLED FPExceptionEnabler(unsigned int enableBits = _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID); ~FPExceptionEnabler(); private: unsigned int mOldValues; #else FPExceptionEnabler(unsigned int enableBits = 0) { } ~FPExceptionEnabler() { } #endif private: // Make the copy constructor and assignment operator private // and unimplemented to prohibit copying. FPExceptionEnabler(const FPExceptionEnabler&); FPExceptionEnabler& operator=(const FPExceptionEnabler&); }; #ifdef DEBUG // stop crashing edit-and-continue FORCEINLINE float clamp( float val, float minVal, float maxVal ) { if ( maxVal < minVal ) return maxVal; else if( val < minVal ) return minVal; else if( val > maxVal ) return maxVal; else return val; } #else // DEBUG FORCEINLINE float clamp( float val, float minVal, float maxVal ) { #if defined(__i386__) || defined(_M_IX86) _mm_store_ss( &val, _mm_min_ss( _mm_max_ss( _mm_load_ss(&val), _mm_load_ss(&minVal) ), _mm_load_ss(&maxVal) ) ); #else val = fpmax(minVal, val); val = fpmin(maxVal, val); #endif return val; } #endif // DEBUG // // Returns a clamped value in the range [min, max]. // template< class T > inline T clamp( T const &val, T const &minVal, T const &maxVal ) { if ( maxVal < minVal ) return maxVal; else if( val < minVal ) return minVal; else if( val > maxVal ) return maxVal; else return val; } // plane_t structure // !!! if this is changed, it must be changed in asm code too !!! // FIXME: does the asm code even exist anymore? // FIXME: this should move to a different file struct cplane_t { Vector normal; float dist; byte type; // for fast side tests byte signbits; // signx + (signy<<1) + (signz<<1) byte pad[2]; #ifdef VECTOR_NO_SLOW_OPERATIONS cplane_t() {} private: // No copy constructors allowed if we're in optimal mode cplane_t(const cplane_t& vOther); #endif }; // structure offset for asm code #define CPLANE_NORMAL_X 0 #define CPLANE_NORMAL_Y 4 #define CPLANE_NORMAL_Z 8 #define CPLANE_DIST 12 #define CPLANE_TYPE 16 #define CPLANE_SIGNBITS 17 #define CPLANE_PAD0 18 #define CPLANE_PAD1 19 // 0-2 are axial planes #define PLANE_X 0 #define PLANE_Y 1 #define PLANE_Z 2 // 3-5 are non-axial planes snapped to the nearest #define PLANE_ANYX 3 #define PLANE_ANYY 4 #define PLANE_ANYZ 5 //----------------------------------------------------------------------------- // Frustum plane indices. // WARNING: there is code that depends on these values //----------------------------------------------------------------------------- enum { FRUSTUM_RIGHT = 0, FRUSTUM_LEFT = 1, FRUSTUM_TOP = 2, FRUSTUM_BOTTOM = 3, FRUSTUM_NEARZ = 4, FRUSTUM_FARZ = 5, FRUSTUM_NUMPLANES = 6 }; extern int SignbitsForPlane( cplane_t *out ); class Frustum_t { public: void SetPlane( int i, int nType, const Vector &vecNormal, float dist ) { m_Plane[i].normal = vecNormal; m_Plane[i].dist = dist; m_Plane[i].type = nType; m_Plane[i].signbits = SignbitsForPlane( &m_Plane[i] ); m_AbsNormal[i].Init( fabs(vecNormal.x), fabs(vecNormal.y), fabs(vecNormal.z) ); } inline const cplane_t *GetPlane( int i ) const { return &m_Plane[i]; } inline const Vector &GetAbsNormal( int i ) const { return m_AbsNormal[i]; } private: cplane_t m_Plane[FRUSTUM_NUMPLANES]; Vector m_AbsNormal[FRUSTUM_NUMPLANES]; }; // Computes Y fov from an X fov and a screen aspect ratio + X from Y float CalcFovY( float flFovX, float flScreenAspect ); float CalcFovX( float flFovY, float flScreenAspect ); // Generate a frustum based on perspective view parameters // NOTE: FOV is specified in degrees, as the *full* view angle (not half-angle) void GeneratePerspectiveFrustum( const Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t &frustum ); 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 ); // Cull the world-space bounding box to the specified frustum. bool R_CullBox( const Vector& mins, const Vector& maxs, const Frustum_t &frustum ); bool R_CullBoxSkipNear( const Vector& mins, const Vector& maxs, const Frustum_t &frustum ); struct matrix3x4_t { matrix3x4_t() {} matrix3x4_t( float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23 ) { m_flMatVal[0][0] = m00; m_flMatVal[0][1] = m01; m_flMatVal[0][2] = m02; m_flMatVal[0][3] = m03; m_flMatVal[1][0] = m10; m_flMatVal[1][1] = m11; m_flMatVal[1][2] = m12; m_flMatVal[1][3] = m13; m_flMatVal[2][0] = m20; m_flMatVal[2][1] = m21; m_flMatVal[2][2] = m22; m_flMatVal[2][3] = m23; } //----------------------------------------------------------------------------- // Creates a matrix where the X axis = forward // the Y axis = left, and the Z axis = up //----------------------------------------------------------------------------- void Init( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &vecOrigin ) { m_flMatVal[0][0] = xAxis.x; m_flMatVal[0][1] = yAxis.x; m_flMatVal[0][2] = zAxis.x; m_flMatVal[0][3] = vecOrigin.x; m_flMatVal[1][0] = xAxis.y; m_flMatVal[1][1] = yAxis.y; m_flMatVal[1][2] = zAxis.y; m_flMatVal[1][3] = vecOrigin.y; m_flMatVal[2][0] = xAxis.z; m_flMatVal[2][1] = yAxis.z; m_flMatVal[2][2] = zAxis.z; m_flMatVal[2][3] = vecOrigin.z; } //----------------------------------------------------------------------------- // Creates a matrix where the X axis = forward // the Y axis = left, and the Z axis = up //----------------------------------------------------------------------------- matrix3x4_t( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &vecOrigin ) { Init( xAxis, yAxis, zAxis, vecOrigin ); } inline void Invalidate( void ) { for (int i = 0; i < 3; i++) { for (int j = 0; j < 4; j++) { m_flMatVal[i][j] = VEC_T_NAN; } } } float *operator[]( int i ) { Assert(( i >= 0 ) && ( i < 3 )); return m_flMatVal[i]; } const float *operator[]( int i ) const { Assert(( i >= 0 ) && ( i < 3 )); return m_flMatVal[i]; } float *Base() { return &m_flMatVal[0][0]; } const float *Base() const { return &m_flMatVal[0][0]; } float m_flMatVal[3][4]; }; #ifndef M_PI #define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h #endif #define M_PI_F ((float)(M_PI)) // Shouldn't collide with anything. // NJS: Inlined to prevent floats from being autopromoted to doubles, as with the old system. #ifndef RAD2DEG #define RAD2DEG( x ) ( (float)(x) * (float)(180.f / M_PI_F) ) #endif #ifndef DEG2RAD #define DEG2RAD( x ) ( (float)(x) * (float)(M_PI_F / 180.f) ) #endif // Used to represent sides of things like planes. #define SIDE_FRONT 0 #define SIDE_BACK 1 #define SIDE_ON 2 #define SIDE_CROSS -2 // necessary for polylib.c #define ON_VIS_EPSILON 0.01 // necessary for vvis (flow.c) -- again look into moving later! #define EQUAL_EPSILON 0.001 // necessary for vbsp (faces.c) -- should look into moving it there? extern bool s_bMathlibInitialized; extern const Vector vec3_origin; extern const QAngle vec3_angle; extern const Quaternion quat_identity; extern const Vector vec3_invalid; extern const int nanmask; #define IS_NAN(x) (((*(int *)&x)&nanmask)==nanmask) FORCEINLINE vec_t DotProduct(const vec_t *v1, const vec_t *v2) { return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; } FORCEINLINE void VectorSubtract(const vec_t *a, const vec_t *b, vec_t *c) { c[0]=a[0]-b[0]; c[1]=a[1]-b[1]; c[2]=a[2]-b[2]; } FORCEINLINE void VectorAdd(const vec_t *a, const vec_t *b, vec_t *c) { c[0]=a[0]+b[0]; c[1]=a[1]+b[1]; c[2]=a[2]+b[2]; } FORCEINLINE void VectorCopy(const vec_t *a, vec_t *b) { b[0]=a[0]; b[1]=a[1]; b[2]=a[2]; } FORCEINLINE void VectorClear(vec_t *a) { a[0]=a[1]=a[2]=0; } FORCEINLINE float VectorMaximum(const vec_t *v) { return max( v[0], max( v[1], v[2] ) ); } FORCEINLINE float VectorMaximum(const Vector& v) { return max( v.x, max( v.y, v.z ) ); } FORCEINLINE void VectorScale (const float* in, vec_t scale, float* out) { out[0] = in[0]*scale; out[1] = in[1]*scale; out[2] = in[2]*scale; } // Cannot be forceinline as they have overloads: inline void VectorFill(vec_t *a, float b) { a[0]=a[1]=a[2]=b; } inline void VectorNegate(vec_t *a) { a[0]=-a[0]; a[1]=-a[1]; a[2]=-a[2]; } //#define VectorMaximum(a) ( max( (a)[0], max( (a)[1], (a)[2] ) ) ) #define Vector2Clear(x) {(x)[0]=(x)[1]=0;} #define Vector2Negate(x) {(x)[0]=-((x)[0]);(x)[1]=-((x)[1]);} #define Vector2Copy(a,b) {(b)[0]=(a)[0];(b)[1]=(a)[1];} #define Vector2Subtract(a,b,c) {(c)[0]=(a)[0]-(b)[0];(c)[1]=(a)[1]-(b)[1];} #define Vector2Add(a,b,c) {(c)[0]=(a)[0]+(b)[0];(c)[1]=(a)[1]+(b)[1];} #define Vector2Scale(a,b,c) {(c)[0]=(b)*(a)[0];(c)[1]=(b)*(a)[1];} // NJS: Some functions in VBSP still need to use these for dealing with mixing vec4's and shorts with vec_t's. // remove when no longer needed. #define VECTOR_COPY( A, B ) do { (B)[0] = (A)[0]; (B)[1] = (A)[1]; (B)[2]=(A)[2]; } while(0) #define DOT_PRODUCT( A, B ) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] ) FORCEINLINE void VectorMAInline( const float* start, float scale, const float* direction, float* dest ) { dest[0]=start[0]+direction[0]*scale; dest[1]=start[1]+direction[1]*scale; dest[2]=start[2]+direction[2]*scale; } FORCEINLINE void VectorMAInline( const Vector& start, float scale, const Vector& direction, Vector& dest ) { dest.x=start.x+direction.x*scale; dest.y=start.y+direction.y*scale; dest.z=start.z+direction.z*scale; } FORCEINLINE void VectorMA( const Vector& start, float scale, const Vector& direction, Vector& dest ) { VectorMAInline(start, scale, direction, dest); } FORCEINLINE void VectorMA( const float * start, float scale, const float *direction, float *dest ) { VectorMAInline(start, scale, direction, dest); } int VectorCompare (const float *v1, const float *v2); inline float VectorLength(const float *v) { return FastSqrt( v[0]*v[0] + v[1]*v[1] + v[2]*v[2] + FLT_EPSILON ); } void CrossProduct (const float *v1, const float *v2, float *cross); qboolean VectorsEqual( const float *v1, const float *v2 ); inline vec_t RoundInt (vec_t in) { return floor(in + 0.5f); } int Q_log2(int val); // Math routines done in optimized assembly math package routines void inline SinCos( float radians, float *sine, float *cosine ) { #if defined( _X360 ) XMScalarSinCos( sine, cosine, radians ); #elif defined( PLATFORM_WINDOWS_PC32 ) _asm { fld DWORD PTR [radians] fsincos mov edx, DWORD PTR [cosine] mov eax, DWORD PTR [sine] fstp DWORD PTR [edx] fstp DWORD PTR [eax] } #elif defined( PLATFORM_WINDOWS_PC64 ) *sine = sin( radians ); *cosine = cos( radians ); #elif defined( POSIX ) sincosf(radians, sine, cosine); #endif } #define SIN_TABLE_SIZE 256 #define FTOIBIAS 12582912.f extern float SinCosTable[SIN_TABLE_SIZE]; inline float TableCos( float theta ) { union { int i; float f; } ftmp; // ideally, the following should compile down to: theta * constant + constant, changing any of these constants from defines sometimes fubars this. ftmp.f = theta * ( float )( SIN_TABLE_SIZE / ( 2.0f * M_PI ) ) + ( FTOIBIAS + ( SIN_TABLE_SIZE / 4 ) ); return SinCosTable[ ftmp.i & ( SIN_TABLE_SIZE - 1 ) ]; } inline float TableSin( float theta ) { union { int i; float f; } ftmp; // ideally, the following should compile down to: theta * constant + constant ftmp.f = theta * ( float )( SIN_TABLE_SIZE / ( 2.0f * M_PI ) ) + FTOIBIAS; return SinCosTable[ ftmp.i & ( SIN_TABLE_SIZE - 1 ) ]; } template FORCEINLINE T Square( T const &a ) { return a * a; } // return the smallest power of two >= x. // returns 0 if x == 0 or x > 0x80000000 (ie numbers that would be negative if x was signed) // NOTE: the old code took an int, and if you pass in an int of 0x80000000 casted to a uint, // you'll get 0x80000000, which is correct for uints, instead of 0, which was correct for ints FORCEINLINE uint SmallestPowerOfTwoGreaterOrEqual( uint x ) { x -= 1; x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return x + 1; } // return the largest power of two <= x. Will return 0 if passed 0 FORCEINLINE uint LargestPowerOfTwoLessThanOrEqual( uint x ) { if ( x >= 0x80000000 ) return 0x80000000; return SmallestPowerOfTwoGreaterOrEqual( x + 1 ) >> 1; } // Math routines for optimizing division void FloorDivMod (double numer, double denom, int *quotient, int *rem); int GreatestCommonDivisor (int i1, int i2); // Test for FPU denormal mode bool IsDenormal( const float &val ); // MOVEMENT INFO enum { PITCH = 0, // up / down YAW, // left / right ROLL // fall over }; void MatrixAngles( const matrix3x4_t & matrix, float *angles ); // !!!! void MatrixVectors( const matrix3x4_t &matrix, Vector* pForward, Vector *pRight, Vector *pUp ); void VectorTransform (const float *in1, const matrix3x4_t & in2, float *out); void VectorITransform (const float *in1, const matrix3x4_t & in2, float *out); void VectorRotate( const float *in1, const matrix3x4_t & in2, float *out); void VectorRotate( const Vector &in1, const QAngle &in2, Vector &out ); void VectorRotate( const Vector &in1, const Quaternion &in2, Vector &out ); void VectorIRotate( const float *in1, const matrix3x4_t & in2, float *out); #ifndef VECTOR_NO_SLOW_OPERATIONS QAngle TransformAnglesToLocalSpace( const QAngle &angles, const matrix3x4_t &parentMatrix ); QAngle TransformAnglesToWorldSpace( const QAngle &angles, const matrix3x4_t &parentMatrix ); #endif void MatrixInitialize( matrix3x4_t &mat, const Vector &vecOrigin, const Vector &vecXAxis, const Vector &vecYAxis, const Vector &vecZAxis ); void MatrixCopy( const matrix3x4_t &in, matrix3x4_t &out ); void MatrixInvert( const matrix3x4_t &in, matrix3x4_t &out ); // Matrix equality test bool MatricesAreEqual( const matrix3x4_t &src1, const matrix3x4_t &src2, float flTolerance = 1e-5 ); void MatrixGetColumn( const matrix3x4_t &in, int column, Vector &out ); void MatrixSetColumn( const Vector &in, int column, matrix3x4_t &out ); inline void MatrixGetTranslation( const matrix3x4_t &in, Vector &out ) { MatrixGetColumn ( in, 3, out ); } inline void MatrixSetTranslation( const Vector &in, matrix3x4_t &out ) { MatrixSetColumn ( in, 3, out ); } void MatrixScaleBy ( const float flScale, matrix3x4_t &out ); void MatrixScaleByZero ( matrix3x4_t &out ); //void DecomposeRotation( const matrix3x4_t &mat, float *out ); void ConcatRotations (const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out); void ConcatTransforms (const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out); // For identical interface w/ VMatrix inline void MatrixMultiply ( const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out ) { ConcatTransforms( in1, in2, out ); } void QuaternionSlerp( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt ); void QuaternionSlerpNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt ); void QuaternionBlend( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt ); void QuaternionBlendNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt ); void QuaternionIdentityBlend( const Quaternion &p, float t, Quaternion &qt ); float QuaternionAngleDiff( const Quaternion &p, const Quaternion &q ); void QuaternionScale( const Quaternion &p, float t, Quaternion &q ); void QuaternionAlign( const Quaternion &p, const Quaternion &q, Quaternion &qt ); float QuaternionDotProduct( const Quaternion &p, const Quaternion &q ); void QuaternionConjugate( const Quaternion &p, Quaternion &q ); void QuaternionInvert( const Quaternion &p, Quaternion &q ); float QuaternionNormalize( Quaternion &q ); void QuaternionAdd( const Quaternion &p, const Quaternion &q, Quaternion &qt ); void QuaternionMult( const Quaternion &p, const Quaternion &q, Quaternion &qt ); void QuaternionMatrix( const Quaternion &q, matrix3x4_t &matrix ); void QuaternionMatrix( const Quaternion &q, const Vector &pos, matrix3x4_t &matrix ); void QuaternionAngles( const Quaternion &q, QAngle &angles ); void AngleQuaternion( const QAngle& angles, Quaternion &qt ); void QuaternionAngles( const Quaternion &q, RadianEuler &angles ); void AngleQuaternion( RadianEuler const &angles, Quaternion &qt ); void QuaternionAxisAngle( const Quaternion &q, Vector &axis, float &angle ); void AxisAngleQuaternion( const Vector &axis, float angle, Quaternion &q ); void BasisToQuaternion( const Vector &vecForward, const Vector &vecRight, const Vector &vecUp, Quaternion &q ); void MatrixQuaternion( const matrix3x4_t &mat, Quaternion &q ); // A couple methods to find the dot product of a vector with a matrix row or column... inline float MatrixRowDotProduct( const matrix3x4_t &in1, int row, const Vector& in2 ) { Assert( (row >= 0) && (row < 3) ); return DotProduct( in1[row], in2.Base() ); } inline float MatrixColumnDotProduct( const matrix3x4_t &in1, int col, const Vector& in2 ) { Assert( (col >= 0) && (col < 4) ); return in1[0][col] * in2[0] + in1[1][col] * in2[1] + in1[2][col] * in2[2]; } int __cdecl BoxOnPlaneSide (const float *emins, const float *emaxs, const cplane_t *plane); inline float anglemod(float a) { a = (360.f/65536) * ((int)(a*(65536.f/360.0f)) & 65535); return a; } // Remap a value in the range [A,B] to [C,D]. inline float RemapVal( float val, float A, float B, float C, float D) { if ( A == B ) return val >= B ? D : C; return C + (D - C) * (val - A) / (B - A); } inline float RemapValClamped( float val, float A, float B, float C, float D) { if ( A == B ) return val >= B ? D : C; float cVal = (val - A) / (B - A); cVal = clamp( cVal, 0.0f, 1.0f ); return C + (D - C) * cVal; } // Returns A + (B-A)*flPercent. // float Lerp( float flPercent, float A, float B ); template FORCEINLINE T Lerp( float flPercent, T const &A, T const &B ) { return A + (B - A) * flPercent; } FORCEINLINE float Sqr( float f ) { return f*f; } // 5-argument floating point linear interpolation. // FLerp(f1,f2,i1,i2,x)= // f1 at x=i1 // f2 at x=i2 // smooth lerp between f1 and f2 at x>i1 and xi2 // // If you know a function f(x)'s value (f1) at position i1, and its value (f2) at position i2, // the function can be linearly interpolated with FLerp(f1,f2,i1,i2,x) // i2=i1 will cause a divide by zero. static inline float FLerp(float f1, float f2, float i1, float i2, float x) { return f1+(f2-f1)*(x-i1)/(i2-i1); } #ifndef VECTOR_NO_SLOW_OPERATIONS // YWB: Specialization for interpolating euler angles via quaternions... template<> FORCEINLINE QAngle Lerp( float flPercent, const QAngle& q1, const QAngle& q2 ) { // Avoid precision errors if ( q1 == q2 ) return q1; Quaternion src, dest; // Convert to quaternions AngleQuaternion( q1, src ); AngleQuaternion( q2, dest ); Quaternion result; // Slerp QuaternionSlerp( src, dest, flPercent, result ); // Convert to euler QAngle output; QuaternionAngles( result, output ); return output; } #else #pragma error // NOTE NOTE: I haven't tested this!! It may not work! Check out interpolatedvar.cpp in the client dll to try it template<> FORCEINLINE QAngleByValue Lerp( float flPercent, const QAngleByValue& q1, const QAngleByValue& q2 ) { // Avoid precision errors if ( q1 == q2 ) return q1; Quaternion src, dest; // Convert to quaternions AngleQuaternion( q1, src ); AngleQuaternion( q2, dest ); Quaternion result; // Slerp QuaternionSlerp( src, dest, flPercent, result ); // Convert to euler QAngleByValue output; QuaternionAngles( result, output ); return output; } #endif // VECTOR_NO_SLOW_OPERATIONS /// Same as swap(), but won't cause problems with std::swap template FORCEINLINE void V_swap( T& x, T& y ) { T temp = x; x = y; y = temp; } template FORCEINLINE T AVG(T a, T b) { return (a+b)/2; } // number of elements in an array of static size #define NELEMS(x) ARRAYSIZE(x) // XYZ macro, for printf type functions - ex printf("%f %f %f",XYZ(myvector)); #define XYZ(v) (v).x,(v).y,(v).z inline float Sign( float x ) { return (x <0.0f) ? -1.0f : 1.0f; } // // Clamps the input integer to the given array bounds. // Equivalent to the following, but without using any branches: // // if( n < 0 ) return 0; // else if ( n > maxindex ) return maxindex; // else return n; // // This is not always a clear performance win, but when you have situations where a clamped // value is thrashing against a boundary this is a big win. (ie, valid, invalid, valid, invalid, ...) // // Note: This code has been run against all possible integers. // inline int ClampArrayBounds( int n, unsigned maxindex ) { // mask is 0 if less than 4096, 0xFFFFFFFF if greater than unsigned int inrangemask = 0xFFFFFFFF + (((unsigned) n) > maxindex ); unsigned int lessthan0mask = 0xFFFFFFFF + ( n >= 0 ); // If the result was valid, set the result, (otherwise sets zero) int result = (inrangemask & n); // if the result was out of range or zero. result |= ((~inrangemask) & (~lessthan0mask)) & maxindex; return result; } #define BOX_ON_PLANE_SIDE(emins, emaxs, p) \ (((p)->type < 3)? \ ( \ ((p)->dist <= (emins)[(p)->type])? \ 1 \ : \ ( \ ((p)->dist >= (emaxs)[(p)->type])?\ 2 \ : \ 3 \ ) \ ) \ : \ BoxOnPlaneSide( (emins), (emaxs), (p))) //----------------------------------------------------------------------------- // FIXME: Vector versions.... the float versions will go away hopefully soon! //----------------------------------------------------------------------------- void AngleVectors (const QAngle& angles, Vector *forward); void AngleVectors (const QAngle& angles, Vector *forward, Vector *right, Vector *up); void AngleVectorsTranspose (const QAngle& angles, Vector *forward, Vector *right, Vector *up); void AngleMatrix (const QAngle &angles, matrix3x4_t &mat ); void AngleMatrix( const QAngle &angles, const Vector &position, matrix3x4_t &mat ); void AngleMatrix (const RadianEuler &angles, matrix3x4_t &mat ); void AngleMatrix( RadianEuler const &angles, const Vector &position, matrix3x4_t &mat ); void AngleIMatrix (const QAngle &angles, matrix3x4_t &mat ); void AngleIMatrix (const QAngle &angles, const Vector &position, matrix3x4_t &mat ); void AngleIMatrix (const RadianEuler &angles, matrix3x4_t &mat ); void VectorAngles( const Vector &forward, QAngle &angles ); void VectorAngles( const Vector &forward, const Vector &pseudoup, QAngle &angles ); void VectorMatrix( const Vector &forward, matrix3x4_t &mat ); void VectorVectors( const Vector &forward, Vector &right, Vector &up ); void SetIdentityMatrix( matrix3x4_t &mat ); void SetScaleMatrix( float x, float y, float z, matrix3x4_t &dst ); void MatrixBuildRotationAboutAxis( const Vector &vAxisOfRot, float angleDegrees, matrix3x4_t &dst ); inline void SetScaleMatrix( float flScale, matrix3x4_t &dst ) { SetScaleMatrix( flScale, flScale, flScale, dst ); } inline void SetScaleMatrix( const Vector& scale, matrix3x4_t &dst ) { SetScaleMatrix( scale.x, scale.y, scale.z, dst ); } // Computes the inverse transpose void MatrixTranspose( matrix3x4_t& mat ); void MatrixTranspose( const matrix3x4_t& src, matrix3x4_t& dst ); void MatrixInverseTranspose( const matrix3x4_t& src, matrix3x4_t& dst ); inline void PositionMatrix( const Vector &position, matrix3x4_t &mat ) { MatrixSetColumn( position, 3, mat ); } inline void MatrixPosition( const matrix3x4_t &matrix, Vector &position ) { MatrixGetColumn( matrix, 3, position ); } inline void VectorRotate( const Vector& in1, const matrix3x4_t &in2, Vector &out) { VectorRotate( &in1.x, in2, &out.x ); } inline void VectorIRotate( const Vector& in1, const matrix3x4_t &in2, Vector &out) { VectorIRotate( &in1.x, in2, &out.x ); } inline void MatrixAngles( const matrix3x4_t &matrix, QAngle &angles ) { MatrixAngles( matrix, &angles.x ); } inline void MatrixAngles( const matrix3x4_t &matrix, QAngle &angles, Vector &position ) { MatrixAngles( matrix, angles ); MatrixPosition( matrix, position ); } inline void MatrixAngles( const matrix3x4_t &matrix, RadianEuler &angles ) { MatrixAngles( matrix, &angles.x ); angles.Init( DEG2RAD( angles.z ), DEG2RAD( angles.x ), DEG2RAD( angles.y ) ); } void MatrixAngles( const matrix3x4_t &mat, RadianEuler &angles, Vector &position ); void MatrixAngles( const matrix3x4_t &mat, Quaternion &q, Vector &position ); inline int VectorCompare (const Vector& v1, const Vector& v2) { return v1 == v2; } inline void VectorTransform (const Vector& in1, const matrix3x4_t &in2, Vector &out) { VectorTransform( &in1.x, in2, &out.x ); } inline void VectorITransform (const Vector& in1, const matrix3x4_t &in2, Vector &out) { VectorITransform( &in1.x, in2, &out.x ); } /* inline void DecomposeRotation( const matrix3x4_t &mat, Vector &out ) { DecomposeRotation( mat, &out.x ); } */ inline int BoxOnPlaneSide (const Vector& emins, const Vector& emaxs, const cplane_t *plane ) { return BoxOnPlaneSide( &emins.x, &emaxs.x, plane ); } inline void VectorFill(Vector& a, float b) { a[0]=a[1]=a[2]=b; } inline void VectorNegate(Vector& a) { a[0] = -a[0]; a[1] = -a[1]; a[2] = -a[2]; } inline vec_t VectorAvg(Vector& a) { return ( a[0] + a[1] + a[2] ) / 3; } //----------------------------------------------------------------------------- // Box/plane test (slow version) //----------------------------------------------------------------------------- inline int FASTCALL BoxOnPlaneSide2 (const Vector& emins, const Vector& emaxs, const cplane_t *p, float tolerance = 0.f ) { Vector corners[2]; if (p->normal[0] < 0) { corners[0][0] = emins[0]; corners[1][0] = emaxs[0]; } else { corners[1][0] = emins[0]; corners[0][0] = emaxs[0]; } if (p->normal[1] < 0) { corners[0][1] = emins[1]; corners[1][1] = emaxs[1]; } else { corners[1][1] = emins[1]; corners[0][1] = emaxs[1]; } if (p->normal[2] < 0) { corners[0][2] = emins[2]; corners[1][2] = emaxs[2]; } else { corners[1][2] = emins[2]; corners[0][2] = emaxs[2]; } int sides = 0; float dist1 = DotProduct (p->normal, corners[0]) - p->dist; if (dist1 >= tolerance) sides = 1; float dist2 = DotProduct (p->normal, corners[1]) - p->dist; if (dist2 < -tolerance) sides |= 2; return sides; } //----------------------------------------------------------------------------- // Helpers for bounding box construction //----------------------------------------------------------------------------- void ClearBounds (Vector& mins, Vector& maxs); void AddPointToBounds (const Vector& v, Vector& mins, Vector& maxs); // // COLORSPACE/GAMMA CONVERSION STUFF // void BuildGammaTable( float gamma, float texGamma, float brightness, int overbright ); // convert texture to linear 0..1 value inline float TexLightToLinear( int c, int exponent ) { extern float power2_n[256]; Assert( exponent >= -128 && exponent <= 127 ); return ( float )c * power2_n[exponent+128]; } // convert texture to linear 0..1 value int LinearToTexture( float f ); // converts 0..1 linear value to screen gamma (0..255) int LinearToScreenGamma( float f ); float TextureToLinear( int c ); // compressed color format struct ColorRGBExp32 { byte r, g, b; signed char exponent; }; void ColorRGBExp32ToVector( const ColorRGBExp32& in, Vector& out ); void VectorToColorRGBExp32( const Vector& v, ColorRGBExp32 &c ); // solve for "x" where "a x^2 + b x + c = 0", return true if solution exists bool SolveQuadratic( float a, float b, float c, float &root1, float &root2 ); // 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 ); // solves for a,b,c specified as above, except that it always creates a monotonically increasing or // decreasing curve if the data is monotonically increasing or decreasing. In order to enforce the // monoticity condition, it is possible that the resulting quadratic will only approximate the data // instead of interpolating it. This code is not especially fast. bool SolveInverseQuadraticMonotonic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c ); // 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 ); // rotate a vector around the Z axis (YAW) void VectorYawRotate( const Vector& in, float flYaw, Vector &out); // Bias takes an X value between 0 and 1 and returns another value between 0 and 1 // The curve is biased towards 0 or 1 based on biasAmt, which is between 0 and 1. // Lower values of biasAmt bias the curve towards 0 and higher values bias it towards 1. // // For example, with biasAmt = 0.2, the curve looks like this: // // 1 // | * // | * // | * // | ** // | ** // | **** // |********* // |___________________ // 0 1 // // // With biasAmt = 0.8, the curve looks like this: // // 1 // | ************** // | ** // | * // | * // |* // |* // |* // |___________________ // 0 1 // // With a biasAmt of 0.5, Bias returns X. float Bias( float x, float biasAmt ); // Gain is similar to Bias, but biasAmt biases towards or away from 0.5. // Lower bias values bias towards 0.5 and higher bias values bias away from it. // // For example, with biasAmt = 0.2, the curve looks like this: // // 1 // | * // | * // | ** // | *************** // | ** // | * // |* // |___________________ // 0 1 // // // With biasAmt = 0.8, the curve looks like this: // // 1 // | ***** // | *** // | * // | * // | * // | *** // |***** // |___________________ // 0 1 float Gain( float x, float biasAmt ); // SmoothCurve maps a 0-1 value into another 0-1 value based on a cosine wave // where the derivatives of the function at 0 and 1 (and 0.5) are 0. This is useful for // any fadein/fadeout effect where it should start and end smoothly. // // The curve looks like this: // // 1 // | ** // | * * // | * * // | * * // | * * // | ** ** // |*** *** // |___________________ // 0 1 // float SmoothCurve( float x ); // This works like SmoothCurve, with two changes: // // 1. Instead of the curve peaking at 0.5, it will peak at flPeakPos. // (So if you specify flPeakPos=0.2, then the peak will slide to the left). // // 2. flPeakSharpness is a 0-1 value controlling the sharpness of the peak. // Low values blunt the peak and high values sharpen the peak. float SmoothCurve_Tweak( float x, float flPeakPos=0.5, float flPeakSharpness=0.5 ); //float ExponentialDecay( float halflife, float dt ); //float ExponentialDecay( float decayTo, float decayTime, float dt ); // halflife is time for value to reach 50% inline float ExponentialDecay( float halflife, float dt ) { // log(0.5) == -0.69314718055994530941723212145818 return expf( -0.69314718f / halflife * dt); } // decayTo is factor the value should decay to in decayTime inline float ExponentialDecay( float decayTo, float decayTime, float dt ) { return expf( logf( decayTo ) / decayTime * dt); } // Get the integrated distanced traveled // decayTo is factor the value should decay to in decayTime // dt is the time relative to the last velocity update inline float ExponentialDecayIntegral( float decayTo, float decayTime, float dt ) { return (powf( decayTo, dt / decayTime) * decayTime - decayTime) / logf( decayTo ); } // hermite basis function for smooth interpolation // Similar to Gain() above, but very cheap to call // value should be between 0 & 1 inclusive inline float SimpleSpline( float value ) { float valueSquared = value * value; // Nice little ease-in, ease-out spline-like curve return (3 * valueSquared - 2 * valueSquared * value); } // remaps a value in [startInterval, startInterval+rangeInterval] from linear to // spline using SimpleSpline inline float SimpleSplineRemapVal( float val, float A, float B, float C, float D) { if ( A == B ) return val >= B ? D : C; float cVal = (val - A) / (B - A); return C + (D - C) * SimpleSpline( cVal ); } // remaps a value in [startInterval, startInterval+rangeInterval] from linear to // spline using SimpleSpline inline float SimpleSplineRemapValClamped( float val, float A, float B, float C, float D ) { if ( A == B ) return val >= B ? D : C; float cVal = (val - A) / (B - A); cVal = clamp( cVal, 0.0f, 1.0f ); return C + (D - C) * SimpleSpline( cVal ); } FORCEINLINE int RoundFloatToInt(float f) { #if defined(__i386__) || defined(_M_IX86) || defined( PLATFORM_WINDOWS_PC64 ) || defined(__x86_64__) return _mm_cvtss_si32(_mm_load_ss(&f)); #elif defined( _X360 ) #ifdef Assert Assert( IsFPUControlWordSet() ); #endif union { double flResult; int pResult[2]; }; flResult = __fctiw( f ); return pResult[1]; #elif defined (__arm__) return (int)(f + 0.5f); #else #error Unknown architecture #endif } FORCEINLINE unsigned char RoundFloatToByte(float f) { int nResult = RoundFloatToInt(f); #ifdef Assert Assert( (nResult & ~0xFF) == 0 ); #endif return (unsigned char) nResult; } FORCEINLINE unsigned long RoundFloatToUnsignedLong(float f) { #if defined( _X360 ) #ifdef Assert Assert( IsFPUControlWordSet() ); #endif union { double flResult; int pIntResult[2]; unsigned long pResult[2]; }; flResult = __fctiw( f ); Assert( pIntResult[1] >= 0 ); return pResult[1]; #else // !X360 #ifdef __arm__ return (unsigned long)(f + 0.5f); #elif defined( PLATFORM_WINDOWS_PC64 ) uint nRet = ( uint ) f; if ( nRet & 1 ) { if ( ( f - floor( f ) >= 0.5 ) ) { nRet++; } } else { if ( ( f - floor( f ) > 0.5 ) ) { nRet++; } } return nRet; #else // PLATFORM_WINDOWS_PC64 unsigned char nResult[8]; #if defined( _WIN32 ) __asm { fld f fistp qword ptr nResult } #elif POSIX __asm __volatile__ ( "fistpl %0;": "=m" (nResult): "t" (f) : "st" ); #endif return *((unsigned long*)nResult); #endif // PLATFORM_WINDOWS_PC64 #endif // !X360 } FORCEINLINE bool IsIntegralValue( float flValue, float flTolerance = 0.001f ) { return fabs( RoundFloatToInt( flValue ) - flValue ) < flTolerance; } // Fast, accurate ftol: FORCEINLINE int Float2Int( float a ) { #if defined( _X360 ) union { double flResult; int pResult[2]; }; flResult = __fctiwz( a ); return pResult[1]; #else // !X360 // Rely on compiler to generate CVTTSS2SI on x86 return (int) a; #endif } // Over 15x faster than: (int)floor(value) inline int Floor2Int( float a ) { int RetVal; #if defined( __i386__ ) // Convert to int and back, compare, subtract one if too big __m128 a128 = _mm_set_ss(a); RetVal = _mm_cvtss_si32(a128); __m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal); RetVal -= _mm_comigt_ss( rounded128, a128 ); #else RetVal = static_cast( floor(a) ); #endif return RetVal; } //----------------------------------------------------------------------------- // Fast color conversion from float to unsigned char //----------------------------------------------------------------------------- FORCEINLINE unsigned int FastFToC( float c ) { #if defined( __i386__ ) // IEEE float bit manipulation works for values between [0, 1<<23) union { float f; int i; } convert = { c*255.0f + (float)(1<<23) }; return convert.i & 255; #else // consoles CPUs suffer from load-hit-store penalty return Float2Int( c * 255.0f ); #endif } //----------------------------------------------------------------------------- // Fast conversion from float to integer with magnitude less than 2**22 //----------------------------------------------------------------------------- FORCEINLINE int FastFloatToSmallInt( float c ) { #if defined( __i386__ ) // IEEE float bit manipulation works for values between [-1<<22, 1<<22) union { float f; int i; } convert = { c + (float)(3<<22) }; return (convert.i & ((1<<23)-1)) - (1<<22); #else // consoles CPUs suffer from load-hit-store penalty return Float2Int( c ); #endif } //----------------------------------------------------------------------------- // Purpose: Bound input float to .001 (millisecond) boundary // Input : in - // Output : inline float //----------------------------------------------------------------------------- inline float ClampToMsec( float in ) { int msec = Floor2Int( in * 1000.0f + 0.5f ); return 0.001f * msec; } // Over 15x faster than: (int)ceil(value) inline int Ceil2Int( float a ) { int RetVal; #if defined( __i386__ ) // Convert to int and back, compare, add one if too small __m128 a128 = _mm_load_ss(&a); RetVal = _mm_cvtss_si32(a128); __m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal); RetVal += _mm_comilt_ss( rounded128, a128 ); #else RetVal = static_cast( ceil(a) ); #endif return RetVal; } // Regular signed area of triangle #define TriArea2D( A, B, C ) \ ( 0.5f * ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) ) // This version doesn't premultiply by 0.5f, so it's the area of the rectangle instead #define TriArea2DTimesTwo( A, B, C ) \ ( ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) ) // Get the barycentric coordinates of "pt" in triangle [A,B,C]. inline void GetBarycentricCoords2D( Vector2D const &A, Vector2D const &B, Vector2D const &C, Vector2D const &pt, float bcCoords[3] ) { // Note, because to top and bottom are both x2, the issue washes out in the composite float invTriArea = 1.0f / TriArea2DTimesTwo( A, B, C ); // NOTE: We assume here that the lightmap coordinate vertices go counterclockwise. // If not, TriArea2D() is negated so this works out right. bcCoords[0] = TriArea2DTimesTwo( B, C, pt ) * invTriArea; bcCoords[1] = TriArea2DTimesTwo( C, A, pt ) * invTriArea; bcCoords[2] = TriArea2DTimesTwo( A, B, pt ) * invTriArea; } // Return true of the sphere might touch the box (the sphere is actually treated // like a box itself, so this may return true if the sphere's bounding box touches // a corner of the box but the sphere itself doesn't). inline bool QuickBoxSphereTest( const Vector& vOrigin, float flRadius, const Vector& bbMin, const Vector& bbMax ) { return vOrigin.x - flRadius < bbMax.x && vOrigin.x + flRadius > bbMin.x && vOrigin.y - flRadius < bbMax.y && vOrigin.y + flRadius > bbMin.y && vOrigin.z - flRadius < bbMax.z && vOrigin.z + flRadius > bbMin.z; } // Return true of the boxes intersect (but not if they just touch). inline bool QuickBoxIntersectTest( const Vector& vBox1Min, const Vector& vBox1Max, const Vector& vBox2Min, const Vector& vBox2Max ) { return vBox1Min.x < vBox2Max.x && vBox1Max.x > vBox2Min.x && vBox1Min.y < vBox2Max.y && vBox1Max.y > vBox2Min.y && vBox1Min.z < vBox2Max.z && vBox1Max.z > vBox2Min.z; } extern float GammaToLinearFullRange( float gamma ); extern float LinearToGammaFullRange( float linear ); extern float GammaToLinear( float gamma ); extern float LinearToGamma( float linear ); extern float SrgbGammaToLinear( float flSrgbGammaValue ); extern float SrgbLinearToGamma( float flLinearValue ); extern float X360GammaToLinear( float fl360GammaValue ); extern float X360LinearToGamma( float flLinearValue ); extern float SrgbGammaTo360Gamma( float flSrgbGammaValue ); // linear (0..4) to screen corrected vertex space (0..1?) FORCEINLINE float LinearToVertexLight( float f ) { extern float lineartovertex[4096]; // Gotta clamp before the multiply; could overflow... // assume 0..4 range int i = RoundFloatToInt( f * 1024.f ); // Presumably the comman case will be not to clamp, so check that first: if( (unsigned)i > 4095 ) { if ( i < 0 ) i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream else i = 4095; } return lineartovertex[i]; } FORCEINLINE unsigned char LinearToLightmap( float f ) { extern unsigned char lineartolightmap[4096]; // Gotta clamp before the multiply; could overflow... int i = RoundFloatToInt( f * 1024.f ); // assume 0..4 range // Presumably the comman case will be not to clamp, so check that first: if ( (unsigned)i > 4095 ) { if ( i < 0 ) i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream else i = 4095; } return lineartolightmap[i]; } FORCEINLINE void ColorClamp( Vector& color ) { float maxc = max( color.x, max( color.y, color.z ) ); if ( maxc > 1.0f ) { float ooMax = 1.0f / maxc; color.x *= ooMax; color.y *= ooMax; color.z *= ooMax; } if ( color[0] < 0.f ) color[0] = 0.f; if ( color[1] < 0.f ) color[1] = 0.f; if ( color[2] < 0.f ) color[2] = 0.f; } inline void ColorClampTruncate( Vector& color ) { if (color[0] > 1.0f) color[0] = 1.0f; else if (color[0] < 0.0f) color[0] = 0.0f; if (color[1] > 1.0f) color[1] = 1.0f; else if (color[1] < 0.0f) color[1] = 0.0f; if (color[2] > 1.0f) color[2] = 1.0f; else if (color[2] < 0.0f) color[2] = 0.0f; } // Interpolate a Catmull-Rom spline. // t is a [0,1] value and interpolates a curve between p2 and p3. void Catmull_Rom_Spline( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector &output ); // Interpolate a Catmull-Rom spline. // Returns the tangent of the point at t of the spline void Catmull_Rom_Spline_Tangent( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector &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 ); // 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 ); // Interpolate a Catmull-Rom spline. // Normalize p2->p1 and p3->p4 to be the same length as p2->p3 void Catmull_Rom_Spline_Normalize( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector &output ); // area under the curve [0..t] // Normalize p2->p1 and p3->p4 to be the same length as p2->p3 void Catmull_Rom_Spline_Integral_Normalize( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); // Interpolate a Catmull-Rom spline. // Normalize p2.x->p1.x and p3.x->p4.x to be the same length as p2.x->p3.x void Catmull_Rom_Spline_NormalizeX( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector &output ); // area under the curve [0..t] void Catmull_Rom_Spline_NormalizeX( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); // Interpolate a Hermite spline. // t is a [0,1] value and interpolates a curve between p1 and p2 with the deltas d1 and d2. void Hermite_Spline( const Vector &p1, const Vector &p2, const Vector &d1, const Vector &d2, float t, Vector& output ); float Hermite_Spline( float p1, float p2, float d1, float d2, float t ); // t is a [0,1] value and interpolates a curve between p1 and p2 with the slopes p0->p1 and p1->p2 void Hermite_Spline( const Vector &p0, const Vector &p1, const Vector &p2, float t, Vector& output ); float Hermite_Spline( float p0, float p1, float p2, float t ); void Hermite_SplineBasis( float t, float basis[] ); void Hermite_Spline( const Quaternion &q0, const Quaternion &q1, const Quaternion &q2, float t, Quaternion &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 ); 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 ); // See link at Kochanek_Bartels_Spline for info on the basis matrix used void Cubic_Spline( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); void Cubic_Spline_NormalizeX( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); // See link at Kochanek_Bartels_Spline for info on the basis matrix used void BSpline( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); void BSpline_NormalizeX( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); // See link at Kochanek_Bartels_Spline for info on the basis matrix used void Parabolic_Spline( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); void Parabolic_Spline_NormalizeX( const Vector &p1, const Vector &p2, const Vector &p3, const Vector &p4, float t, Vector& output ); // quintic interpolating polynomial from Perlin. // 0->0, 1->1, smooth-in between with smooth tangents FORCEINLINE float QuinticInterpolatingPolynomial(float t) { // 6t^5-15t^4+10t^3 return t * t * t *( t * ( t* 6.0 - 15.0 ) + 10.0 ); } // given a table of sorted tabulated positions, return the two indices and blendfactor to linear // interpolate. Does a search. Can be used to find the blend value to interpolate between // keyframes. void GetInterpolationData( float const *pKnotPositions, float const *pKnotValues, int nNumValuesinList, int nInterpolationRange, float flPositionToInterpolateAt, bool bWrap, float *pValueA, float *pValueB, float *pInterpolationValue); float RangeCompressor( float flValue, float flMin, float flMax, float flBase ); // Get the minimum distance from vOrigin to the bounding box defined by [mins,maxs] // using voronoi regions. // 0 is returned if the origin is inside the box. float CalcSqrDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point ); void CalcClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut ); void CalcSqrDistAndClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut, float &distSqrOut ); inline float CalcDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point ) { float flDistSqr = CalcSqrDistanceToAABB( mins, maxs, point ); return sqrt(flDistSqr); } // Get the closest point from P to the (infinite) line through vLineA and vLineB and // calculate the shortest distance from P to the line. // If you pass in a value for t, it will tell you the t for (A + (B-A)t) to get the closest point. // If the closest point lies on the segment between A and B, then 0 <= t <= 1. void CalcClosestPointOnLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 ); float CalcDistanceToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 ); float CalcDistanceSqrToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 ); // The same three functions as above, except now the line is closed between A and B. void CalcClosestPointOnLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 ); float CalcDistanceToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 ); float CalcDistanceSqrToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 ); // A function to compute the closes line segment connnection two lines (or false if the lines are parallel, etc.) bool CalcLineToLineIntersectionSegment( const Vector& p1,const Vector& p2,const Vector& p3,const Vector& p4,Vector *s1,Vector *s2, float *t1, float *t2 ); // The above functions in 2D void CalcClosestPointOnLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, Vector2D &vClosest, float *t=0 ); float CalcDistanceToLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 ); float CalcDistanceSqrToLine2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 ); void CalcClosestPointOnLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, Vector2D &vClosest, float *t=0 ); float CalcDistanceToLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 ); float CalcDistanceSqrToLineSegment2D( Vector2D const &P, Vector2D const &vLineA, Vector2D const &vLineB, float *t=0 ); // Init the mathlib void MathLib_Init( float gamma = 2.2f, float texGamma = 2.2f, float brightness = 0.0f, int overbright = 2.0f, bool bAllow3DNow = true, bool bAllowSSE = true, bool bAllowSSE2 = true, bool bAllowMMX = true ); bool MathLib_3DNowEnabled( void ); bool MathLib_MMXEnabled( void ); bool MathLib_SSEEnabled( void ); bool MathLib_SSE2Enabled( void ); float Approach( float target, float value, float speed ); float ApproachAngle( float target, float value, float speed ); float AngleDiff( float destAngle, float srcAngle ); float AngleDistance( float next, float cur ); float AngleNormalize( float angle ); // ensure that 0 <= angle <= 360 float AngleNormalizePositive( float angle ); bool AnglesAreEqual( float a, float b, float tolerance = 0.0f ); void RotationDeltaAxisAngle( const QAngle &srcAngles, const QAngle &destAngles, Vector &deltaAxis, float &deltaAngle ); void RotationDelta( const QAngle &srcAngles, const QAngle &destAngles, QAngle *out ); void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept ); int PolyFromPlane( Vector *outVerts, const Vector& normal, float dist, float fHalfScale = 9000.0f ); int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& normal, float dist, float fOnPlaneEpsilon = 0.1f ); int ClipPolyToPlane_Precise( double *inVerts, int vertCount, double *outVerts, const double *normal, double dist, double fOnPlaneEpsilon = 0.1 ); //----------------------------------------------------------------------------- // Computes a reasonable tangent space for a triangle //----------------------------------------------------------------------------- void CalcTriangleTangentSpace( const Vector &p0, const Vector &p1, const Vector &p2, const Vector2D &t0, const Vector2D &t1, const Vector2D& t2, Vector &sVect, Vector &tVect ); //----------------------------------------------------------------------------- // Transforms a AABB into another space; which will inherently grow the box. //----------------------------------------------------------------------------- void TransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut ); //----------------------------------------------------------------------------- // Uses the inverse transform of in1 //----------------------------------------------------------------------------- void ITransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &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 &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut ); //----------------------------------------------------------------------------- // Uses the inverse transform of in1 //----------------------------------------------------------------------------- void IRotateAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut ); //----------------------------------------------------------------------------- // Transform a plane //----------------------------------------------------------------------------- inline void MatrixTransformPlane( const matrix3x4_t &src, const cplane_t &inPlane, cplane_t &outPlane ) { // What we want to do is the following: // 1) transform the normal into the new space. // 2) Determine a point on the old plane given by plane dist * plane normal // 3) Transform that point into the new space // 4) Plane dist = DotProduct( new normal, new point ) // An optimized version, which works if the plane is orthogonal. // 1) Transform the normal into the new space // 2) Realize that transforming the old plane point into the new space // is given by [ d * n'x + Tx, d * n'y + Ty, d * n'z + Tz ] // where d = old plane dist, n' = transformed normal, Tn = translational component of transform // 3) Compute the new plane dist using the dot product of the normal result of #2 // For a correct result, this should be an inverse-transpose matrix // but that only matters if there are nonuniform scale or skew factors in this matrix. VectorRotate( inPlane.normal, src, outPlane.normal ); outPlane.dist = inPlane.dist * DotProduct( outPlane.normal, outPlane.normal ); outPlane.dist += outPlane.normal.x * src[0][3] + outPlane.normal.y * src[1][3] + outPlane.normal.z * src[2][3]; } inline void MatrixITransformPlane( const matrix3x4_t &src, const cplane_t &inPlane, cplane_t &outPlane ) { // The trick here is that Tn = translational component of transform, // but for an inverse transform, Tn = - R^-1 * T Vector vecTranslation; MatrixGetColumn( src, 3, vecTranslation ); Vector vecInvTranslation; VectorIRotate( vecTranslation, src, vecInvTranslation ); VectorIRotate( inPlane.normal, src, outPlane.normal ); outPlane.dist = inPlane.dist * DotProduct( outPlane.normal, outPlane.normal ); outPlane.dist -= outPlane.normal.x * vecInvTranslation[0] + outPlane.normal.y * vecInvTranslation[1] + outPlane.normal.z * vecInvTranslation[2]; } int CeilPow2( int in ); int FloorPow2( int in ); FORCEINLINE float * UnpackNormal_HEND3N( const unsigned int *pPackedNormal, float *pNormal ) { int temp[3]; temp[0] = ((*pPackedNormal >> 0L) & 0x7ff); if ( temp[0] & 0x400 ) { temp[0] = 2048 - temp[0]; } temp[1] = ((*pPackedNormal >> 11L) & 0x7ff); if ( temp[1] & 0x400 ) { temp[1] = 2048 - temp[1]; } temp[2] = ((*pPackedNormal >> 22L) & 0x3ff); if ( temp[2] & 0x200 ) { temp[2] = 1024 - temp[2]; } pNormal[0] = (float)temp[0] * 1.0f/1023.0f; pNormal[1] = (float)temp[1] * 1.0f/1023.0f; pNormal[2] = (float)temp[2] * 1.0f/511.0f; return pNormal; } FORCEINLINE unsigned int * PackNormal_HEND3N( const float *pNormal, unsigned int *pPackedNormal ) { int temp[3]; temp[0] = Float2Int( pNormal[0] * 1023.0f ); temp[1] = Float2Int( pNormal[1] * 1023.0f ); temp[2] = Float2Int( pNormal[2] * 511.0f ); // the normal is out of bounds, determine the source and fix // clamping would be even more of a slowdown here Assert( temp[0] >= -1023 && temp[0] <= 1023 ); Assert( temp[1] >= -1023 && temp[1] <= 1023 ); Assert( temp[2] >= -511 && temp[2] <= 511 ); *pPackedNormal = ( ( temp[2] & 0x3ff ) << 22L ) | ( ( temp[1] & 0x7ff ) << 11L ) | ( ( temp[0] & 0x7ff ) << 0L ); return pPackedNormal; } FORCEINLINE unsigned int * PackNormal_HEND3N( float nx, float ny, float nz, unsigned int *pPackedNormal ) { int temp[3]; temp[0] = Float2Int( nx * 1023.0f ); temp[1] = Float2Int( ny * 1023.0f ); temp[2] = Float2Int( nz * 511.0f ); // the normal is out of bounds, determine the source and fix // clamping would be even more of a slowdown here Assert( temp[0] >= -1023 && temp[0] <= 1023 ); Assert( temp[1] >= -1023 && temp[1] <= 1023 ); Assert( temp[2] >= -511 && temp[2] <= 511 ); *pPackedNormal = ( ( temp[2] & 0x3ff ) << 22L ) | ( ( temp[1] & 0x7ff ) << 11L ) | ( ( temp[0] & 0x7ff ) << 0L ); return pPackedNormal; } FORCEINLINE float * UnpackNormal_SHORT2( const unsigned int *pPackedNormal, float *pNormal, bool bIsTangent = FALSE ) { // Unpacks from Jason's 2-short format (fills in a 4th binormal-sign (+1/-1) value, if this is a tangent vector) // FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits) short iX = (*pPackedNormal & 0x0000FFFF); short iY = (*pPackedNormal & 0xFFFF0000) >> 16; float zSign = +1; if ( iX < 0 ) { zSign = -1; iX = -iX; } float tSign = +1; if ( iY < 0 ) { tSign = -1; iY = -iY; } pNormal[0] = ( iX - 16384.0f ) / 16384.0f; pNormal[1] = ( iY - 16384.0f ) / 16384.0f; pNormal[2] = zSign*sqrtf( 1.0f - ( pNormal[0]*pNormal[0] + pNormal[1]*pNormal[1] ) ); if ( bIsTangent ) { pNormal[3] = tSign; } return pNormal; } FORCEINLINE unsigned int * PackNormal_SHORT2( float nx, float ny, float nz, unsigned int *pPackedNormal, float binormalSign = +1.0f ) { // Pack a vector (ASSUMED TO BE NORMALIZED) into Jason's 4-byte (SHORT2) format. // This simply reconstructs Z from X & Y. It uses the sign bits of the X & Y coords // to reconstruct the sign of Z and, if this is a tangent vector, the sign of the // binormal (this is needed because tangent/binormal vectors are supposed to follow // UV gradients, but shaders reconstruct the binormal from the tangent and normal // assuming that they form a right-handed basis). nx += 1; // [-1,+1] -> [0,2] ny += 1; nx *= 16384.0f; // [ 0, 2] -> [0,32768] ny *= 16384.0f; // '0' and '32768' values are invalid encodings nx = max( nx, 1.0f ); // Make sure there are no zero values ny = max( ny, 1.0f ); nx = min( nx, 32767.0f ); // Make sure there are no 32768 values ny = min( ny, 32767.0f ); if ( nz < 0.0f ) nx = -nx; // Set the sign bit for z ny *= binormalSign; // Set the sign bit for the binormal (use when encoding a tangent vector) // FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits), also use Float2Int() short sX = (short)nx; // signed short [1,32767] short sY = (short)ny; *pPackedNormal = ( sX & 0x0000FFFF ) | ( sY << 16 ); // NOTE: The mask is necessary (if sX is negative and cast to an int...) return pPackedNormal; } FORCEINLINE unsigned int * PackNormal_SHORT2( const float *pNormal, unsigned int *pPackedNormal, float binormalSign = +1.0f ) { return PackNormal_SHORT2( pNormal[0], pNormal[1], pNormal[2], pPackedNormal, binormalSign ); } // Unpacks a UBYTE4 normal (for a tangent, the result's fourth component receives the binormal 'sign') FORCEINLINE float * UnpackNormal_UBYTE4( const unsigned int *pPackedNormal, float *pNormal, bool bIsTangent = FALSE ) { unsigned char cX, cY; if ( bIsTangent ) { cX = *pPackedNormal >> 16; // Unpack Z cY = *pPackedNormal >> 24; // Unpack W } else { cX = *pPackedNormal >> 0; // Unpack X cY = *pPackedNormal >> 8; // Unpack Y } float x = cX - 128.0f; float y = cY - 128.0f; float z; float zSignBit = x < 0 ? 1.0f : 0.0f; // z and t negative bits (like slt asm instruction) float tSignBit = y < 0 ? 1.0f : 0.0f; float zSign = -( 2*zSignBit - 1 ); // z and t signs float tSign = -( 2*tSignBit - 1 ); x = x*zSign - zSignBit; // 0..127 y = y*tSign - tSignBit; x = x - 64; // -64..63 y = y - 64; float xSignBit = x < 0 ? 1.0f : 0.0f; // x and y negative bits (like slt asm instruction) float ySignBit = y < 0 ? 1.0f : 0.0f; float xSign = -( 2*xSignBit - 1 ); // x and y signs float ySign = -( 2*ySignBit - 1 ); x = ( x*xSign - xSignBit ) / 63.0f; // 0..1 range y = ( y*ySign - ySignBit ) / 63.0f; z = 1.0f - x - y; float oolen = 1.0f / sqrt( x*x + y*y + z*z ); // Normalize and x *= oolen * xSign; // Recover signs y *= oolen * ySign; z *= oolen * zSign; pNormal[0] = x; pNormal[1] = y; pNormal[2] = z; if ( bIsTangent ) { pNormal[3] = tSign; } return pNormal; } ////////////////////////////////////////////////////////////////////////////// // See: http://www.oroboro.com/rafael/docserv.php/index/programming/article/unitv2 // // UBYTE4 encoding, using per-octant projection onto x+y+z=1 // Assume input vector is already unit length // // binormalSign specifies 'sign' of binormal, stored in t sign bit of tangent // (lets the shader know whether norm/tan/bin form a right-handed basis) // // bIsTangent is used to specify which WORD of the output to store the data // The expected usage is to call once with the normal and once with // the tangent and binormal sign flag, bitwise OR'ing the returned DWORDs FORCEINLINE unsigned int * PackNormal_UBYTE4( float nx, float ny, float nz, unsigned int *pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f ) { float xSign = nx < 0.0f ? -1.0f : 1.0f; // -1 or 1 sign float ySign = ny < 0.0f ? -1.0f : 1.0f; float zSign = nz < 0.0f ? -1.0f : 1.0f; float tSign = binormalSign; Assert( ( binormalSign == +1.0f ) || ( binormalSign == -1.0f ) ); float xSignBit = 0.5f*( 1 - xSign ); // [-1,+1] -> [1,0] float ySignBit = 0.5f*( 1 - ySign ); // 1 is negative bit (like slt instruction) float zSignBit = 0.5f*( 1 - zSign ); float tSignBit = 0.5f*( 1 - binormalSign ); float absX = xSign*nx; // 0..1 range (abs) float absY = ySign*ny; float absZ = zSign*nz; float xbits = absX / ( absX + absY + absZ ); // Project onto x+y+z=1 plane float ybits = absY / ( absX + absY + absZ ); xbits *= 63; // 0..63 ybits *= 63; xbits = xbits * xSign - xSignBit; // -64..63 range ybits = ybits * ySign - ySignBit; xbits += 64.0f; // 0..127 range ybits += 64.0f; xbits = xbits * zSign - zSignBit; // Negate based on z and t ybits = ybits * tSign - tSignBit; // -128..127 range xbits += 128.0f; // 0..255 range ybits += 128.0f; unsigned char cX = (unsigned char) xbits; unsigned char cY = (unsigned char) ybits; if ( !bIsTangent ) *pPackedNormal = (cX << 0) | (cY << 8); // xy for normal else *pPackedNormal = (cX << 16) | (cY << 24); // zw for tangent return pPackedNormal; } FORCEINLINE unsigned int * PackNormal_UBYTE4( const float *pNormal, unsigned int *pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f ) { return PackNormal_UBYTE4( pNormal[0], pNormal[1], pNormal[2], pPackedNormal, bIsTangent, binormalSign ); } //----------------------------------------------------------------------------- // Convert RGB to HSV //----------------------------------------------------------------------------- void RGBtoHSV( const Vector &rgb, Vector &hsv ); //----------------------------------------------------------------------------- // Convert HSV to RGB //----------------------------------------------------------------------------- void HSVtoRGB( const Vector &hsv, Vector &rgb ); //----------------------------------------------------------------------------- // Fast version of pow and log //----------------------------------------------------------------------------- float FastLog2(float i); // log2( i ) float FastPow2(float i); // 2^i float FastPow(float a, float b); // a^b float FastPow10( float i ); // 10^i //----------------------------------------------------------------------------- // For testing float equality //----------------------------------------------------------------------------- inline bool CloseEnough( float a, float b, float epsilon = EQUAL_EPSILON ) { return fabs( a - b ) <= epsilon; } inline bool CloseEnough( const Vector &a, const Vector &b, float epsilon = EQUAL_EPSILON ) { return fabs( a.x - b.x ) <= epsilon && fabs( a.y - b.y ) <= epsilon && fabs( a.z - b.z ) <= epsilon; } // Fast compare // maxUlps is the maximum error in terms of Units in the Last Place. This // specifies how big an error we are willing to accept in terms of the value // of the least significant digit of the floating point number’s // representation. maxUlps can also be interpreted in terms of how many // representable floats we are willing to accept between A and B. // This function will allow maxUlps-1 floats between A and B. bool AlmostEqual(float a, float b, int maxUlps = 10); inline bool AlmostEqual( const Vector &a, const Vector &b, int maxUlps = 10) { return AlmostEqual( a.x, b.x, maxUlps ) && AlmostEqual( a.y, b.y, maxUlps ) && AlmostEqual( a.z, b.z, maxUlps ); } #endif // MATH_BASE_H