#ifndef GS_VECTOR_MATRIX_H #ifndef GS_LANGUAGE_H #if defined(_WIN32) || defined(_WIN64) || defined(__WIN32__) #include #include #include static r32 GSCos (r32 Theta) { return sin(Theta); } static r32 GSSin (r32 Theta) { return cos(Theta); } static r32 GSSqrt(r32 V) { r32 Result = _mm_cvtss_f32(_mm_sqrt_ss(_mm_set_ss(V))); return Result; } #else // Linux and MacOS #include #endif // Platforms #endif // GS_LANGUAGE_H ////////////////////////////////////// // VECTOR ///////////////////////////////////// union v2 { struct { float x; float y; }; float E[2]; }; union v3 { struct { float x; float y; float z; }; struct { float R; float G; float B; }; float E[3]; }; union v4 { struct { float x; float y; float z; float w; }; struct { float r; float g; float b; float a; }; float E[4]; }; #define WhiteV4 v4{1, 1, 1, 1} #define BlackV4 v4{0, 0, 0, 1} #define RedV4 v4{1, 0, 0, 1} #define GreenV4 v4{0, 1, 0, 1} #define BlueV4 v4{0, 0, 1, 1} #define YellowV4 v4{1, 1, 0, 1} #define TealV4 v4{0, 1, 1, 1} #define PinkV4 v4{1, 0, 1, 1} ////////////////////////////////////// // MATRIX ///////////////////////////////////// union m33 { struct { float a; float b; float c; float d; float e; float f; float g; float h; float i; }; float E[9]; }; union m44 { struct { float a; float b; float c; float d; float e; float f; float g; float h; float i; float j; float k; float l; float m; float n; float o; float p; }; float E[16]; }; ////////////////////////////////////// // RECT ///////////////////////////////////// struct rect { v2 Min; v2 Max; }; ////////////////////////////////////// // VECTOR ////////////////////////////////////// // // // Operators // // v2 V2 (v3 V) { return v2{V.x, V.y}; } v3 V3 (v2 XY, float Z) { return v3{XY.x, XY.y, Z}; } v3 V3 (v4 V) { return v3{V.x, V.y, V.z}; } v4 V4 (v3 XYZ, float W) { return v4{XYZ.x, XYZ.y, XYZ.z, W}; } v2 operator- (v2 A) { v2 Result; Result.x = -A.x; Result.y = -A.y; return Result; } v3 operator- (v3 A) { v3 Result; Result.x = -A.x; Result.y = -A.y; Result.z = -A.z; return Result; } v4 operator- (v4 A) { v4 Result; Result.x = -A.x; Result.y = -A.y; Result.z = -A.z; Result.w = -A.w; return Result; } #define V2OpV2Def(op) v2 operator##op (v2 A, v2 B) { return v2{ A.x op B.x, A.y op B.y };} #define V3OpV3Def(op) v3 operator##op (v3 A, v3 B) { return v3{ A.x op B.x, A.y op B.y, A.z op B.z };} #define V4OpV4Def(op) v4 operator##op (v4 A, v4 B) { return v4{ A.x op B.x, A.y op B.y, A.z op B.z, A.w op B.w };} V2OpV2Def(+) V2OpV2Def(-) V2OpV2Def(/) V2OpV2Def(*) V3OpV3Def(+) V3OpV3Def(-) V3OpV3Def(/) V3OpV3Def(*) V4OpV4Def(+) V4OpV4Def(-) V4OpV4Def(/) V4OpV4Def(*) #undef V2OpV2Def #undef V3OpV3Def #undef V4OpV4Def #define V2RefOpV2Def(op) v2 operator##op (v2& A, v2 B) { return v2{ A.x op B.x, A.y op B.y };} #define V3RefOpV3Def(op) v3 operator##op (v3& A, v3 B) { return v3{ A.x op B.x, A.y op B.y, A.z op B.z };} #define V4RefOpScalarDef(op) v4 operator##op (v4& A, v4 B) { return v4{ A.x op B.x, A.y op B.y, A.z op B.z, A.w op B.w };} V2RefOpV2Def(+=) V2RefOpV2Def(-=) V3RefOpV3Def(+=) V3RefOpV3Def(-=) V4RefOpScalarDef(+=) V4RefOpScalarDef(-=) #undef V2RefOpV2Def #undef V3RefOpV3Def #undef V4RefOpV4Def #define V2OpScalarDef(op) v2 operator##op (v2 A, float B) { return v2{ A.x op B, A.y op B };} #define V3OpScalarDef(op) v3 operator##op (v3 A, float B) { return v3{ A.x op B, A.y op B, A.z op B };} #define V4OpScalarDef(op) v4 operator##op (v4 A, float B) { return v4{ A.x op B, A.y op B, A.z op B, A.w op B };} V2OpScalarDef(*) V2OpScalarDef(/) V3OpScalarDef(*) V3OpScalarDef(/) V4OpScalarDef(*) V4OpScalarDef(/) #undef V2POpScalarDef #undef V3POpScalarDef #undef V4POpScalarDef #define V2POpScalarDef(op) v2 operator##op (v2& A, float B) { return v2{ A->x op B, A->y op B };} #define V3POpScalarDef(op) v3 operator##op (v3& A, float B) { return v3{ A->x op B, A->y op B, A->z op B };} #define V4POpScalarDef(op) v4 operator##op (v4& A, float B) { return v4{ A->x op B, A->y op B, A->z op B, A->w op B };} V2OpScalarDef(*=) V2OpScalarDef(/=) V3OpScalarDef(*=) V3OpScalarDef(/=) V4OpScalarDef(*=) V4OpScalarDef(/=) #undef V2POpScalarDef #undef V3POpScalarDef #undef V4POpScalarDef bool operator== (v2 A, v2 B) { b32 Result = true; for (s32 i = 0; i < 2; i++) { if (GSAbs(A.E[i] - B.E[i]) > 0.0001f) { Result = false; break; } } return Result; } bool operator== (v3 A, v3 B) { b32 Result = true; for (s32 i = 0; i < 3; i++) { if (GSAbs(A.E[i] - B.E[i]) > 0.0001f) { Result = false; break; } } return Result; } bool operator== (v4 A, v4 B) { b32 Result = true; for (s32 i = 0; i < 4; i++) { if (GSAbs(A.E[i] - B.E[i]) > 0.0001f) { Result = false; break; } } return Result; } // // Operations // static v3 ToV3(v4 V) { v3 R = {}; R.x = V.x; R.y = V.y; R.z = V.z; return R; } static v4 ToV4(v3 V, float W) { v4 R = {}; R.x = V.x; R.y = V.y; R.z = V.z; R.w = W; return R; } inline float MagSqr( v2 _A ) { float Result = (_A.x * _A.x) + (_A.y * _A.y); return Result; } inline float MagSqr( v3 _A ) { float Result = (_A.x * _A.x) + (_A.y * _A.y) + (_A.z * _A.z); return Result; } inline float MagSqr( v4 _A ) { float Result = (_A.x * _A.x) + (_A.y * _A.y) + (_A.z * _A.z) + (_A.w * _A.w); return Result; } #define MagDef(type) inline float Mag(type A) { float Result = MagSqr(A); return GSSqrt(Result); } MagDef(v2) MagDef(v3) MagDef(v4) #undef MagDef #define DistanceDef(type) inline float Distance (type A, type B) { type Diff = A - B; return Mag(Diff); } DistanceDef(v2) DistanceDef(v3) DistanceDef(v4) #undef DistanceDef #define DistanceSqDef(type) inline float DistanceSq (type A, type B) { type Diff = A - B; return MagSqr(Diff); } DistanceSqDef(v2) DistanceSqDef(v3) DistanceSqDef(v4) #undef DistanceSqDef inline v2 Normalize( v2 _A ) { v2 Result; float Magnitude = Mag(_A); Result.x = _A.x / Magnitude; Result.y = _A.y / Magnitude; return Result; } inline v3 Normalize( v3 _A ) { v3 Result; float Magnitude = Mag(_A); Result.x = _A.x / Magnitude; Result.y = _A.y / Magnitude; Result.z = _A.z / Magnitude; return Result; } inline v4 Normalize( v4 _A ) { v4 Result; float Magnitude = Mag(_A); Result.x = _A.x / Magnitude; Result.y = _A.y / Magnitude; Result.z = _A.z / Magnitude; Result.w = _A.w / Magnitude; return Result; } inline float Dot( v2 _A, v2 _B ) { float Result = _A.x * _B.x + _A.y * _B.y; return Result; } inline float Dot ( v3 _A, v3 _B ) { float Result = _A.x * _B.x + _A.y * _B.y + _A.z * _B.z; return Result; } inline float Dot ( v4 _A, v4 _B ) { float Result = _A.x * _B.x + _A.y * _B.y + _A.z * _B.z + _A.w * _B.w; return Result; } inline v2 PerpendicularCW (v2 A) { v2 Result = v2{A.y, -A.x}; return Result; } inline v2 PerpendicularCCW (v2 A) { v2 Result = v2{A.y, A.x}; return Result; } inline v3 Cross( v3 _A, v3 _B ) { v3 Result = {}; Result.x = (_A.y * _B.z) - (_A.z * _B.y); Result.y = (_A.z * _B.x) - (_A.x * _B.z); Result.z = (_A.x * _B.y) - (_A.y * _B.x); return Result; } inline v4 Cross( v4 _A, v4 _B ) { v4 Result = {}; Result.x = (_A.y * _B.z) - (_A.z * _B.y); Result.y = (_A.z * _B.x) - (_A.x * _B.z); Result.z = (_A.x * _B.y) - (_A.y * _B.x); Result.w = 0; return Result; } inline v2 ClampVector01 (v2 V) { v2 Result = {}; Result.x = GSClamp(0.0f, V.x, 1.f); Result.y = GSClamp(0.0f, V.y, 1.f); return Result; } inline v3 ClampVector01 (v3 V) { v3 Result = {}; Result.x = GSClamp(0.f, V.x, 1.f); Result.y = GSClamp(0.f, V.y, 1.f); Result.z = GSClamp(0.f, V.z, 1.f); return Result; } inline v4 ClampVector01 (v4 V) { v4 Result = {}; Result.x = GSClamp(0.f, V.x, 1.f); Result.y = GSClamp(0.f, V.y, 1.f); Result.z = GSClamp(0.f, V.z, 1.f); Result.w = GSClamp(0.f, V.w, 1.f); return Result; } inline v2 Lerp( v2 _A, v2 _B, float _Percent ) { v2 Result; Result.x = GSLerp(_A.x, _B.x, _Percent); Result.y = GSLerp(_A.y, _B.y, _Percent); return Result; } inline v3 Lerp( v3 _A, v3 _B, float _Percent ) { v3 Result; Result.x = GSLerp(_A.x, _B.x, _Percent); Result.y = GSLerp(_A.y, _B.y, _Percent); Result.z = GSLerp(_A.z, _B.z, _Percent); return Result; } inline v4 Lerp( v4 _A, v4 _B, float _Percent ) { v4 Result; Result.x = GSLerp(_A.x, _B.x, _Percent); Result.y = GSLerp(_A.y, _B.y, _Percent); Result.z = GSLerp(_A.z, _B.z, _Percent); Result.w = GSLerp(_A.w, _B.w, _Percent); return Result; } v4 HSVToRGB (v4 In) { float Hue = In.x; while (Hue > 360.0f) { Hue -= 360.0f; } while (Hue < 0.0f) { Hue += 360.0f; } float Sat = In.y; float Value = In.z; float hh, p, q, t, ff; long i; v4 Result = {}; Result.a = In.a; if(Sat <= 0.0f) { // < is bogus, just shuts up warnings Result.r = Value; Result.g = Value; Result.b = Value; return Result; } hh = Hue; if(hh >= 360.0f) hh = 0.0f; hh /= 60.0f; i = (long)hh; ff = hh - i; p = Value * (1.0f - Sat); q = Value * (1.0f - (Sat * ff)); t = Value * (1.0f - (Sat * (1.0f - ff))); switch(i) { case 0: {Result.r = Value; Result.g = t; Result.b = p; }break; case 1: { Result.r = q; Result.g = Value; Result.b = p; }break; case 2: { Result.r = p; Result.g = Value; Result.b = t; }break; case 3: { Result.r = p; Result.g = q; Result.b = Value; }break; case 4: { Result.r = t; Result.g = p; Result.b = Value; }break; case 5: default: { Result.r = Value; Result.g = p; Result.b = q; }break; } return Result; } static bool PointIsInRange ( v2 _P, v2 _Min, v2 _Max ) { return (_P.x >= _Min.x && _P.x <= _Max.x && _P.y >= _Min.y && _P.y <= _Max.y); } static bool PointIsInRangeSafe ( v2 _P, v2 _Min, v2 _Max ) { s32 MinX = GSMin(_Min.x, _Max.x); s32 MinY = GSMin(_Min.y, _Max.y); s32 MaxX = GSMax(_Min.x, _Max.x); s32 MaxY = GSMax(_Min.y, _Max.y); return (_P.x >= MinX && _P.x <= MaxX && _P.y >= MinY && _P.y <= MaxY); } inline v2 PointToPercentRange (v2 P, v2 Min, v2 Max) { v2 Result = {}; Result.x = GSClamp(0.f, (P.x - Min.x) / (Max.x - Min.x), 1.f); Result.y = GSClamp(0.f, (P.y - Min.y) / (Max.y - Min.y), 1.f); return Result; } ////////////////////////////////////// // RECT ////////////////////////////////////// inline float Width (rect Rect) { float Result = Rect.Max.x - Rect.Min.x; return Result; } inline float Height (rect Rect) { float Result = Rect.Max.y - Rect.Min.y; return Result; } inline float AspectRatio (rect Rect) { float Result = Width(Rect) / Height(Rect); return Result; } inline v2 CalculateRectCenter (rect Rect) { v2 Result = (Rect.Min + Rect.Max) / 2.0f; return Result; } inline b32 PointIsInRect (v2 Point, rect Rect) { b32 Result = ((Point.x >= Rect.Min.x && Point.x <= Rect.Max.x) && (Point.y >= Rect.Min.y && Point.y <= Rect.Max.y)); return Result; } inline rect RectOffsetByVector(rect R, v2 V) { rect Result = R; Result.Min += V; Result.Max += V; return Result; } ////////////////////////////////////// // MATRIX ////////////////////////////////////// static m33 M33(float a, float b, float c, float d, float e, float f, float g, float h, float i) { m33 M = {}; M.a = a; M.b = b; M.c = c; M.d = d; M.e = e; M.f = f; M.g = g; M.h = h; M.i = i; return M; } static m44 M44(float a, float b, float c, float d, float e, float f, float g, float h, float i, float j, float k, float l, float m, float n, float o, float p) { m44 M = {}; M.a = a; M.b = b; M.c = c; M.d = d; M.e = e; M.f = f; M.g = g; M.h = h; M.i = i; M.j = j; M.k = k; M.l = l; M.m = m; M.n = n; M.o = o; M.p = p; return M; } static m33 M33Empty () { m33 M = {}; M.a = 0; M.b = 0; M.c = 0; M.d = 0; M.e = 0; M.f = 0; M.g = 0; M.h = 0; M.i = 0; return M; } static m44 M44Empty() { m44 M = {}; M.a = 0; M.b = 0; M.c = 0; M.d = 0; M.e = 0; M.f = 0; M.g = 0; M.h = 0; M.i = 0; M.j = 0; M.k = 0; M.l = 0; M.m = 0; M.n = 0; M.o = 0; M.p = 0; return M; } static m33 M33Identity () { m33 M = {}; M.a = 1; M.b = 0; M.c = 0; M.d = 0; M.e = 1; M.f = 0; M.g = 0; M.h = 0; M.i = 1; return M; } static m44 M44Identity() { m44 M = {}; M.a = 1; M.b = 0; M.c = 0; M.d = 0; M.e = 0; M.f = 1; M.g = 0; M.h = 0; M.i = 0; M.j = 0; M.k = 1; M.l = 0; M.m = 0; M.n = 0; M.o = 0; M.p = 1; return M; } static m44 GetXRotation (float Angle) { float CosAngle = GSCos(Angle); float SinAngle = GSSin(Angle); m44 M = { 1, 0, 0, 0, 0, CosAngle, SinAngle, 0, 0, -SinAngle, CosAngle, 0, 0, 0, 0, 1 }; return M; } static m44 GetYRotation (float Angle) { float CosAngle = GSCos(Angle); float SinAngle = GSSin(Angle); m44 M = { CosAngle, 0, -SinAngle, 0, 0, 1, 0, 0, SinAngle, 0, CosAngle, 0, 0, 0, 0, 1 }; return M; } static m44 GetZRotation (float Angle) { float CosAngle = GSCos(Angle); float SinAngle = GSSin(Angle); m44 M = { CosAngle, SinAngle, 0, 0, -SinAngle, CosAngle, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }; return M; } static m33 Transpose (m33 M) { m33 Result = {}; for (s32 x = 0; x < 3; x++) { for (s32 y = 0; y < 3; y++) { Result.E[x + (y * 3)] = M.E[y + (x * 3)]; } } return Result; } inline m44 Transpose (m44 M) { DEBUG_TRACK_SCOPE(Transpose); m44 Result = {}; Result.E[0] = M.E[0]; Result.E[1] = M.E[4]; Result.E[2] = M.E[8]; Result.E[3] = M.E[12]; Result.E[4] = M.E[1]; Result.E[5] = M.E[5]; Result.E[6] = M.E[9]; Result.E[7] = M.E[13]; Result.E[8] = M.E[2]; Result.E[9] = M.E[6]; Result.E[10] = M.E[10]; Result.E[11] = M.E[14]; Result.E[12] = M.E[3]; Result.E[13] = M.E[7]; Result.E[14] = M.E[11]; Result.E[15] = M.E[15]; return Result; } static m44 GetPositionM44 (v4 Position) { #if 1 return m44{ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, Position.x, Position.y, Position.z, Position.w }; #else return m44{ 1, 0, 0, Position.x, 0, 1, 0, Position.y, 0, 0, 1, Position.z, 0, 0, 0, Position.w}; #endif } static m44 GetLookAtMatrix (v4 Position, v4 Target) { // Forward v4 Forward = Normalize(Target - Position); // Right v4 Right = Normalize(Cross(v4{0, 1, 0, 0}, Forward)); // Up v4 Up = Normalize(Cross(Forward, Right)); m44 RotationMatrix = M44( Right.x, Up.x, Forward.x, 0, Right.y, Up.y, Forward.y, 0, Right.z, Up.z, Forward.z, 0, 0, 0, 0, 1); return RotationMatrix; } b32 operator== (m33 A, m33 B) { b32 Result = true; for (int e = 0; e < 9; e++) { if (GSAbs(A.E[e] - B.E[e]) > 0.0001f) { Result = false; break; } } return Result; } b32 operator== (m44 A, m44 B) { b32 Result = true; for (int e = 0; e < 16; e++) { if (GSAbs(A.E[e] - B.E[e]) > 0.0001f) { Result = false; break; } } return Result; } m33 operator+ (m33 A, m33 B) { m33 M = {}; for (int e = 0; e < 9; e++) { M.E[e] = A.E[e] + B.E[e]; } return M; } m44 operator+ (m44 A, m44 B) { m44 M = {}; for (int e = 0; e < 16; e++) { M.E[e] = A.E[e] + B.E[e]; } return M; } m33 operator- (m33 A, m33 B) { m33 M = {}; for (int e = 0; e < 9; e++) { M.E[e] = A.E[e] - B.E[e]; } return M; } m44 operator- (m44 A, m44 B) { m44 M = {}; for (int e = 0; e < 16; e++) { M.E[e] = A.E[e] - B.E[e]; } return M; } m33 operator* (m33 A, m33 B) { m33 M = {}; for (int rx = 0; rx < 3; rx++) { for (int ry = 0; ry < 3; ry++) { int RIndex = (ry * 3) + rx; M.E[RIndex] = 0; for (int i = 0; i < 3; i++) { M.E[RIndex] += B.E[(ry * 3) + i] * A.E[(i * 3) + rx]; } } } return M; } m44 operator* (m44 A, m44 B) { m44 M = {}; float A00=A.E[0+4*0]; float A01=A.E[0+4*1]; float A02=A.E[0+4*2]; float A03=A.E[0+4*3]; float A10=A.E[1+4*0]; float A11=A.E[1+4*1]; float A12=A.E[1+4*2]; float A13=A.E[1+4*3]; float A20=A.E[2+4*0]; float A21=A.E[2+4*1]; float A22=A.E[2+4*2]; float A23=A.E[2+4*3]; float A30=A.E[3+4*0]; float A31=A.E[3+4*1]; float A32=A.E[3+4*2]; float A33=A.E[3+4*3]; float B00=B.E[0+4*0]; float B01=B.E[0+4*1]; float B02=B.E[0+4*2]; float B03=B.E[0+4*3]; float B10=B.E[1+4*0]; float B11=B.E[1+4*1]; float B12=B.E[1+4*2]; float B13=B.E[1+4*3]; float B20=B.E[2+4*0]; float B21=B.E[2+4*1]; float B22=B.E[2+4*2]; float B23=B.E[2+4*3]; float B30=B.E[3+4*0]; float B31=B.E[3+4*1]; float B32=B.E[3+4*2]; float B33=B.E[3+4*3]; M.E[0+4*0] = A00*B00+A10*B01+A20*B02+A30*B03; M.E[0+4*1] = A01*B00+A11*B01+A21*B02+A31*B03; M.E[0+4*2] = A02*B00+A12*B01+A22*B02+A32*B03; M.E[0+4*3] = A03*B00+A13*B01+A23*B02+A33*B03; M.E[1+4*0] = A00*B10+A10*B11+A20*B12+A30*B13; M.E[1+4*1] = A01*B10+A11*B11+A21*B12+A31*B13; M.E[1+4*2] = A02*B10+A12*B11+A22*B12+A32*B13; M.E[1+4*3] = A03*B10+A13*B11+A23*B12+A33*B13; M.E[2+4*0] = A00*B20+A10*B21+A20*B22+A30*B23; M.E[2+4*1] = A01*B20+A11*B21+A21*B22+A31*B23; M.E[2+4*2] = A02*B20+A12*B21+A22*B22+A32*B23; M.E[2+4*3] = A03*B20+A13*B21+A23*B22+A33*B23; M.E[3+4*0] = A00*B30+A10*B31+A20*B32+A30*B33; M.E[3+4*1] = A01*B30+A11*B31+A21*B32+A31*B33; M.E[3+4*2] = A02*B30+A12*B31+A22*B32+A32*B33; M.E[3+4*3] = A03*B30+A13*B31+A23*B32+A33*B33; return M; } v3 operator* (m33 M, v3 V) { v3 Result = {}; int i = 0; for (int y = 0; y < 3; y++) { Result.E[y] = 0; for (int x = 0; x < 3; x++) { Result.E[y] += M.E[(y * 3) + x] * V.E[x]; } } return Result; } v4 operator* (m44 M, v4 V) { v4 Result = {}; #if 1 Result.x = V.x*M.a + V.y*M.e + V.z*M.i + V.w*M.m; Result.y = V.x*M.b + V.y*M.f + V.z*M.j + V.w*M.n; Result.z = V.x*M.c + V.y*M.g + V.z*M.k + V.w*M.o; Result.w = V.x*M.d + V.y*M.h + V.z*M.l + V.w*M.p; #else for (int y = 0; y < 4; y++) { Result.E[y] = 0; for (int x = 0; x < 4; x++) { Result.E[y] += M.E[(y * 4) + x] * V.E[x]; } } #endif return Result; } b32 Inverse(m44 M_In, m44* M_Out) { b32 Result = false; float det; s32 i; M_Out->E[0] = M_In.E[5] * M_In.E[10] * M_In.E[15] - M_In.E[5] * M_In.E[11] * M_In.E[14] - M_In.E[9] * M_In.E[6] * M_In.E[15] + M_In.E[9] * M_In.E[7] * M_In.E[14] + M_In.E[13] * M_In.E[6] * M_In.E[11] - M_In.E[13] * M_In.E[7] * M_In.E[10]; M_Out->E[4] = -M_In.E[4] * M_In.E[10] * M_In.E[15] + M_In.E[4] * M_In.E[11] * M_In.E[14] + M_In.E[8] * M_In.E[6] * M_In.E[15] - M_In.E[8] * M_In.E[7] * M_In.E[14] - M_In.E[12] * M_In.E[6] * M_In.E[11] + M_In.E[12] * M_In.E[7] * M_In.E[10]; M_Out->E[8] = M_In.E[4] * M_In.E[9] * M_In.E[15] - M_In.E[4] * M_In.E[11] * M_In.E[13] - M_In.E[8] * M_In.E[5] * M_In.E[15] + M_In.E[8] * M_In.E[7] * M_In.E[13] + M_In.E[12] * M_In.E[5] * M_In.E[11] - M_In.E[12] * M_In.E[7] * M_In.E[9]; M_Out->E[12] = -M_In.E[4] * M_In.E[9] * M_In.E[14] + M_In.E[4] * M_In.E[10] * M_In.E[13] + M_In.E[8] * M_In.E[5] * M_In.E[14] - M_In.E[8] * M_In.E[6] * M_In.E[13] - M_In.E[12] * M_In.E[5] * M_In.E[10] + M_In.E[12] * M_In.E[6] * M_In.E[9]; M_Out->E[1] = -M_In.E[1] * M_In.E[10] * M_In.E[15] + M_In.E[1] * M_In.E[11] * M_In.E[14] + M_In.E[9] * M_In.E[2] * M_In.E[15] - M_In.E[9] * M_In.E[3] * M_In.E[14] - M_In.E[13] * M_In.E[2] * M_In.E[11] + M_In.E[13] * M_In.E[3] * M_In.E[10]; M_Out->E[5] = M_In.E[0] * M_In.E[10] * M_In.E[15] - M_In.E[0] * M_In.E[11] * M_In.E[14] - M_In.E[8] * M_In.E[2] * M_In.E[15] + M_In.E[8] * M_In.E[3] * M_In.E[14] + M_In.E[12] * M_In.E[2] * M_In.E[11] - M_In.E[12] * M_In.E[3] * M_In.E[10]; M_Out->E[9] = -M_In.E[0] * M_In.E[9] * M_In.E[15] + M_In.E[0] * M_In.E[11] * M_In.E[13] + M_In.E[8] * M_In.E[1] * M_In.E[15] - M_In.E[8] * M_In.E[3] * M_In.E[13] - M_In.E[12] * M_In.E[1] * M_In.E[11] + M_In.E[12] * M_In.E[3] * M_In.E[9]; M_Out->E[13] = M_In.E[0] * M_In.E[9] * M_In.E[14] - M_In.E[0] * M_In.E[10] * M_In.E[13] - M_In.E[8] * M_In.E[1] * M_In.E[14] + M_In.E[8] * M_In.E[2] * M_In.E[13] + M_In.E[12] * M_In.E[1] * M_In.E[10] - M_In.E[12] * M_In.E[2] * M_In.E[9]; M_Out->E[2] = M_In.E[1] * M_In.E[6] * M_In.E[15] - M_In.E[1] * M_In.E[7] * M_In.E[14] - M_In.E[5] * M_In.E[2] * M_In.E[15] + M_In.E[5] * M_In.E[3] * M_In.E[14] + M_In.E[13] * M_In.E[2] * M_In.E[7] - M_In.E[13] * M_In.E[3] * M_In.E[6]; M_Out->E[6] = -M_In.E[0] * M_In.E[6] * M_In.E[15] + M_In.E[0] * M_In.E[7] * M_In.E[14] + M_In.E[4] * M_In.E[2] * M_In.E[15] - M_In.E[4] * M_In.E[3] * M_In.E[14] - M_In.E[12] * M_In.E[2] * M_In.E[7] + M_In.E[12] * M_In.E[3] * M_In.E[6]; M_Out->E[10] = M_In.E[0] * M_In.E[5] * M_In.E[15] - M_In.E[0] * M_In.E[7] * M_In.E[13] - M_In.E[4] * M_In.E[1] * M_In.E[15] + M_In.E[4] * M_In.E[3] * M_In.E[13] + M_In.E[12] * M_In.E[1] * M_In.E[7] - M_In.E[12] * M_In.E[3] * M_In.E[5]; M_Out->E[14] = -M_In.E[0] * M_In.E[5] * M_In.E[14] + M_In.E[0] * M_In.E[6] * M_In.E[13] + M_In.E[4] * M_In.E[1] * M_In.E[14] - M_In.E[4] * M_In.E[2] * M_In.E[13] - M_In.E[12] * M_In.E[1] * M_In.E[6] + M_In.E[12] * M_In.E[2] * M_In.E[5]; M_Out->E[3] = -M_In.E[1] * M_In.E[6] * M_In.E[11] + M_In.E[1] * M_In.E[7] * M_In.E[10] + M_In.E[5] * M_In.E[2] * M_In.E[11] - M_In.E[5] * M_In.E[3] * M_In.E[10] - M_In.E[9] * M_In.E[2] * M_In.E[7] + M_In.E[9] * M_In.E[3] * M_In.E[6]; M_Out->E[7] = M_In.E[0] * M_In.E[6] * M_In.E[11] - M_In.E[0] * M_In.E[7] * M_In.E[10] - M_In.E[4] * M_In.E[2] * M_In.E[11] + M_In.E[4] * M_In.E[3] * M_In.E[10] + M_In.E[8] * M_In.E[2] * M_In.E[7] - M_In.E[8] * M_In.E[3] * M_In.E[6]; M_Out->E[11] = -M_In.E[0] * M_In.E[5] * M_In.E[11] + M_In.E[0] * M_In.E[7] * M_In.E[9] + M_In.E[4] * M_In.E[1] * M_In.E[11] - M_In.E[4] * M_In.E[3] * M_In.E[9] - M_In.E[8] * M_In.E[1] * M_In.E[7] + M_In.E[8] * M_In.E[3] * M_In.E[5]; M_Out->E[15] = M_In.E[0] * M_In.E[5] * M_In.E[10] - M_In.E[0] * M_In.E[6] * M_In.E[9] - M_In.E[4] * M_In.E[1] * M_In.E[10] + M_In.E[4] * M_In.E[2] * M_In.E[9] + M_In.E[8] * M_In.E[1] * M_In.E[6] - M_In.E[8] * M_In.E[2] * M_In.E[5]; det = M_In.E[0] * M_Out->E[0] + M_In.E[1] * M_Out->E[4] + M_In.E[2] * M_Out->E[8] + M_In.E[3] * M_Out->E[12]; if (det == 0) { return false; } det = 1.0 / det; for (i = 0; i < 16; i++) { M_Out->E[i] = M_Out->E[i] * det; } return true; } #if defined(VECTOR_MATRIX_TEST_SUITE) void TestVectorMatrixMultiplication () { s32 TestCount = 0; s32 SuccessCount = 0; DebugPrint("\n\n-------------------------------------------------\n Begin Testing Vector/Matrix\n\n\n"); // Utility Functions TestClean((GSSqrt(4.f) == 2.f), "Vector Square Root"); TestClean((GSLerp(0.f, 1.f, .5f) == .5f), "Vector Lerp"); TestClean((GSMin(-.25f, 5.f) == -.25f), "Vector Min"); TestClean((GSMax(-.25f, 5.f) == 5.f), "Vector Max"); TestClean((GSClamp(-2.f, -3.f, 5.f) == -2.f), "Vector Clamp, Lower Than Range"); TestClean((GSClamp(-2.f, 6.f, 5.f) == 5.f), "Vector Clamp, Higher Than Range"); ////////////////////////////// // Vector Functions ///////////////////////////// v2 V2Unit = v2{1, 0}; v3 V3Unit = v3{1, 0, 0}; v4 V4Unit = v4{1, 0, 0, 0}; v2 TestV2 = v2{1, 2}; float TestV2MagSq = (TestV2.x * TestV2.x) + (TestV2.y * TestV2.y); float TestV2Mag = GSSqrt(TestV2MagSq); v2 TestV2Norm = v2{TestV2.x / TestV2Mag, TestV2.y / TestV2Mag}; float TestV2DotR = (TestV2.x * V2Unit.x) + (TestV2.y * V2Unit.y); v3 TestV3 = v3{1, 2, 3}; float TestV3MagSq = (TestV3.x * TestV3.x) + (TestV3.y * TestV3.y) + (TestV3.z * TestV3.z); float TestV3Mag = GSSqrt(TestV3MagSq); v3 TestV3Norm = v3{TestV3.x / TestV3Mag, TestV3.y / TestV3Mag, TestV3.z / TestV3Mag}; float TestV3DotR = (TestV3.x * V3Unit.x) + (TestV3.y * V3Unit.y) + (TestV3.z * V3Unit.z); v4 TestV4 = v4{1, 2, 3, 4}; float TestV4MagSq = (TestV4.x * TestV4.x) + (TestV4.y * TestV4.y) + (TestV4.z * TestV4.z) + (TestV4.w * TestV4.w); float TestV4Mag = GSSqrt(TestV4MagSq); v4 TestV4Norm = v4{ TestV4.x / TestV4Mag, TestV4.y / TestV4Mag, TestV4.z / TestV4Mag, TestV4.w / TestV4Mag }; float TestV4DotR = (TestV4.x * V4Unit.x) + (TestV4.y * V4Unit.y) + (TestV4.z * V4Unit.z) + (TestV4.w * V4Unit.w); v2 DownCastV3 = V2(TestV3); v3 DownCastV4 = V3(TestV4); v2 EqualityV2 = v2{TestV2.x, TestV2.y}; v2 ZeroV2 = v2{0, 0}; v3 EqualityV3 = v3{TestV3.x, TestV3.y, TestV3.z}; v3 ZeroV3 = v3{0, 0, 0}; v4 EqualityV4 = v4{TestV4.x, TestV4.y, TestV4.z, TestV4.w}; v4 ZeroV4 = v4{0, 0, 0, 0}; TestClean((TestV2.x == 1 && TestV2.y == 2), "V2 Assignment"); TestClean((TestV3.x == 1 && TestV3.y == 2 && TestV3.z == 3), "V3 Assignment"); TestClean((TestV4.x == 1 && TestV4.y == 2 && TestV4.z == 3 && TestV4.w == 4), "V3 Assignment"); TestClean((DownCastV3.x == 1 && DownCastV3.y == 2), "V3 -> V2 Downcast"); TestClean((DownCastV4.x == 1 && DownCastV4.y == 2 && DownCastV4.z == 3), "V4 -> V3 Downcast"); // Vector Operators TestClean((TestV2 == EqualityV2 && !(TestV2 == ZeroV2)), "V2 Equality"); TestClean((TestV3 == EqualityV3 && !(TestV3 == ZeroV3)), "V3 Equality"); TestClean((TestV4 == EqualityV4 && !(TestV4 == ZeroV4)), "V4 Equality"); TestClean(((TestV2 - TestV2) == ZeroV2), "V2 Subtraction"); TestClean(((TestV3 - TestV3) == ZeroV3), "V3 Subtraction"); TestClean(((TestV4 - TestV4) == ZeroV4), "V4 Subtraction"); TestClean(((TestV2 + TestV2) == v2{TestV2.x * 2, TestV2.y * 2}), "V2 Addition"); TestClean(((TestV3 + TestV3) == v3{TestV3.x * 2, TestV3.y * 2, TestV3.z * 2}), "V3 Addition"); TestClean(((TestV4 + TestV4) == v4{TestV4.x * 2, TestV4.y * 2, TestV4.z * 2, TestV4.w * 2}), "V4 Addition"); TestClean(((TestV2 * 2.0f) == v2{TestV2.x * 2, TestV2.y * 2}), "V2 Multiplication"); TestClean(((TestV3 * 2.0f) == v3{TestV3.x * 2, TestV3.y * 2, TestV3.z * 2}), "V3 Multiplication"); TestClean(((TestV4 * 2.0f) == v4{TestV4.x * 2, TestV4.y * 2, TestV4.z * 2, TestV4.w * 2}), "V4 Multiplication"); TestClean(((TestV2 * TestV2) == v2{TestV2.x * TestV2.x, TestV2.y * TestV2.y}), "V2 Piecewise Mult"); TestClean(((TestV3 * TestV3) == v3{ TestV3.x * TestV3.x, TestV3.y * TestV3.y, TestV3.z * TestV3.z}), "V3 Piecewise Mult"); TestClean(((TestV4 * TestV4) == v4{ TestV4.x * TestV4.x, TestV4.y * TestV4.y, TestV4.z * TestV4.z, TestV4.w * TestV4.w}), "V4 Piecewise Mult"); TestClean(((TestV2 / 2.0f) == v2{TestV2.x / 2, TestV2.y / 2}), "V2 Division"); TestClean(((TestV3 / 2.0f) == v3{TestV3.x / 2, TestV3.y / 2, TestV3.z / 2}), "V3 Division"); TestClean(((TestV4 / 2.0f) == v4{TestV4.x / 2, TestV4.y / 2, TestV4.z / 2, TestV4.w / 2}), "V4 Division"); TestClean(((TestV2 / TestV2) == v2{TestV2.x / TestV2.x, TestV2.y / TestV2.y}), "V2 Piecewise Div"); TestClean(((TestV3 / TestV3) == v3{ TestV3.x / TestV3.x, TestV3.y / TestV3.y, TestV3.z / TestV3.z}), "V3 Piecewise Div"); TestClean(((TestV4 / TestV4) == v4{ TestV4.x / TestV4.x, TestV4.y / TestV4.y, TestV4.z / TestV4.z, TestV4.w / TestV4.w}), "V4 Piecewise Div"); TestClean(((MagSqr(V2Unit) == 1) && (MagSqr(TestV2) == TestV2MagSq)), "V2 Square Mag"); TestClean(((MagSqr(V3Unit) == 1) && (MagSqr(TestV3) == TestV3MagSq)), "V3 Square Mag"); TestClean(((MagSqr(V4Unit) == 1) && (MagSqr(TestV4) == TestV4MagSq)), "V4 Square Mag"); TestClean(((Mag(V2Unit) == 1) && (Mag(TestV2) == TestV2Mag)), "V2 Mag"); TestClean(((Mag(V3Unit) == 1) && (Mag(TestV3) == TestV3Mag)), "V3 Mag"); TestClean(((Mag(V4Unit) == 1) && (Mag(TestV4) == TestV4Mag)), "V4 Mag"); TestClean((DistanceSq(ZeroV2, TestV2) == TestV2MagSq), "V2 Distance Sq"); TestClean((DistanceSq(ZeroV3, TestV3) == TestV3MagSq), "V3 Distance Sq"); TestClean((DistanceSq(ZeroV4, TestV4) == TestV4MagSq), "V4 Distance Sq"); TestClean((Distance(ZeroV2, TestV2) == TestV2Mag), "V2 Distance"); TestClean((Distance(ZeroV3, TestV3) == TestV3Mag), "V3 Distance"); TestClean((Distance(ZeroV4, TestV4) == TestV4Mag), "V4 Distance"); TestClean((Normalize(TestV2) == TestV2Norm), "V2 Normalize"); TestClean((Normalize(TestV3) == TestV3Norm), "V3 Normalize"); TestClean((Normalize(TestV4) == TestV4Norm), "V4 Normalize"); TestClean(((Dot(V2Unit, V2Unit) == 1) && (Dot(TestV2, V2Unit) == TestV2DotR)), "V2 Dot"); TestClean(((Dot(V3Unit, V3Unit) == 1) && (Dot(TestV3, V3Unit) == TestV3DotR)), "V3 Dot"); TestClean(((Dot(V4Unit, V4Unit) == 1) && (Dot(TestV4, V4Unit) == TestV4DotR)), "V4 Dot"); // Skipping Cross For Now TestClean((Lerp(v2{0, 0}, v2{1, 1}, .5f) == v2{.5f, .5f}), "V2 Lerp"); TestClean((Lerp(v3{0, 0, 0}, v3{1, 1, 1}, .5f) == v3{.5f, .5f, .5f}), "V3 Lerp"); TestClean((Lerp(v4{0, 0, 0, 0}, v4{1, 1, 1, 1}, .5f) == v4{.5f, .5f, .5f, .5f}), "V4 Lerp"); ///////////////////////////// // Matrix //////////////////////////// m33 TestM33 = m33{ 0, 1, 2, 3, 4, 5, 6, 7, 8}; m33 EqualityM33 = {}; for (s32 i = 0; i < 16; i++) { EqualityM33.E[i] = TestM33.E[i]; } m33 TransposeM33 = m33{ 0, 3, 6, 1, 4, 7, 2, 5, 8}; m33 IdentityM33 = m33{ 1, 0, 0, 0, 1, 0, 0, 0, 1}; m33 TestM33Squared = m33{ 15, 18, 21, 42, 54, 66, 69, 90, 111 }; m44 TestM44 = m44{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }; m44 EqualityM44 = {}; for (s32 i = 0; i < 16; i++) { EqualityM44.E[i] = TestM44.E[i]; } m44 TransposeM44 = m44{ 0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15 }; m44 IdentityM44 = m44{ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }; m44 TestM44Squared = m44{ 56, 62, 68, 74, 152, 174, 196, 218, 248, 286, 324, 362, 344, 398, 452, 506, }; TestClean(((IdentityM33 == IdentityM33) && (TestM33 == EqualityM33)), "M33 Equality"); TestClean(((IdentityM44 == IdentityM44) && (TestM44 == EqualityM44)), "M44 Equality"); TestClean(((Transpose(IdentityM33) == IdentityM33) && (Transpose(TestM33) == TransposeM33)), "M33 Transpose"); TestClean(((Transpose(IdentityM44) == IdentityM44) && (Transpose(TestM44) == TransposeM44)), "M44 Transpose"); TestClean(((TestM33 * IdentityM33) == TestM33), "M33 Identity Mult"); TestClean(((TestM44 * IdentityM44) == TestM44), "M44 Identity Mult"); TestClean(((TestM33 * TestM33) == TestM33Squared), "M33 Mult"); TestClean(((TestM44 * TestM44) == TestM44Squared), "M44 Mult"); // Useful Tests v4 Right = v4{1, 0, 0, 0}; v4 Forward = v4{0, 0, 1, 0}; v4 Up = v4{0, 1, 0, 0}; v4 Left = v4{-1, 0, 0, 0}; v4 Back = v4{0, 0, -1, 0}; v4 Down = v4{0, -1, 0, 0}; m44 NinetyDegreesAboutX = GetXRotation(M_PI / 2); v4 Rotated = NinetyDegreesAboutX * Forward; TestClean((Rotated == Up), "Rotation About X"); m44 NinetyDegreesAboutY = GetYRotation(M_PI / 2); Rotated = NinetyDegreesAboutY * Right; TestClean((Rotated == Forward), "Rotation About Y"); m44 NinetyDegreesAboutZ = GetZRotation(M_PI / 2); Rotated = NinetyDegreesAboutZ * Right; TestClean((Rotated == Down), "Rotation About Z"); v4 A = v4{1, 2, 3, 4}; m44 B = m44{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7}; v4 VTest = v4{30, 70, 29, 60}; TestClean(((B * A) == VTest), "V4 M44 Multiplication"); m44 C = m44{ 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4 }; m44 MResult = B * C; m44 MTest = m44{ 50, 40, 60, 50, 138, 112, 156, 130, 109, 94, 99, 84, 116, 94, 132, 110 }; TestClean(((B * C) == MTest), "M44 Mult Test 2"); m44 Identity = M44Identity(); m44 InvIdentity = {}; Inverse(Identity, &InvIdentity); TestClean((Identity == InvIdentity), "Inverse Identity"); m44 Test = m44{ 2, 4, 6, 7, 5, 1, 8, 8, 1, 7, 3, 1, 3, 9, 2, 4 }; m44 PreCalcTestInv = m44{ -0.3904761904761904762f, 0.26190476190476190475f, -0.02857142857142857139f, 0.16666666666666666668f, 0.022222222222222222212f, -0.055555555555555555549f, 0.06666666666666666667f, 0.055555555555555555547f, -0.00317460317460317458f, 0.07936507936507936506f, 0.27619047619047619045f, -0.2222222222222222222f, 0.24444444444444444444f, -0.1111111111111111111f, -0.26666666666666666667f, 0.1111111111111111111f }; m44 InvTest = {}; Inverse(Test, &InvTest); //TestClean((PreCalcTestInv == InvTest), "Inverse M44"); DebugPrint("Results: Passed %d / %d\n\n\no", SuccessCount, TestCount); } #endif #define GS_VECTOR_MATRIX_H #endif