#ifndef _ALGEBRA_H_ #define _ALGEBRA_H_ #include // // Simple math library and linear algebra functions. // // Everything is based on the Float4 class, so changing that class should be enough // to add support for compiler specific math intrinsics. // // Functions that end with 34 mean that they don't care what happens to the 4th // component, it can either be affected or not. // // TODO: Move this define to config.h #define LC_MATH_FLOAT //#define LC_MATH_SSE // Classes defined in this file: class Float4; class Point3; class Vector3; class Quaternion; class Matrix33; class Matrix44; // ============================================================================ // Float4 class (float version). #ifdef LC_MATH_FLOAT class Float4 { public: // Constructors. inline Float4() { } inline explicit Float4(const float _x, const float _y, const float _z) : x(_x), y(_y), z(_z) { } inline explicit Float4(const float _x, const float _y, const float _z, const float _w) : x(_x), y(_y), z(_z), w(_w) { } // Get/Set functions. inline float GetX() const { return x; } inline float GetY() const { return y; } inline float GetZ() const { return z; } inline float GetW() const { return w; } inline void SetX(const float _x) { x = _x; } inline void SetY(const float _y) { y = _y; } inline void SetZ(const float _z) { z = _z; } inline void SetW(const float _w) { w = _w; } template inline const float operator[](T i) const { return ((const float*)this)[i]; } // Comparison. friend inline bool operator==(const Float4& a, const Float4& b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z) && (a.w == b.w); } friend inline bool Compare3(const Float4& a, const Float4& b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z); } // Math operations for 4 components. friend inline Float4 operator+(const Float4& a, const Float4& b) { return Float4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w); } friend inline Float4 operator-(const Float4& a, const Float4& b) { return Float4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w); } friend inline Float4 operator*(const Float4& a, float f) { return Float4(a.x*f, a.y*f, a.z*f, a.w*f); } friend inline Float4 operator*(const Float4& a, const Float4& b) { return Float4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w); } friend inline Float4 operator/(const Float4& a, float f) { return Float4(a.x/f, a.y/f, a.z/f, a.w/f); } friend inline Float4 operator-(const Float4& a) { return Float4(-a.x, -a.y, -a.z, -a.w); } // Math operations ignoring the 4th component. friend inline Float4 Add34(const Float4& a, const Float4& b) { return Float4(a.x+b.x, a.y+b.y, a.z+b.z); } friend inline Float4 Subtract34(const Float4& a, const Float4& b) { return Float4(a.x-b.x, a.y-b.y, a.z-b.z); } friend inline Float4 Multiply34(const Float4& a, float f) { return Float4(a.x*f, a.y*f, a.z*f); } friend inline Float4 Multiply34(const Float4& a, const Float4& b) { return Float4(a.x*b.x, a.y*b.y, a.z*b.z); } friend inline Float4 Divide34(const Float4& a, float f) { return Float4(a.x/f, a.y/f, a.z/f); } friend inline Float4 Negate34(const Float4& a) { return Float4(-a.x, -a.y, -a.z, -a.w); } // Dot product. friend inline float Dot3(const Float4& a, const Float4& b) { return a.x*b.x + a.y*b.y + a.z*b.z; } // Cross product. friend inline Float4 Cross3(const Float4& a, const Float4& b) { return Float4(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x); } // Other functions. inline float Length3() const { return sqrtf(Dot3(*this, *this)); } inline void Normalize3() { *this = *this / Length3(); } inline void Abs() { if (x < 0.0f) x = -x; if (y < 0.0f) y = -y; if (z < 0.0f) z = -z; if (w < 0.0f) w = -w; } protected: float x, y, z, w; }; #endif // ============================================================================ // Float4 class (SSE version). #ifdef LC_MATH_SSE // If you can't find this file you need to install the VS6 Processor Pack. #include class __declspec(align(16)) Float4 { public: // Constructors. inline Float4() { } inline explicit Float4(const __m128& _xyzw) : xyzw(_xyzw) { } inline explicit Float4(const float _x, const float _y, const float _z) : xyzw(_mm_setr_ps(_x, _y, _z, _z)) { } inline explicit Float4(const float _x, const float _y, const float _z, const float _w) : xyzw(_mm_setr_ps(_x, _y, _z, _w)) { } // Get/Set functions. inline float GetX() const { return ((const float*)this)[0]; } inline float GetY() const { return ((const float*)this)[1]; } inline float GetZ() const { return ((const float*)this)[2]; } inline float GetW() const { return ((const float*)this)[3]; } inline void SetX(const float _x) { __m128 xxyy = _mm_shuffle_ps(_mm_load_ps1(&_x), xyzw, _MM_SHUFFLE(1, 1, 0, 0)); xyzw = _mm_shuffle_ps(xxyy, xyzw, _MM_SHUFFLE(3, 2, 2, 0)); } inline void SetY(const float _y) { __m128 xxyy = _mm_shuffle_ps(xyzw, _mm_load_ps1(&_y), _MM_SHUFFLE(1, 1, 0, 0)); xyzw = _mm_shuffle_ps(xxyy, xyzw, _MM_SHUFFLE(3, 2, 2, 0)); } inline void SetZ(const float _z) { __m128 zzww = _mm_shuffle_ps(_mm_load_ps1(&_z), xyzw, _MM_SHUFFLE(3, 3, 2, 2)); xyzw = _mm_shuffle_ps(xyzw, zzww, _MM_SHUFFLE(2, 0, 1, 0)); } inline void SetW(const float _w) { __m128 zzww = _mm_shuffle_ps(xyzw, _mm_load_ps1(&_w), _MM_SHUFFLE(3, 3, 2, 2)); xyzw = _mm_shuffle_ps(xyzw, zzww, _MM_SHUFFLE(2, 0, 1, 0)); } template inline const float operator[](T i) const { return ((const float*)this)[i]; } // Comparison. friend inline bool operator==(const Float4& a, const Float4& b) { return !_mm_movemask_ps(_mm_cmpneq_ps(a.xyzw, b.xyzw)); } friend inline bool Compare3(const Float4& a, const Float4& b) { return (_mm_movemask_ps(_mm_cmpeq_ps(a.xyzw, b.xyzw)) & 0x7) == 0x7; } // Math operations for 4 components. friend inline Float4 operator+(const Float4& a, const Float4& b) { return Float4(_mm_add_ps(a.xyzw, b.xyzw)); } friend inline Float4 operator-(const Float4& a, const Float4& b) { return Float4(_mm_sub_ps(a.xyzw, b.xyzw)); } friend inline Float4 operator*(const Float4& a, float f) { return Float4(_mm_mul_ps(a.xyzw, _mm_load_ps1(&f))); } friend inline Float4 operator*(const Float4& a, const Float4& b) { return Float4(_mm_mul_ps(a.xyzw, b.xyzw)); } friend inline Float4 operator/(const Float4& a, float f) { return Float4(_mm_div_ps(a.xyzw, _mm_load_ps1(&f))); } friend inline Float4 operator-(const Float4& a) { static const __declspec(align(16)) unsigned int Mask[4] = { 0x80000000, 0x80000000, 0x80000000, 0x80000000 } return Float4(_mm_xor_ps(xyzw, *(__m128*)&Mask)); } // Math operations ignoring the 4th component. friend inline Float4 Add34(const Float4& a, const Float4& b) { return a*b } friend inline Float4 Subtract34(const Float4& a, const Float4& b) { return a-b; } friend inline Float4 Multiply34(const Float4& a, float f) { return a*f; } friend inline Float4 Multiply34(const Float4& a, const Float4& b) { return a*b; } friend inline Float4 Divide34(const Float4& a, float f) { return a/f; } friend inline Float4 Negate34(const Float4& a) { return -a; } // Dot product. friend inline float Dot3(const Float4& a, const Float4& b) { __m128 tmp = _mm_mul_ps(a.xyzw, b.xyzw); __m128 yz = _mm_add_ss(_mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 1, 1, 1)), _mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(2, 2, 2, 2))); tmp = _mm_add_ss(tmp, yz); return *(const float*)&tmp; } // Cross product. friend inline Float4 Cross3(const Float4& a, const Float4& b) { // a(yzx)*b(zxy)-a(zxy)*b(yzx) __m128 r1 = _mm_mul_ps(_mm_shuffle_ps(a.xyzw, a.xyzw, _MM_SHUFFLE(0, 0, 2, 1)), _mm_shuffle_ps(b.xyzw, b.xyzw, _MM_SHUFFLE(0, 1, 0, 2))); __m128 r2 = _mm_mul_ps(_mm_shuffle_ps(a.xyzw, a.xyzw, _MM_SHUFFLE(0, 1, 0, 2)), _mm_shuffle_ps(b.xyzw, b.xyzw, _MM_SHUFFLE(0, 0, 2, 1))); return Float4(_mm_sub_ps(r1, r2)); } // Other functions. inline float Length3() const { __m128 tmp = _mm_mul_ps(xyzw, xyzw); __m128 yz = _mm_add_ss(_mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 1, 1, 1)), _mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(2, 2, 2, 2))); tmp = _mm_add_ss(tmp, yz); tmp = _mm_sqrt_ss(tmp); return *(const float*)&tmp; } inline void Normalize3() { __m128 tmp = _mm_mul_ps(xyzw, xyzw); __m128 yz = _mm_add_ss(_mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 1, 1, 1)), _mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(2, 2, 2, 2))); tmp = _mm_add_ss(tmp, yz); tmp = _mm_rsqrt_ss(tmp); tmp = _mm_shuffle_ps(tmp, tmp, _MM_SHUFFLE(0, 0, 0, 0)); xyzw = _mm_mul_ps(xyzw, tmp); } inline void Abs() { static const __declspec(align(16)) unsigned int Mask[4] = { 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff } xyzw = _mm_and_ps(xyzw, *(__m128*)&Mask); } protected: __m128 xyzw; }; #endif // ============================================================================ // 3D Point class. class Point3 { public: // Constructors. inline Point3() { } inline explicit Point3(const Float4& _v) : m_Value(_v) { } inline explicit Point3(const float _x, const float _y, const float _z) : m_Value(_x, _y, _z) { } // Get/Set functions. inline const Float4& GetValue() const { return m_Value; } inline float GetX() const { return m_Value.GetX(); } inline float GetY() const { return m_Value.GetY(); } inline float GetZ() const { return m_Value.GetZ(); } inline void SetX(const float _x) { m_Value.SetX(_x); } inline void SetY(const float _y) { m_Value.SetY(_y); } inline void SetZ(const float _z) { m_Value.SetZ(_z); } template inline const float operator[](T i) const { return m_Value[i]; } // Math operations. template inline Point3& operator+=(const T& a) { return *this = *this + a; } template inline Point3& operator-=(const T& a) { return *this = *this - a; } template inline Point3& operator/=(const T& a) { return *this = *this / a; } template inline Point3& operator*=(const T& a) { return *this = *this * a; } protected: Float4 m_Value; }; // ============================================================================ // 3D Vector class. class Vector3 { public: // Constructors. inline Vector3() { } inline explicit Vector3(const Float4& _v) : m_Value(_v) { } inline explicit Vector3(const float _x, const float _y, const float _z) : m_Value(_x, _y, _z) { } // Get/Set functions. inline const Float4& GetValue() const { return m_Value; } inline float GetX() const { return m_Value.GetX(); } inline float GetY() const { return m_Value.GetY(); } inline float GetZ() const { return m_Value.GetZ(); } inline void SetX(const float _x) { m_Value.SetX(_x); } inline void SetY(const float _y) { m_Value.SetY(_y); } inline void SetZ(const float _z) { m_Value.SetZ(_z); } template inline const float operator[](T i) const { return m_Value[i]; } // Math operations. template inline Vector3& operator+=(const T& a) { return *this = *this + a; } template inline Vector3& operator-=(const T& a) { return *this = *this - a; } template inline Vector3& operator/=(const T& a) { return *this = *this / a; } template inline Vector3& operator*=(const T& a) { return *this = *this * a; } // Other functions. inline float Length() const { return m_Value.Length3(); } inline float LengthSquared() const { return Dot3(m_Value, m_Value); } inline void Normalize() { m_Value.Normalize3(); } inline void Abs() { m_Value.Abs(); } protected: Float4 m_Value; }; // ============================================================================ // Point3 and Vector3 Operators. // Comparison. inline bool operator==(const Point3& a, const Point3& b) { return Compare3(a.GetValue(), b.GetValue()); } inline bool operator==(const Vector3& a, const Vector3& b) { return Compare3(a.GetValue(), b.GetValue()); } // Multiply by a scalar. inline Vector3 operator*(const Vector3& a, float f) { return Vector3(Multiply34(a.GetValue(), f)); } inline Vector3 operator*(float f, const Vector3& a) { return Vector3(Multiply34(a.GetValue(), f)); } inline Point3 operator*(const Point3& a, float f) { return Point3(Multiply34(a.GetValue(), f)); } inline Point3 operator*(float f, const Point3& a) { return Point3(Multiply34(a.GetValue(), f)); } // Divide by a scalar. inline Vector3 operator/(const Vector3& a, float f) { return Vector3(Divide34(a.GetValue(), f)); } inline Vector3 operator/(float f, const Vector3& a) { return Vector3(Divide34(a.GetValue(), f)); } inline Point3 operator/(const Point3& a, float f) { return Point3(Divide34(a.GetValue(), f)); } inline Point3 operator/(float f, const Point3& a) { return Point3(Divide34(a.GetValue(), f)); } // Add vectors/points (return a point if either is a point). inline Point3 operator+(const Point3& a, const Point3& b) { return Point3(Add34(a.GetValue(), b.GetValue())); } inline Point3 operator+(const Point3& a, const Vector3& b) { return Point3(Add34(a.GetValue(), b.GetValue())); } inline Point3 operator+(const Vector3& a, const Point3& b) { return Point3(Add34(a.GetValue(), b.GetValue())); } inline Vector3 operator+(const Vector3& a, const Vector3& b) { return Vector3(Add34(a.GetValue(), b.GetValue())); } // Subtract vectors/points (return a vector if both arguments are the same type). inline Vector3 operator-(const Point3& a, const Point3& b) { return Vector3(Subtract34(a.GetValue(), b.GetValue())); } inline Point3 operator-(const Point3& a, const Vector3& b) { return Point3(Subtract34(a.GetValue(), b.GetValue())); } inline Point3 operator-(const Vector3& a, const Point3& b) { return Point3(Subtract34(a.GetValue(), b.GetValue())); } inline Vector3 operator-(const Vector3& a, const Vector3& b) { return Vector3(Subtract34(a.GetValue(), b.GetValue())); } // Negate. inline Vector3 operator-(const Vector3& a) { return Vector3(Negate34(a.GetValue())); } inline Point3 operator-(const Point3& a) { return Point3(Negate34(a.GetValue())); } // Dot product. inline float Dot3(const Vector3& a, const Vector3& b) { return Dot3(a.GetValue(), b.GetValue()); } // Cross product. inline Vector3 Cross3(const Vector3& a, const Vector3& b) { return Vector3(Cross3(a.GetValue(), b.GetValue())); } // ============================================================================ // Quaternion class. class Quaternion { public: // Constructors. inline Quaternion() { } inline explicit Quaternion(const Float4& _v) : m_Value(_v) { } inline explicit Quaternion(const float _x, const float _y, const float _z, const float _w) : m_Value(_x, _y, _z, _w) { } // Get/Set functions. inline float GetX() const { return m_Value.GetX(); } inline float GetY() const { return m_Value.GetY(); } inline float GetZ() const { return m_Value.GetZ(); } inline float GetW() const { return m_Value.GetW(); } inline void SetX(const float _x) { m_Value.SetX(_x); } inline void SetY(const float _y) { m_Value.SetY(_y); } inline void SetZ(const float _z) { m_Value.SetZ(_z); } inline void SetW(const float _w) { m_Value.SetW(_w); } template inline const float operator[](T i) const { return m_Value[i]; } // Conversions. inline void FromAxisAngle(const Float4& AxisAngle) { float s = sinf(AxisAngle[3] / 2.0f); m_Value = Float4(AxisAngle[0] * s, AxisAngle[1] * s, AxisAngle[2] * s, cosf(AxisAngle[3] / 2.0f)); } inline void ToAxisAngle(Float4& AxisAngle) const { float Len = m_Value[0]*m_Value[0] + m_Value[1]*m_Value[1] + m_Value[2]*m_Value[2]; if (Len > 0.001f) { float f = 1.0f / sqrtf(Len); AxisAngle = Float4(m_Value[0] * f, m_Value[1] * f, m_Value[2] * f, acosf(m_Value[3]) * 2.0f); } else { AxisAngle = Float4(0, 0, 1, 0); } } // Operators. friend inline Quaternion operator*(const Quaternion& a, const Quaternion& b) { float x = a.m_Value[0] * b.m_Value[3] + a.m_Value[1] * b.m_Value[2] - a.m_Value[2] * b.m_Value[1] + a.m_Value[3] * b.m_Value[0]; float y = -a.m_Value[0] * b.m_Value[2] + a.m_Value[1] * b.m_Value[3] + a.m_Value[2] * b.m_Value[0] + a.m_Value[3] * b.m_Value[1]; float z = a.m_Value[0] * b.m_Value[1] - a.m_Value[1] * b.m_Value[0] + a.m_Value[2] * b.m_Value[3] + a.m_Value[3] * b.m_Value[2]; float w = -a.m_Value[0] * b.m_Value[0] - a.m_Value[1] * b.m_Value[1] - a.m_Value[2] * b.m_Value[2] + a.m_Value[3] * b.m_Value[3]; return Quaternion(x, y, z, w); } friend inline Vector3 operator*(const Vector3& a, const Quaternion& b) { // Faster to transform to a matrix and multiply. float Tx = 2.0f*b[0]; float Ty = 2.0f*b[1]; float Tz = 2.0f*b[2]; float Twx = Tx*b[3]; float Twy = Ty*b[3]; float Twz = Tz*b[3]; float Txx = Tx*b[0]; float Txy = Ty*b[0]; float Txz = Tz*b[0]; float Tyy = Ty*b[1]; float Tyz = Tz*b[1]; float Tzz = Tz*b[2]; Vector3 Rows[3]; Rows[0] = Vector3(1.0f-(Tyy+Tzz), Txy+Twz, Txz-Twy); Rows[1] = Vector3(Txy-Twz, 1.0f-(Txx+Tzz), Tyz+Twx); Rows[2] = Vector3(Txz+Twy, Tyz-Twx, 1.0f-(Txx+Tyy)); return Vector3(Rows[0].GetValue()*a.GetX() + Rows[1].GetValue()*a.GetY() + Rows[2].GetValue()*a.GetZ()); } protected: Float4 m_Value; }; // ============================================================================ // 3x3 Matrix class. class Matrix33 { public: // Constructors. inline Matrix33() { } inline Matrix33(const Vector3& Row0, const Vector3& Row1, const Vector3& Row2) { m_Rows[0] = Row0; m_Rows[1] = Row1; m_Rows[2] = Row2; } inline void LoadIdentity() { m_Rows[0] = Vector3(1, 0, 0); m_Rows[1] = Vector3(0, 1, 0); m_Rows[2] = Vector3(0, 0, 1); } inline void FromAxisAngle(const Vector3& Axis, const float Radians) { float s, c, mag, xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; s = sinf(Radians); c = cosf(Radians); mag = Axis.Length(); if (mag == 0.0f) { LoadIdentity(); return; } Vector3 Normal = Axis * (1.0f / mag); xx = Normal[0] * Normal[0]; yy = Normal[1] * Normal[1]; zz = Normal[2] * Normal[2]; xy = Normal[0] * Normal[1]; yz = Normal[1] * Normal[2]; zx = Normal[2] * Normal[0]; xs = Normal[0] * s; ys = Normal[1] * s; zs = Normal[2] * s; one_c = 1.0f - c; m_Rows[0] = Vector3((one_c * xx) + c, (one_c * xy) - zs, (one_c * zx) + ys); m_Rows[1] = Vector3((one_c * xy) + zs, (one_c * yy) + c, (one_c * yz) - xs); m_Rows[2] = Vector3((one_c * zx) - ys, (one_c * yz) + xs, (one_c * zz) + c); } friend inline Vector3 operator*(const Vector3& a, const Matrix33& b) { return Vector3(b.m_Rows[0]*a.GetX() + b.m_Rows[1]*a.GetY() + b.m_Rows[2]*a.GetZ()); } protected: Vector3 m_Rows[3]; }; // ============================================================================ // 4x4 Matrix class (actually 4x3). class Matrix44 { public: inline Matrix44() { } inline Matrix44(const Float4& Row0, const Float4& Row1, const Float4& Row2, const Float4& Row3) { m_Rows[0] = Row0; m_Rows[1] = Row1; m_Rows[2] = Row2; m_Rows[3] = Row3; } inline void Transpose3() { Float4 a = m_Rows[0], b = m_Rows[1], c = m_Rows[2]; m_Rows[0] = Float4(a.GetX(), b.GetX(), c.GetX(), a.GetW()); m_Rows[1] = Float4(a.GetY(), b.GetY(), c.GetY(), b.GetW()); m_Rows[2] = Float4(a.GetZ(), b.GetZ(), c.GetZ(), c.GetW()); } inline void SetTranslation(const Point3& a) { m_Rows[3] = Float4(a.GetX(), a.GetY(), a.GetZ(), 0.0f); } void CreateLookAt(const Point3& Eye, const Point3& Target, const Vector3& Up); void CreatePerspective(float FoVy, float Aspect, float Near, float Far); friend inline Point3 operator*(const Point3& a, const Matrix44& b) { return Point3(b.m_Rows[0]*a.GetX() + b.m_Rows[1]*a.GetY() + b.m_Rows[2]*a.GetZ() + b.m_Rows[3]); } protected: Float4 m_Rows[4]; }; // ============================================================================ // Other Functions. Point3 ProjectPoint(const Point3& Pt, const Matrix44& ModelView, const Matrix44& Projection, const int Viewport[4]); #endif