absence_thelab
diff src/common/n3dmath.h @ 0:1cffe3409164
initial commit
author | John Tsiombikas <nuclear@member.fsf.org> |
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date | Thu, 23 Oct 2014 01:46:07 +0300 |
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1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000 1.2 +++ b/src/common/n3dmath.h Thu Oct 23 01:46:07 2014 +0300 1.3 @@ -0,0 +1,425 @@ 1.4 +#ifndef _N3DMATH_H_ 1.5 +#define _N3DMATH_H_ 1.6 + 1.7 +// - n3dmath.h - 1.8 +// Nuc3D 2 Header File 1.9 +// written by: John Tsiombikas (10 Sep 2002) 1.10 +// Last Modification: 14 April 2002 1.11 +// --------------------------- 1.12 +// Mathematical stuff 1.13 + 1.14 +#include <iostream> 1.15 +#include <cmath> 1.16 + 1.17 +#ifdef NUC3D_VER_DIRECT3D 1.18 +#include "d3d8.h" // Direct3D type definitions (D3DMATRIX) 1.19 +#endif //NUC3D_VER_DIRECT3D 1.20 + 1.21 +// forward declarations 1.22 +class Matrix4x4; 1.23 +class Matrix3x3; 1.24 +class Vector3; 1.25 +class Vector2; 1.26 +class Vector4; 1.27 +class Quaternion; 1.28 + 1.29 +// mathematical constants 1.30 +const float Pi = 3.1415926535897932f; 1.31 +const float TwoPi = 6.2831853071795865f;// Pi * 2.0f; 1.32 +const float HalfPi = 1.5707963267948965f; //Pi * 0.5f; 1.33 +const float QuarterPi = 0.7853981633974483f; //Pi * 0.25f; 1.34 +const float ThreeQuartersPi = 2.3561944901923450f; //QuarterPi * 3.0f; 1.35 + 1.36 +const float XSmallNumber = 1.e-8f; 1.37 +const float SmallNumber = 1.e-4f; 1.38 + 1.39 +// basis vectors 1.40 +#define VECTOR3_I (Vector3(1.0f, 0.0f, 0.0f)) 1.41 +#define VECTOR3_J (Vector3(0.0f, 1.0f, 0.0f)) 1.42 +#define VECTOR3_K (Vector3(0.0f, 0.0f, 1.0f)) 1.43 + 1.44 +#define VECTOR2_I (Vector2(1.0f, 0.0f)) 1.45 +#define VECTOR2_J (Vector2(0.0f, 1.0f)) 1.46 + 1.47 +// angle conversion 1.48 +#define DEGTORAD(a) (Pi * (a) / 180) 1.49 +#define RADTODEG(a) ((a) * 180 / Pi) 1.50 + 1.51 + 1.52 + 1.53 +// ------------- Vector3 class ------------- 1.54 + 1.55 +#ifdef NUC3D_VER_DIRECT3D // if we are using Direct3D version 1.56 + 1.57 +class Vector3 : public D3DVECTOR { 1.58 +public: 1.59 + 1.60 +#else // not D3D 1.61 + 1.62 +class Vector3 { 1.63 +public: 1.64 + float x, y, z; 1.65 + 1.66 +#endif //NUC3D_VER_DIRECT3D 1.67 + 1.68 + Vector3(); 1.69 + Vector3(float x, float y, float z); 1.70 + 1.71 + inline float DotProduct(const Vector3 &vec) const; 1.72 + inline Vector3 CrossProduct(const Vector3 &vec) const; 1.73 + 1.74 + inline Vector3 operator +(const Vector3 &vec) const; 1.75 + inline Vector3 operator -(const Vector3 &vec) const; 1.76 + inline Vector3 operator *(float scalar) const; 1.77 + inline Vector3 operator /(float scalar) const; 1.78 + inline void operator +=(const Vector3 &vec); 1.79 + inline void operator -=(const Vector3 &vec); 1.80 + inline void operator *=(float scalar); 1.81 + inline void operator /=(float scalar); 1.82 + inline Vector3 operator -() const; // unary minus for inversion 1.83 + 1.84 + inline bool operator >(const Vector3 &vec) const; 1.85 + inline bool operator <(const Vector3 &vec) const; 1.86 + inline bool operator >(float len) const; 1.87 + inline bool operator <(float len) const; 1.88 + inline bool operator ==(const Vector3 &vec) const; 1.89 + inline bool operator ==(float len) const; 1.90 + 1.91 + inline operator Vector2() const; 1.92 + inline operator Vector4() const; 1.93 + 1.94 + inline float Length() const; 1.95 + inline float LengthSq() const; 1.96 + 1.97 + inline void Normalize(); 1.98 + inline Vector3 Normalized() const; 1.99 + 1.100 + inline Vector3 Reflection(const Vector3 &normal) const; 1.101 + Vector3 Refraction(const Vector3 &normal, float FromIOR, float ToIOR) const; 1.102 + 1.103 + void Transform(const Matrix4x4 &mat); // transform a vector using a transformation matrix 1.104 + void Transform(const Quaternion &quat); // transform by a quaternion 1.105 + 1.106 + // Direct transformations on the vector 1.107 + void Translate(float x, float y, float z); 1.108 + void Rotate(float x, float y, float z); 1.109 + void Rotate(const Vector3 &axis, float angle); 1.110 + void Scale(float x, float y, float z); 1.111 + 1.112 + float &operator [](int index); 1.113 + 1.114 + friend std::ostream &operator <<(std::ostream &out, const Vector3 &vec); 1.115 +}; 1.116 + 1.117 +inline float DotProduct(const Vector3 &vec1, const Vector3 &vec2); 1.118 +inline Vector3 CrossProduct(const Vector3 &vec1, const Vector3 &vec2); 1.119 + 1.120 +////////////////////// 4-dimensional vectors //////////////////////////// 1.121 +class Vector4 { 1.122 +public: 1.123 + float x, y, z, w; 1.124 + 1.125 + Vector4(); 1.126 + Vector4(const Vector4 &vec); 1.127 + Vector4(const Vector3 &vec); // create from a 3 dimensional vector setting w=1 1.128 + Vector4(float x, float y, float z, float w); 1.129 + 1.130 + float DotProduct(const Vector4 &vec) const; 1.131 + Vector4 CrossProduct(const Vector4 &vec1, const Vector4 &vec2) const; 1.132 + 1.133 + Vector4 operator +(const Vector4 &vec) const; 1.134 + Vector4 operator -(const Vector4 &vec) const; 1.135 + Vector4 operator *(float scalar) const; 1.136 + Vector4 operator /(float scalar) const; 1.137 + void operator +=(const Vector4 &vec); 1.138 + void operator -=(const Vector4 &vec); 1.139 + void operator *=(float scalar); 1.140 + void operator /=(float scalar); 1.141 + Vector4 operator -() const; // unary minus for inversion 1.142 + 1.143 + bool operator >(const Vector4 &vec) const; 1.144 + bool operator <(const Vector4 &vec) const; 1.145 + bool operator >(float len) const; 1.146 + bool operator <(float len) const; 1.147 + bool operator ==(const Vector4 &vec) const; 1.148 + bool operator ==(float len) const; 1.149 + 1.150 + operator Vector3() const; 1.151 + 1.152 + float Length() const; 1.153 + float LengthSq() const; 1.154 + 1.155 + void Normalize(); 1.156 + Vector4 Normalized() const; 1.157 + 1.158 + void Transform(const Matrix4x4 &mat); // transform a vector using a transformation matrix 1.159 + 1.160 + // Direct transformations on the vector 1.161 + void Translate(float x, float y, float z, float w); 1.162 + void Rotate(float x, float y, float z); 1.163 + void Rotate(const Vector3 &axis, float angle); 1.164 + void Scale(float x, float y, float z, float w); 1.165 + 1.166 + float &operator [](int index); 1.167 + 1.168 + friend std::ostream &operator <<(std::ostream &out, const Vector3 &vec); 1.169 +}; 1.170 + 1.171 +float DotProduct(const Vector4 &vec1, const Vector4 &vec2); 1.172 +Vector4 CrossProduct(const Vector4 &vec1, const Vector4 &vec2, const Vector4 &vec3); 1.173 + 1.174 +/////////////////////////// 1.175 + 1.176 +class Vector2 { 1.177 +public: 1.178 + float x, y; 1.179 + 1.180 + Vector2(); 1.181 + Vector2(const Vector2 &vec); 1.182 + Vector2(float x, float y); 1.183 + 1.184 + float DotProduct(const Vector2 &vec) const; 1.185 + //Vector2 CrossProduct(const Vector2 &vec) const; 1.186 + 1.187 + Vector2 operator +(const Vector2 &vec) const; 1.188 + Vector2 operator -(const Vector2 &vec) const; 1.189 + Vector2 operator *(float scalar) const; 1.190 + Vector2 operator /(float scalar) const; 1.191 + void operator +=(const Vector2 &vec); 1.192 + void operator -=(const Vector2 &vec); 1.193 + void operator *=(float scalar); 1.194 + void operator /=(float scalar); 1.195 + Vector2 operator -() const; // unary minus for inversion 1.196 + 1.197 + bool operator >(const Vector2 &vec) const; 1.198 + bool operator <(const Vector2 &vec) const; 1.199 + bool operator >(float len) const; 1.200 + bool operator <(float len) const; 1.201 + bool operator ==(const Vector2 &vec) const; 1.202 + bool operator ==(float len) const; 1.203 + 1.204 + operator Vector3() const; 1.205 + 1.206 + float Length() const; 1.207 + float LengthSq() const; 1.208 + 1.209 + void Normalize(); 1.210 + Vector2 Normalized() const; 1.211 + 1.212 + Vector2 Reflection(const Vector2 &normal) const; 1.213 + Vector2 Refraction(const Vector2 &normal, float FromIOR, float ToIOR) const; 1.214 + 1.215 + void Transform(const Matrix3x3 &mat); // transform a vector using a transformation matrix 1.216 + 1.217 + // Direct transformations on the vector 1.218 + void Translate(float x, float y); 1.219 + void Rotate(float angle); 1.220 + void Scale(float x, float y); 1.221 + 1.222 + float &operator [](int index); 1.223 + 1.224 + friend std::ostream &operator <<(std::ostream &out, const Vector2 &vec); 1.225 +}; 1.226 + 1.227 +float DotProduct(const Vector3 &vec1, const Vector3 &vec2); 1.228 + 1.229 + 1.230 +struct Vector2i { 1.231 + int x, y; 1.232 + 1.233 + Vector2i(int x=0, int y=0) {this->x = x; this->y = y;} 1.234 +}; 1.235 + 1.236 + 1.237 +////////////////// Quaternion /////////////////////// 1.238 + 1.239 +class Quaternion { 1.240 +public: 1.241 + float s; 1.242 + Vector3 v; 1.243 + 1.244 + Quaternion(); 1.245 + Quaternion(float s, const Vector3 &v); 1.246 + Quaternion(float s, float x, float y, float z); 1.247 + 1.248 + Quaternion operator +(const Quaternion &quat) const; 1.249 + Quaternion operator -(const Quaternion &quat) const; 1.250 + Quaternion operator -() const; 1.251 + Quaternion operator *(const Quaternion &quat) const; 1.252 + 1.253 + void operator +=(const Quaternion &quat); 1.254 + void operator -=(const Quaternion &quat); 1.255 + void operator *=(const Quaternion &quat); 1.256 + 1.257 + void ResetIdentity(); 1.258 + 1.259 + Quaternion Conjugate() const; 1.260 + 1.261 + float Length() const; 1.262 + float LengthSq() const; 1.263 + 1.264 + void Normalize(); 1.265 + Quaternion Normalized() const; 1.266 + 1.267 + Quaternion Inverse() const; 1.268 + 1.269 + void SetRotation(const Vector3 &axis, float angle); 1.270 + void Rotate(const Vector3 &axis, float angle); 1.271 + 1.272 + Matrix3x3 GetRotationMatrix() const; 1.273 +}; 1.274 + 1.275 + 1.276 + 1.277 +////////////////////////// Matrices ////////////////////////////// 1.278 + 1.279 +#ifdef NUC3D_VER_DIRECT3D // if we are using Direct3D version 1.280 + 1.281 +class Matrix4x4 : public D3DMATRIX { 1.282 +public: 1.283 + 1.284 +#else // Software or OpenGL version 1.285 + 1.286 +class Matrix4x4 { 1.287 +public: 1.288 + float m[4][4]; 1.289 + 1.290 +#endif //NUC3D_VER_DIRECT3D 1.291 + 1.292 + Matrix4x4(); 1.293 + Matrix4x4(const Matrix4x4 &mat); 1.294 + Matrix4x4(const Matrix3x3 &mat); 1.295 + Matrix4x4( float m00, float m01, float m02, float m03, 1.296 + float m10, float m11, float m12, float m13, 1.297 + float m20, float m21, float m22, float m23, 1.298 + float m30, float m31, float m32, float m33 ); 1.299 + 1.300 + // basic operations on matrices 1.301 + Matrix4x4 operator +(const Matrix4x4 &mat) const; 1.302 + Matrix4x4 operator -(const Matrix4x4 &mat) const; 1.303 + Matrix4x4 operator *(const Matrix4x4 &mat) const; 1.304 + Matrix4x4 operator *(float scalar) const; 1.305 + void operator +=(const Matrix4x4 &mat); 1.306 + void operator -=(const Matrix4x4 &mat); 1.307 + void operator *=(const Matrix4x4 &mat); 1.308 + void operator *=(float scalar); 1.309 + 1.310 + void ResetIdentity(); 1.311 + 1.312 + // concatenate various transformation matrices with our current matrix 1.313 + void Translate(float x, float y, float z); 1.314 + void Rotate(float x, float y, float z); 1.315 + void Rotate(const Vector3 &axis, float rads); 1.316 + void Scale(float x, float y, float z); 1.317 + 1.318 + // set the matrix to a specific transformation matrix 1.319 + void SetTranslation(float x, float y, float z); 1.320 + void SetRotation(float x, float y, float z); 1.321 + void SetRotation(const Vector3 &axis, float angle); 1.322 + void SetScaling(float x, float y, float z); 1.323 + 1.324 + // row and column accessors 1.325 + void SetColumnVector(const Vector4 &vec, int columnindex); 1.326 + void SetRowVector(const Vector4 &vec, int rowindex); 1.327 + Vector4 GetColumnVector(int columnindex) const; 1.328 + Vector4 GetRowVector(int rowindex) const; 1.329 + 1.330 + // other operations on matrices 1.331 + void Transpose(); 1.332 + Matrix4x4 Transposed() const; 1.333 + 1.334 + float Determinant() const; 1.335 + Matrix4x4 Adjoint() const; 1.336 + Matrix4x4 Inverse() const; 1.337 +}; 1.338 + 1.339 + 1.340 +////////////////// Matrix3x3 ////////////////// 1.341 +class Matrix3x3 { 1.342 +public: 1.343 + float m[3][3]; 1.344 + 1.345 + Matrix3x3(); 1.346 + Matrix3x3(const Matrix3x3 &mat); 1.347 + Matrix3x3( float m00, float m01, float m02, 1.348 + float m10, float m11, float m12, 1.349 + float m20, float m21, float m22 ); 1.350 + 1.351 + // basic operations on matrices 1.352 + Matrix3x3 operator +(const Matrix3x3 &mat) const; 1.353 + Matrix3x3 operator -(const Matrix3x3 &mat) const; 1.354 + Matrix3x3 operator *(const Matrix3x3 &mat) const; 1.355 + Matrix3x3 operator *(float scalar) const; 1.356 + void operator +=(const Matrix3x3 &mat); 1.357 + void operator -=(const Matrix3x3 &mat); 1.358 + void operator *=(const Matrix3x3 &mat); 1.359 + void operator *=(float scalar); 1.360 + 1.361 + void ResetIdentity(); 1.362 + 1.363 + // concatenate various transformation matrices with our current matrix 1.364 + void Translate(float x, float y); 1.365 + void Rotate(float angle); 1.366 + void Scale(float x, float y); 1.367 + 1.368 + // set the matrix to a specific transformation matrix 1.369 + void SetTranslation(float x, float y); 1.370 + void SetRotation(float angle); 1.371 + void SetScaling(float x, float y); 1.372 + 1.373 + // row and column accessors 1.374 + void SetColumnVector(const Vector3 &vec, int columnindex); 1.375 + void SetRowVector(const Vector3 &vec, int rowindex); 1.376 + Vector3 GetColumnVector(int columnindex) const; 1.377 + Vector3 GetRowVector(int rowindex) const; 1.378 + 1.379 + // other operations on matrices 1.380 + void Transpose(); 1.381 + Matrix3x3 Transposed() const; 1.382 + 1.383 + void OrthoNormalize(); 1.384 + Matrix3x3 OrthoNormalized(); 1.385 + 1.386 + //float Determinant() const; // NYI 1.387 + //Matrix3x3 Adjoint() const; 1.388 + //Matrix3x3 Inverse() const; 1.389 +}; 1.390 + 1.391 +///////////////// ray ///////////////// 1.392 + 1.393 +class Ray { 1.394 +public: 1.395 + Vector3 Origin; 1.396 + Vector3 Direction; 1.397 + float Energy; 1.398 + float CurrentIOR; 1.399 + 1.400 + Ray(); 1.401 + Ray(const Vector3 &origin, const Vector3 &direction); 1.402 +}; 1.403 + 1.404 +// a coordinate system basis 1.405 +class Base { 1.406 +public: 1.407 + Vector3 i, j, k; 1.408 + 1.409 + Base(); 1.410 + Base(const Vector3 &i, const Vector3 &j, const Vector3 &k); 1.411 + Base(const Vector3 &dir, bool LeftHanded=true); 1.412 + 1.413 + void Rotate(float x, float y, float z); 1.414 + void Rotate(const Vector3 &axis, float angle); 1.415 + void Rotate(const Matrix4x4 &mat); 1.416 + void Rotate(const Quaternion &quat); 1.417 + 1.418 + Matrix3x3 CreateRotationMatrix() const; 1.419 +}; 1.420 + 1.421 + 1.422 + 1.423 +float frand(float range); 1.424 + 1.425 + 1.426 +#include "n3dmath.inl" 1.427 + 1.428 +#endif // _N3DMATH_H_ 1.429 \ No newline at end of file