Dogcows Code - chaz/yoink/blob - src/Moof/Math.hh

   1
   2 /*******************************************************************************
   3
   4  Copyright (c) 2009, Charles McGarvey
   5  All rights reserved.
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  11      this list of conditions and the following disclaimer.
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  13      this  list of conditions and the following disclaimer in the documentation
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  16  THIS  SOFTWARE  IS  PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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  27 *******************************************************************************/
  28
  29 #ifndef _MOOF_MATH_HH_
  30 #define _MOOF_MATH_HH_
  31
  32 /**
  33  * @file Math.hh
  34  * General math-related types and functions.
  35  */
  36
  37 #include <cmath>
  38 #include <cml/cml.h>
  39
  40 #include <SDL/SDL_opengl.h>
  41
  42 #if HAVE_CONFIG_H
  43 #include "config.h"
  44 #endif
  45
  46
  47 #if USE_DOUBLE_PRECISION
  48
  49 typedef GLdouble        GLscalar;
  50 #define GL_SCALAR       GL_DOUBLE
  51 #define SCALAR(D)       (D)
  52
  53 #else
  54
  55 typedef GLfloat         GLscalar;
  56 #define GL_SCALAR       GL_FLOAT
  57 #define SCALAR(F)       (F##f)
  58
  59 #endif
  60
  61
  62 namespace Mf {
  63
  64
  65 typedef GLscalar                                                                Scalar;
  66
  67 typedef cml::vector< Scalar, cml::fixed<2> >    Vector2;
  68 typedef cml::vector< Scalar, cml::fixed<3> >    Vector3;
  69 typedef cml::vector< Scalar, cml::fixed<4> >    Vector4;
  70
  71 typedef cml::matrix< Scalar, cml::fixed<2,2>,
  72                 cml::col_basis, cml::col_major >                Matrix2;
  73 typedef cml::matrix< Scalar, cml::fixed<3,3>,
  74                 cml::col_basis, cml::col_major >                Matrix3;
  75 typedef cml::matrix< Scalar, cml::fixed<4,4>,
  76                 cml::col_basis, cml::col_major >                Matrix4;
  77
  78 typedef cml::quaternion< Scalar, cml::fixed<>, cml::vector_first,
  79                 cml::positive_cross >                                   Quaternion;
  80
  81 typedef cml::constants<Scalar>                                  Constants;
  82
  83
  84 inline Vector3 demote(const Vector4& vec)
  85 {
  86         return Vector3(vec[0], vec[1], vec[2]);
  87 }
  88
  89 inline Vector2 demote(const Vector3& vec)
  90 {
  91         return Vector2(vec[0], vec[1]);
  92 }
  93
  94 inline Vector4 promote(const Vector3& vec, Scalar extra = 1.0)
  95 {
  96         return Vector4(vec[0], vec[1], vec[2], extra);
  97 }
  98
  99 inline Vector3 promote(const Vector2& vec, Scalar extra = 1.0)
 100 {
 101         return Vector3(vec[0], vec[1], extra);
 102 }
 103
 104
 105
 106 const Scalar EPSILON = SCALAR(0.000001);
 107
 108 /**
 109  * Check the equality of scalars with a certain degree of error allowed.
 110  */
 111
 112 inline bool isEqual(Scalar a, Scalar b, Scalar epsilon = EPSILON)
 113 {
 114         return std::abs(a - b) < epsilon;
 115 }
 116
 117
 118
 119 // Here are some generic implementations of a few simple integrators.  To use,
 120 // you need one type representing the state and another containing the
 121 // derivatives of the primary state variables.  The state class must implement
 122 // these methods:
 123 //
 124 // void getDerivative(Derivative_Type& derivative, Scalar absoluteTime);
 125 // void step(const Derivative_Type& derivative, Scalar deltaTime);
 126 //
 127 // Additionally, the derivative class must overload a few operators:
 128 //
 129 // Derivative_Type operator+(const Derivative_Type& other) const
 130 // Derivative_Type operator*(const Derivative_Type& other) const
 131
 132 template<typename S, typename D>
 133 inline D evaluate(const S& state, Scalar t)
 134 {
 135         D derivative;
 136         state.getDerivative(derivative, t);
 137         return derivative;
 138 }
 139
 140 template<typename S, typename D>
 141 inline D evaluate(S state,  Scalar t, Scalar dt, const D& derivative)
 142 {
 143         state.step(derivative, dt);
 144         return evaluate<S,D>(state, t + dt);
 145 }
 146
 147
 148 template<typename S, typename D>
 149 inline void euler(S& state, Scalar t, Scalar dt)
 150 {
 151         D a = evaluate<S,D>(state, t);
 152
 153         state.step(a, dt);
 154 }
 155
 156 template<typename S, typename D>
 157 inline void rk2(S& state, Scalar t, Scalar dt)
 158 {
 159         D a = evaluate<S,D>(state, t);
 160         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 161
 162         state.step(b, dt);
 163 }
 164
 165 template<typename S, typename D>
 166 inline void rk4(S& state, Scalar t, Scalar dt)
 167 {
 168         D a = evaluate<S,D>(state, t);
 169         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 170         D c = evaluate<S,D>(state, t, dt * SCALAR(0.5), b);
 171         D d = evaluate<S,D>(state, t, dt, c);
 172
 173         state.step((a + (b + c) * SCALAR(2.0) + d) * SCALAR(1.0/6.0), dt);
 174 }
 175
 176
 177 } // namespace Mf
 178
 179 #endif // _MOOF_MATH_HH_
 180
 181 /** vim: set ts=4 sw=4 tw=80: *************************************************/
 182