Dogcows Code - chaz/yoink/blob - src/moof/math.hh

   1
   2 /*]  Copyright (c) 2009-2010, Charles McGarvey  [**************************
   3 **]  All rights reserved.
   4 *
   5 * vi:ts=4 sw=4 tw=75
   6 *
   7 * Distributable under the terms and conditions of the 2-clause BSD license;
   8 * see the file COPYING for a complete text of the license.
   9 *
  10 **************************************************************************/
  11
  12 #ifndef _MOOF_MATH_HH_
  13 #define _MOOF_MATH_HH_
  14
  15 /**
  16  * \file math.hh
  17  * General math-related types and functions.
  18  */
  19
  20 #include <cmath>
  21
  22 #include <SDL/SDL_opengl.h>
  23
  24 #include <cml/cml.h>
  25
  26 #if HAVE_CONFIG_H
  27 #include "config.h"
  28 #endif
  29
  30
  31 #if USE_DOUBLE_PRECISION
  32 typedef GLdouble        GLscalar;
  33 #define GL_SCALAR       GL_DOUBLE
  34 #define SCALAR(D)       (D)
  35 #else
  36 typedef GLfloat         GLscalar;
  37 #define GL_SCALAR       GL_FLOAT
  38 #define SCALAR(F)       (F##f)
  39 #endif
  40
  41
  42 namespace moof {
  43
  44
  45 using namespace cml;
  46
  47
  48 typedef GLscalar scalar;
  49
  50 typedef vector< scalar, fixed<2> > vector2;
  51 typedef vector< scalar, fixed<3> > vector3;
  52 typedef vector< scalar, fixed<4> > vector4;
  53
  54 typedef matrix< scalar, fixed<2,2>, col_basis, col_major > matrix2;
  55 typedef matrix< scalar, fixed<3,3>, col_basis, col_major > matrix3;
  56 typedef matrix< scalar, fixed<4,4>, col_basis, col_major > matrix4;
  57
  58 typedef quaternion< scalar, fixed<>, vector_first, positive_cross >     quaternion;
  59
  60 typedef constants<scalar> constants;
  61
  62
  63 inline vector3 demote(const vector4& vec)
  64 {
  65         return vector3(vec[0], vec[1], vec[2]);
  66 }
  67
  68 inline vector2 demote(const vector3& vec)
  69 {
  70         return vector2(vec[0], vec[1]);
  71 }
  72
  73 inline vector4 promote(const vector3& vec, scalar extra = SCALAR(0.0))
  74 {
  75         return vector4(vec[0], vec[1], vec[2], extra);
  76 }
  77
  78 inline vector3 promote(const vector2& vec, scalar extra = SCALAR(0.0))
  79 {
  80         return vector3(vec[0], vec[1], extra);
  81 }
  82
  83
  84 const scalar EPSILON = SCALAR(0.000001);
  85
  86 /**
  87  * Check the equality of scalars with a certain degree of error allowed.
  88  */
  89
  90 inline bool is_equal(scalar a, scalar b, scalar epsilon = EPSILON)
  91 {
  92         return std::abs(a - b) < epsilon;
  93 }
  94
  95
  96 // Here are some generic implementations of a few simple integrators.  To
  97 // use, you need one type representing the state and another containing the
  98 // derivatives of the primary state variables.  The state class must
  99 // implement these methods:
 100 //
 101 // void calculate_derivative(Derivative_Type& derivative, scalar absoluteTime);
 102 // void step(const Derivative_Type& derivative, scalar deltaTime);
 103 //
 104 // Additionally, the derivative class must overload a few operators:
 105 //
 106 // Derivative_Type operator + (const Derivative_Type& other) const
 107 // Derivative_Type operator * (const Derivative_Type& other) const
 108
 109 template <class S, class D>
 110 inline D evaluate(const S& state, scalar t)
 111 {
 112         D derivative;
 113         state.calculate_derivative(derivative, t);
 114         return derivative;
 115 }
 116
 117 template <class S, class D>
 118 inline D evaluate(S state,  scalar t, scalar dt, const D& derivative)
 119 {
 120         state.step(derivative, dt);
 121         return evaluate<S,D>(state, t + dt);
 122 }
 123
 124
 125 template <class S, class D>
 126 inline void euler(S& state, scalar t, scalar dt)
 127 {
 128         D a = evaluate<S,D>(state, t);
 129
 130         state.step(a, dt);
 131 }
 132
 133 template <class S, class D>
 134 inline void rk2(S& state, scalar t, scalar dt)
 135 {
 136         D a = evaluate<S,D>(state, t);
 137         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 138
 139         state.step(b, dt);
 140 }
 141
 142 template <class S, class D>
 143 inline void rk4(S& state, scalar t, scalar dt)
 144 {
 145         D a = evaluate<S,D>(state, t);
 146         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 147         D c = evaluate<S,D>(state, t, dt * SCALAR(0.5), b);
 148         D d = evaluate<S,D>(state, t, dt, c);
 149
 150         state.step((a + (b + c) * SCALAR(2.0) + d) * SCALAR(1.0/6.0), dt);
 151 }
 152
 153
 154 } // namespace moof
 155
 156 #endif // _MOOF_MATH_HH_
 157