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

   1
   2 /*******************************************************************************
   3
   4  Copyright (c) 2009, Charles McGarvey
   5  All rights reserved.
   6
   7  Redistribution   and   use  in  source  and  binary  forms,  with  or  without
   8  modification, are permitted provided that the following conditions are met:
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  10    * Redistributions  of  source  code  must retain the above copyright notice,
  11      this list of conditions and the following disclaimer.
  12    * Redistributions  in binary form must reproduce the above copyright notice,
  13      this  list of conditions and the following disclaimer in the documentation
  14      and/or other materials provided with the distribution.
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  16  THIS  SOFTWARE  IS  PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  17  AND  ANY  EXPRESS  OR  IMPLIED  WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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  19  DISCLAIMED.  IN  NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
  20  FOR  ANY  DIRECT,  INDIRECT,  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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  22  SERVICES;  LOSS  OF  USE,  DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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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 <Moof/OpenGL.hh>               // GLscalar
  41
  42
  43 namespace Mf {
  44
  45
  46 typedef GLscalar                                                                Scalar;
  47
  48 typedef cml::vector< Scalar, cml::fixed<2> >    Vector2;
  49 typedef cml::vector< Scalar, cml::fixed<3> >    Vector3;
  50 typedef cml::vector< Scalar, cml::fixed<4> >    Vector4;
  51
  52 typedef cml::matrix< Scalar, cml::fixed<2,2>,
  53                 cml::col_basis, cml::col_major >                Matrix2;
  54 typedef cml::matrix< Scalar, cml::fixed<3,3>,
  55                 cml::col_basis, cml::col_major >                Matrix3;
  56 typedef cml::matrix< Scalar, cml::fixed<4,4>,
  57                 cml::col_basis, cml::col_major >                Matrix4;
  58
  59 typedef cml::quaternion< Scalar, cml::fixed<>, cml::vector_first,
  60                 cml::positive_cross >                                   Quaternion;
  61
  62 typedef cml::constants<Scalar>                                  Constants;
  63
  64
  65 inline Vector3 demote(const Vector4& vec)
  66 {
  67         return Vector3(vec[0], vec[1], vec[2]);
  68 }
  69
  70 inline Vector2 demote(const Vector3& vec)
  71 {
  72         return Vector2(vec[0], vec[1]);
  73 }
  74
  75 inline Vector4 promote(const Vector3& vec, Scalar extra = 1.0)
  76 {
  77         return Vector4(vec[0], vec[1], vec[2], extra);
  78 }
  79
  80 inline Vector3 promote(const Vector2& vec, Scalar extra = 1.0)
  81 {
  82         return Vector3(vec[0], vec[1], extra);
  83 }
  84
  85
  86
  87 const Scalar EPSILON = SCALAR(0.000001);
  88
  89 /**
  90  * Check the equality of scalars with a certain degree of error allowed.
  91  */
  92
  93 inline bool isEqual(Scalar a, Scalar b, Scalar epsilon = EPSILON)
  94 {
  95         return std::abs(a - b) < epsilon;
  96 }
  97
  98
  99
 100 // Here are some generic implementations of a few simple integrators.  To use,
 101 // you need one type representing the state and another containing the
 102 // derivatives of the primary state variables.  The state class must implement
 103 // these methods:
 104 //
 105 // void getDerivative(Derivative_Type& derivative, Scalar absoluteTime);
 106 // void step(const Derivative_Type& derivative, Scalar deltaTime);
 107 //
 108 // Additionally, the derivative class must overload a few operators:
 109 //
 110 // Derivative_Type operator+(const Derivative_Type& other) const
 111 // Derivative_Type operator*(const Derivative_Type& other) const
 112
 113 template<typename S, typename D>
 114 inline D evaluate(const S& state, Scalar t)
 115 {
 116         D derivative;
 117         state.getDerivative(derivative, t);
 118         return derivative;
 119 }
 120
 121 template<typename S, typename D>
 122 inline D evaluate(S state,  Scalar t, Scalar dt, const D& derivative)
 123 {
 124         state.step(derivative, dt);
 125         return evaluate<S,D>(state, t + dt);
 126 }
 127
 128
 129 template<typename S, typename D>
 130 inline void euler(S& state, Scalar t, Scalar dt)
 131 {
 132         D a = evaluate<S,D>(state, t);
 133
 134         state.step(a, dt);
 135 }
 136
 137 template<typename S, typename D>
 138 inline void rk2(S& state, Scalar t, Scalar dt)
 139 {
 140         D a = evaluate<S,D>(state, t);
 141         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 142
 143         state.step(b, dt);
 144 }
 145
 146 template<typename S, typename D>
 147 inline void rk4(S& state, Scalar t, Scalar dt)
 148 {
 149         D a = evaluate<S,D>(state, t);
 150         D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
 151         D c = evaluate<S,D>(state, t, dt * SCALAR(0.5), b);
 152         D d = evaluate<S,D>(state, t, dt, c);
 153
 154         state.step((a + (b + c) * SCALAR(2.0) + d) * SCALAR(1.0/6.0), dt);
 155 }
 156
 157
 158 } // namespace Mf
 159
 160 #endif // _MOOF_MATH_HH_
 161
 162 /** vim: set ts=4 sw=4 tw=80: *************************************************/
 163