the massive refactoring effort

[chaz/yoink] / src / moof / math.hh

diff --git a/src/moof/math.hh b/src/moof/math.hh
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+
+/*]  Copyright (c) 2009-2010, Charles McGarvey  [**************************
+**]  All rights reserved.
+*
+* vi:ts=4 sw=4 tw=75
+*
+* Distributable under the terms and conditions of the 2-clause BSD license;
+* see the file COPYING for a complete text of the license.
+*
+**************************************************************************/
+
+#ifndef _MOOF_MATH_HH_
+#define _MOOF_MATH_HH_
+
+/**
+ * \file math.hh
+ * General math-related types and functions.
+ */
+
+#include <cmath>
+
+#include <SDL/SDL_opengl.h>
+
+#include <moof/cml/cml.h>
+
+#if HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+
+#if USE_DOUBLE_PRECISION
+typedef GLdouble       GLscalar;
+#define GL_SCALAR      GL_DOUBLE
+#define SCALAR(D)      (D)
+#else
+typedef GLfloat                GLscalar;
+#define GL_SCALAR      GL_FLOAT
+#define SCALAR(F)      (F##f)
+#endif
+
+
+namespace moof {
+
+
+using namespace cml;
+
+
+typedef GLscalar scalar;
+
+typedef vector< scalar, fixed<2> > vector2;
+typedef vector< scalar, fixed<3> > vector3;
+typedef vector< scalar, fixed<4> > vector4;
+
+typedef matrix< scalar, fixed<2,2>, col_basis, col_major > matrix2;
+typedef matrix< scalar, fixed<3,3>, col_basis, col_major > matrix3;
+typedef matrix< scalar, fixed<4,4>, col_basis, col_major > matrix4;
+
+typedef quaternion< scalar, fixed<>, vector_first, positive_cross >    quaternion;
+
+typedef constants<scalar> constants;
+
+
+inline vector3 demote(const vector4& vec)
+{
+       return vector3(vec[0], vec[1], vec[2]);
+}
+
+inline vector2 demote(const vector3& vec)
+{
+       return vector2(vec[0], vec[1]);
+}
+
+inline vector4 promote(const vector3& vec, scalar extra = SCALAR(0.0))
+{
+       return vector4(vec[0], vec[1], vec[2], extra);
+}
+
+inline vector3 promote(const vector2& vec, scalar extra = SCALAR(0.0))
+{
+       return vector3(vec[0], vec[1], extra);
+}
+
+
+const scalar EPSILON = SCALAR(0.000001);
+
+/**
+ * Check the equality of scalars with a certain degree of error allowed.
+ */
+
+inline bool is_equal(scalar a, scalar b, scalar epsilon = EPSILON)
+{
+       return std::abs(a - b) < epsilon;
+}
+
+
+// Here are some generic implementations of a few simple integrators.  To
+// use, you need one type representing the state and another containing the
+// derivatives of the primary state variables.  The state class must
+// implement these methods:
+//
+// void calculate_derivative(Derivative_Type& derivative, scalar absoluteTime);
+// void step(const Derivative_Type& derivative, scalar deltaTime);
+//
+// Additionally, the derivative class must overload a few operators:
+//
+// Derivative_Type operator + (const Derivative_Type& other) const
+// Derivative_Type operator * (const Derivative_Type& other) const
+
+template <class S, class D>
+inline D evaluate(const S& state, scalar t)
+{
+       D derivative;
+       state.calculate_derivative(derivative, t);
+       return derivative;
+}
+
+template <class S, class D>
+inline D evaluate(S state,  scalar t, scalar dt, const D& derivative)
+{
+       state.step(derivative, dt);
+       return evaluate<S,D>(state, t + dt);
+}
+
+
+template <class S, class D>
+inline void euler(S& state, scalar t, scalar dt)
+{
+       D a = evaluate<S,D>(state, t);
+
+       state.step(a, dt);
+}
+
+template <class S, class D>
+inline void rk2(S& state, scalar t, scalar dt)
+{
+       D a = evaluate<S,D>(state, t);
+       D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
+
+       state.step(b, dt);
+}
+
+template <class S, class D>
+inline void rk4(S& state, scalar t, scalar dt)
+{
+       D a = evaluate<S,D>(state, t);
+       D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
+       D c = evaluate<S,D>(state, t, dt * SCALAR(0.5), b);
+       D d = evaluate<S,D>(state, t, dt, c);
+
+       state.step((a + (b + c) * SCALAR(2.0) + d) * SCALAR(1.0/6.0), dt);
+}
+
+
+} // namespace moof
+
+#endif // _MOOF_MATH_HH_
+