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82 lines
3.0 KiB
82 lines
3.0 KiB
15 years ago
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#ifndef Magnum_Math_GeometryUtils_h
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#define Magnum_Math_GeometryUtils_h
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/*
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Copyright © 2010, 2011 Vladimír Vondruš <mosra@centrum.cz>
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This file is part of Magnum.
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Magnum is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License version 3
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only, as published by the Free Software Foundation.
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Magnum is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License version 3 for more details.
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*/
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/** @file
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* @brief Class Magnum::Math::GeometryUtils
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*/
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#include "Matrix3.h"
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namespace Magnum { namespace Math {
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/**
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@brief Geometry utils
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*/
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template<class T> class GeometryUtils {
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public:
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/**
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* @brief Intersection of a plane and line
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* @param plane Plane defined by three points
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* @param a Starting point of the line
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* @param b Ending point of the line
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* @return Value, NaN if the line lies on the plane or infinity if the
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* intersection doesn't exist. Intersection point can be then computed
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* with <tt>a+intersection(...)*b</tt>. If returned value is in range
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* @f$ [ 0 ; 1 ] @f$, the intersection is inside the line segment
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* defined by @c a and @c b.
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*
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* First the parametric equation of the plane is computed,
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* @f$ cx + dy + ez = f @f$. Parameters @f$ (c, d, e) @f$ are cross
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* product of two vectors defining the plane, parameter @f$ f @f$ is
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* computed using @f$ (c, d, e) @f$ and one of points defining the
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* plane.
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* @f[
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* \begin{array}{lcl}
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* (g, h, i) & = & plane \\
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* (c, d, e) & = & (h - g) \times (i - g) \\
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* f & = & (c, d, e) \cdot g
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* \end{array}
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* @f]
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*
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* Using parametric equation and points @f$ a @f$ and @f$ b @f$, value
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* of @f$ t @f$ is computed and returned.
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* @f[
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* \begin{array}{lcl}
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* \Delta b & = & b - a \\
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* f & = & (c, d, e) \cdot (a + \Delta b \cdot t) \\
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* t & = & \frac{f - (c, d, e) \cdot a}
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* {(c, d, e) \cdot \Delta b}
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* \end{array}
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* @f]
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*/
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static T intersection(const Matrix3<T>& plane, const Vector3<T>& a, const Vector3<T>& b) {
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/* Cross product of two vectors defining the plane */
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Vector3<T> crossProduct = Vector3<T>::cross(plane.at(1)-plane.at(0), plane.at(2)-plane.at(0));
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/* Compute f with cross product and one of the points defining the
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plane */
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T f = crossProduct*plane.at(0);
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/* Compute t */
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return (f-crossProduct*a)/(crossProduct*(b-a));
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}
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};
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}}
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#endif
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