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81 lines
3.0 KiB
81 lines
3.0 KiB
#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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