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68 lines
2.8 KiB
68 lines
2.8 KiB
#ifndef Magnum_Math_Geometry_Intersection_h |
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#define Magnum_Math_Geometry_Intersection_h |
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/* |
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Copyright © 2010, 2011, 2012 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::Geometry::Intersection |
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*/ |
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#include "Math/Vector3.h" |
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namespace Magnum { namespace Math { namespace Geometry { |
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/** @brief Functions for computing intersections */ |
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class Intersection { |
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public: |
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Intersection() = delete; |
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/** |
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* @brief %Intersection of a plane and line |
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* @param planePosition Plane position |
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* @param planeNormal Plane normal |
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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 %Intersection point position, NaN if the line lies on the |
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* plane or infinity if the intersection doesn't exist. %Intersection |
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* point can be computed from the position with `a+intersection(...)*b`. |
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* If returned value is in range @f$ [ 0 ; 1 ] @f$, the intersection |
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* is inside the line segment defined by `a` and `b`. |
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* |
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* First the parameter *f* of parametric equation of the plane |
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* is computed from plane normal **n** and plane position: @f[ |
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* \begin{pmatrix} n_0 \\ n_1 \\ n_2 \end{pmatrix} \cdot |
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* \begin{pmatrix} x \\ y \\ z \end{pmatrix} - f = 0 |
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* @f] |
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* Using plane normal **n**, parameter *f* and points **a** and **b**, |
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* value of *t* is computed and returned. @f[ |
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* \begin{array}{rcl} |
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* \Delta \boldsymbol b & = & \boldsymbol b - \boldsymbol a \\ |
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* f & = & \boldsymbol n \cdot (\boldsymbol a + \Delta \boldsymbol b \cdot t) \\ |
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* \Rightarrow t & = & \cfrac{f - \boldsymbol n \cdot \boldsymbol a}{\boldsymbol n \cdot \Delta \boldsymbol b} |
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* \end{array} |
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* @f] |
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*/ |
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template<class T> static T planeLine(const Vector3<T>& planePosition, const Vector3<T>& planeNormal, const Vector3<T>& a, const Vector3<T>& b) { |
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/* Compute f from normal and plane position */ |
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T f = Vector3<T>::dot(planePosition, planeNormal); |
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/* Compute t */ |
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return (f-Vector3<T>::dot(planeNormal, a))/Vector3<T>::dot(planeNormal, b-a); |
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} |
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}; |
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}}} |
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#endif
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