/* *  Little Green BATS (2006) * *  Authors: 	Martin Klomp (martin@ai.rug.nl) *		Mart van de Sanden (vdsanden@ai.rug.nl) *		Sander van Dijk (sgdijk@ai.rug.nl) *		A. Bram Neijt (bneijt@gmail.com) *		Matthijs Platje (mplatje@gmail.com) * *  Date: 	September 14, 2006 * *  Website:	http://www.littlegreenbats.nl * *  Comment:	Please feel free to contact us if you have any  *		problems or questions about the code. * * *  License: 	This program is free software; you can redistribute  *		it and/or modify it under the terms of the GNU General *		Public License as published by the Free Software  *		Foundation; either version 2 of the License, or (at  *		your option) any later version. * *   		This program is distributed in the hope that it will *		be useful, but WITHOUT ANY WARRANTY; without even the *		implied warranty of MERCHANTABILITY or FITNESS FOR A *		PARTICULAR PURPOSE.  See the GNU General Public *		License for more details. * *   		You should have received a copy of the GNU General *		Public License along with this program; if not, write *		to the Free Software Foundation, Inc., 59 Temple Place -  *		Suite 330, Boston, MA  02111-1307, USA. * */#ifndef __INC_BATS_MATH_HH_#define __INC_BATS_MATH_HH_#include "vector3.hh"//#include <cmath>namespace bats{  /** Math has a few helpfull mathematical functions	*/  class Math  {  public:  /** Calculates the distance from a given point to the closest point on a given line	*	* To calculate the distance between a point \f$(x, y)\f$ and a line starting at <br>	* point \f$(l_{x1}, l_{y1})\f$ with a normalized vector \f$(l_{x2}, l_{y2})\f$: <br>	*	* First calculate the perpendicular of the normalized vector, resulting in \f$(p_x, p_y)\f$ <br>	* The result is then given by the length of \f$(l_{x2}, l_{y2} * u) - (x, y)\f$ where \f$u\f$ equals	*	* \f$u = (\frac{p_x}{p_y} * (l_{x2} - y) + (x - l_{x1})) / (l_{x2} - (\frac{p_x}{p_y} * l_{y2}))\f$	*	* @param l0 the starting point of the line.    * @param lVect the normalized vector of the line.    * @param point The point.	* @return The distance from the line to the point	*/    static double distanceLinePoint(Vector3D const &l0,				    Vector3D const &lVect,				    Vector3D const &point);  /**    * Calculates the nearest point on a given line to a given point.    *	* First determine wether a perpendicular line between the point and the line exists. <br>	* If there is such a line, this will give the nearest point on the line.	*	* To calculate the distance between a point \f$(x, y)\f$ and a line starting at <br>	* point \f$(l_{x1}, l_{y1})\f$ with a normalized vector \f$(l_{x2}, l_{y2})\f$: <br>	*	* First calculate the perpendicular of the normalized vector, resulting in \f$(p_x, p_y)\f$ <br>	* The result is then given by the length of \f$(l_{x2}, l_{y2} * u) - (x, y)\f$ where \f$u\f$ equals	*	* \f$u = (\frac{p_x}{p_y} * (l_{x2} - y) + (x - l_{x1})) / (l_{x2} - (\frac{p_x}{p_y} * l_{y2}))\f$	*	* When no perpendicular line is posible within the segment, use the closest endpoint of the line.	*    * @param l0 The starting point of the line.    * @param lVect The not normalized line vector.    * @param point The other point.	* @return The point on the line closest to the given point    */    static Vector3D linePointClosestToPoint(Vector3D const &l0,					    Vector3D const &lVect,					    Vector3D const &point);    /**    * Calculates the perpendicular vector to @v.	*	* The perpendicular vector to \f$v = (x, y)\f$ is given by \f$(1.0, -1.0 / \frac{x}{y})\f$	*	* @param v A vector	* @return The perpendicular vector to v    */    static Vector3D calcPerpend(Vector3D const &v);	/** Calculate the point where a given line intersects a given plane	*	* To calculate the point where a line with starting position \f$(l_{x1}, l_{y1}, l_{z1})\f$ and <br>	* direction \f$(l_{x2}, l_{y2}, l_{z2})\f$ intersects a plane \f$(a, b, c, d)\f$:	*	* \f$x = l_{x1} + f * l_{x2}\f$	*    * \f$a * x + b * y + c * z + d = 0\f$ <br>    * \f$a * l_{x1} + a * f * l_{x2} + b * l_{y1} + b * f * l_{y2} + c * l_{z1} + c * f * l_{z2} + d = 0\f$	*    * \f$f * (a * l_{x2} + b * l_{y2} + c * l_{z2}) = - a * l_{x1} - b * l_{y1} - c * l_{z1} - d\f$ <br>	* \f$f = (- a * l_{x1} - b * l_{y1} - c * l_{z1} - d) / (a * l_{x2} + b * l_{y2} + c * l_{z2})\f$	*	* The result is than given by the vector: (position + direction * \f$f\f$)	*	* @param position The starting point of the line	* @param direction The direction of the line	* @param plane The plane to intersect	* @return The position where the line intersects the plane	*/    static Vector3D intersectVectorPlane(Vector3D const& position, Vector3D const& direction, double plane[]);      /*static double trunc(double val, unsigned decimals)    {      return round(val * pow(10, decimals)) / pow(10, decimals);    }*/  };};#endif // __INC_BATS_MATH_HH_