MathTools.h

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// *****************************************************************
// Filename:    MathTools.h
// Copyright:   Kai Welke, Chair Prof. Dillmann (IAIM),
//              Institute for Computer Science and Engineering (CSE),
//              University of Karlsruhe. All rights reserved.
// Author:      Kai Welke
// Date:        12.06.2007
// *****************************************************************
 
#pragma once
 
// *****************************************************************
// defines
// *****************************************************************
#include <math.h>
#ifndef M_PI
#define M_PI 3.141592653589793
#endif
 
// *****************************************************************
// includes
// *****************************************************************
#include <Eigen/Core>
#include <Eigen/Geometry>
 
#include "Structs.h"
 
// *****************************************************************
// class MathTools
// *****************************************************************
class MathTools
{
public:
    // transformation of coordinates and paths
    static TTransform determinePathTransformation(TPath* p1, TPath* p2);
    static TPath* transformPath(TTransform transform, TPath* pPath);
    static TPath* inverseTransformPath(TTransform transform, TPath* pPath);
 
    static TTransform determineTransformation(TSphereCoord start1,
                                              TSphereCoord start2,
                                              TSphereCoord end1,
                                              TSphereCoord end2);
    static TSphereCoord transform(TSphereCoord sc, TTransform transform);
    static TSphereCoord inverseTransform(TSphereCoord sc, TTransform transform);
 
    static void determineTransformationAlphaBeta(TSphereCoord sc1,
                                                 TSphereCoord sc2,
                                                 float& fAlpha,
                                                 float& fBeta,
                                                 Eigen::Vector3d& betaAxis);
    static TSphereCoord
    transformAlphaBeta(TSphereCoord sc, float fAlpha, float fBeta, Eigen::Vector3d betaAxis);
    static TSphereCoord
    inverseTransformAlphaBeta(TSphereCoord sc, float fAlpha, float fBeta, Eigen::Vector3d betaAxis);
 
    // calculations on sphere coordimates
    static float
    CalculateCrossProductFromDifference(TSphereCoord p1, TSphereCoord p2, TSphereCoord p3);
    static float getDistanceOnArc(TSphereCoord p1, TSphereCoord p2);
    static float getDistance(TSphereCoord p1, TSphereCoord p2, float fRadius);
 
    // extended 2d math
    static bool IntersectLines(Eigen::Vector2d p1,
                               Eigen::Vector2d m1,
                               Eigen::Vector2d p2,
                               Eigen::Vector2d m2,
                               Eigen::Vector2d& res);
 
    // extended 3d math
    static Eigen::Vector3d dropAPerpendicular(Eigen::Vector3d point,
                                              Eigen::Vector3d linepoint,
                                              Eigen::Vector3d linevector);
    static float
    AngleAndDirection(Eigen::Vector3d vector1, Eigen::Vector3d vector2, Eigen::Vector3d normal);
 
    // coorrdinate conversion
    static void convert(TSphereCoord in, Eigen::Vector3d& out);
    static void convert(TSphereCoord in, Eigen::Vector3f& out);
    static void convert(Eigen::Vector3d in, TSphereCoord& out);
    static void convert(Eigen::Vector3f in, TSphereCoord& out);
    static void convertWithDistance(TSphereCoord in, Eigen::Vector3d& out);
 
    static double Angle(Eigen::Vector3d vec1, Eigen::Vector3d vec2);
};