math2d.cpp

/*
    Copyright (c) 2011, <copyright holder> <email>
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        * Neither the name of the <organization> nor the
        names of its contributors may be used to endorse or promote products
        derived from this software without specific prior written permission.

    THIS SOFTWARE IS PROVIDED BY <copyright holder> <email> ''AS IS'' AND ANY
    EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
    WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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*/


#include "math2d.h"
#include "math.h"
#include "Eigen/Dense"

namespace tr{  
  
  
double triangleArea(Point2 &pt1, Point2 &pt2, Point2 &pt3)
{
  double c = ( pt1 - pt2 ).norm();
  double a = ( pt2 - pt3 ).norm();
  double b = ( pt3 - pt1 ).norm();
  
  double s = ( a + b + c ) / 2;
  
  return sqrt( s * ( s - a ) * ( s - b ) * ( s - c ) );
}

double triangleArea(Eigen::Vector2f& pt1, Eigen::Vector2f& pt2, Eigen::Vector2f& pt3)
{
  double c = ( pt1 - pt2 ).norm();
  double a = ( pt2 - pt3 ).norm();
  double b = ( pt3 - pt1 ).norm();
  
  double s = ( a + b + c ) / 2;
  
  return sqrt( s * ( s - a ) * ( s - b ) * ( s - c ) );
}


double triangleArea( cv::Point2f pt1 , cv::Point2f pt2 , cv::Point2f pt3 )
{
	double c = distance( pt1 , pt2 );//( pt1 - pt2 ).norm();
    double a = distance( pt2 , pt3 );//( pt2 - pt3 ).norm();
    double b = distance( pt3 , pt1 );//( pt3 - pt1 ).norm();
  
  double s = ( a + b + c ) / 2;
  
  return sqrt( s * ( s - a ) * ( s - b ) * ( s - c ) );
}


void lineEquation(cv::Point2f &point1, cv::Point2f &point2, float &m, float &c)
{
    m = ( point2.y - point1.y ) / ( point2.x - point1.x ) ;

    c = point1.y - m * point1.x;
}


void lineEquation( cv::Point &point1, cv::Point &point2, float &m, float &c )
{
    m = ( point2.y - point1.y ) / ( point2.x - point1.x ) ;

    c = point1.y - m * point1.x;
}
  

void closestPointOnLine( Point2 &point , Point2 &origin , Vector2 &direction , Point2 &closestPoint )
{
  closestPoint = origin + direction * ( point - origin ).dot( direction );
}  


float lineToLineIntersection2D( Point2 &point1 , Point2 &point2 , Point2 &point3 , Point2 &point4 , Point2 &intersection)
{
  float delX12 = point1.x() - point2.x();
  float delX34 = point3.x() - point4.x();
  float delX42 = point4.x() - point2.x();
  float delY12 = point1.y() - point2.y();
  float delY34 = point3.y() - point4.y();
  float delY42 = point4.y() - point2.y();
  
  float v = ( delX12 * delY42 - delX42 * delY12 ) / ( delX34 * delY12 - delY34 * delX12 ) ;
  
  intersection = v * point3 + ( 1 - v ) * point4;
  
  return v;
}


float lineToLineIntersection2D( cv::Point2f point1 , cv::Point2f point2 , cv::Point2f point3 , cv::Point2f point4 , cv::Point2f& intersection )
{
  float delX12 = point1.x - point2.x;
  float delX34 = point3.x - point4.x;
  float delX42 = point4.x - point2.x;
  float delY12 = point1.y - point2.y;
  float delY34 = point3.y - point4.y;
  float delY42 = point4.y - point2.y;
  
  float v = ( delX12 * delY42 - delX42 * delY12 ) / ( delX34 * delY12 - delY34 * delX12 ) ;
  
  intersection.x = v * point3.x + ( 1 - v ) * point4.x;
  intersection.y = v * point3.y + ( 1 - v ) * point4.y;
  
  return v;
}


float lineToLineIntersection2D( tr::Point2f point1, tr::Point2f point2, tr::Point2f point3, tr::Point2f point4, std::pair< float, float >& coefficients)
{
  float delX12 = point1.x() - point2.x();
  float delX34 = point3.x() - point4.x();
  float delX42 = point4.x() - point2.x();
  float delY12 = point1.y() - point2.y();
  float delY34 = point3.y() - point4.y();
  float delY42 = point4.y() - point2.y(); 
  
  coefficients.first = ( delX42 * delY34 - delX34 * delY42 ) / ( delX12 * delY34 - delY12 * delX34 );
  coefficients.second = ( delX12 * delY42 - delX42 * delY12 ) / ( delX34 * delY12 - delY34 * delX12 ) ;

  return coefficients.first;
}

double lineToLineIntersection2D(Eigen::Vector2d point1, Eigen::Vector2d point2, Eigen::Vector2d point3, Eigen::Vector2d point4, std::pair< double, double > &coefficients)
{
	float delX12 = point1.x() - point2.x();
	float delX34 = point3.x() - point4.x();
	float delX42 = point4.x() - point2.x();
	float delY12 = point1.y() - point2.y();
	float delY34 = point3.y() - point4.y();
	float delY42 = point4.y() - point2.y();

	coefficients.first = (delX42 * delY34 - delX34 * delY42) / (delX12 * delY34 - delY12 * delX34);
	coefficients.second = (delX12 * delY42 - delX42 * delY12) / (delX34 * delY12 - delY34 * delX12);

	return coefficients.first;
}

void lineToLineIntersection2D( Point2 &point1 , Point2 &point2 , Point2 &point3 , Point2 &point4 , Point2& intersection , std::pair< float , float >& coefficients)
{
  float delX12 = point1.x() - point2.x();
  float delX34 = point3.x() - point4.x();
  float delX42 = point4.x() - point2.x();
  float delY12 = point1.y() - point2.y();
  float delY34 = point3.y() - point4.y();
  float delY42 = point4.y() - point2.y(); 
  
  coefficients.first = ( delX42 * delY34 - delX34 * delY42 ) / ( delX12 * delY34 - delY12 * delX34 );
  coefficients.second = ( delX12 * delY42 - delX42 * delY12 ) / ( delX34 * delY12 - delY34 * delX12 ) ;
  
  intersection = coefficients.second * point3 + ( 1 - coefficients.second )  * point4;
  
}


void lineToLineIntersection2D( cv::Point2f point1 , cv::Point2f point2, cv::Point2f point3, cv::Point2f point4, cv::Point2f& intersection, std::pair< float, float >& coefficients)
{
  float delX12 = point1.x - point2.x;
  float delX34 = point3.x - point4.x;
  float delX42 = point4.x - point2.x;
  float delY12 = point1.y - point2.y;
  float delY34 = point3.y - point4.y;
  float delY42 = point4.y - point2.y; 
  
  coefficients.first = ( delX42 * delY34 - delX34 * delY42 ) / ( delX12 * delY34 - delY12 * delX34 );
  coefficients.second = ( delX12 * delY42 - delX42 * delY12 ) / ( delX34 * delY12 - delY34 * delX12 ) ;
  
  intersection.x = coefficients.second * point3.x + ( 1 - coefficients.second ) * point4.x;
  intersection.y = coefficients.second * point3.y + ( 1 - coefficients.second ) * point4.y;
  
}


void lineToLineIntersection2D(cv::Point2f point1, cv::Point2f point2, cv::Point2f point3, cv::Point2f point4, cv::Point2f& intersection, std::pair< double, double > &coefficients)
{
	float delX12 = point1.x - point2.x;
	float delX34 = point3.x - point4.x;
	float delX42 = point4.x - point2.x;
	float delY12 = point1.y - point2.y;
	float delY34 = point3.y - point4.y;
	float delY42 = point4.y - point2.y;

	coefficients.first = (delX42 * delY34 - delX34 * delY42) / (delX12 * delY34 - delY12 * delX34);
	coefficients.second = (delX12 * delY42 - delX42 * delY12) / (delX34 * delY12 - delY34 * delX12);

	intersection.x = coefficients.second * point3.x + (1 - coefficients.second) * point4.x;
	intersection.y = coefficients.second * point3.y + (1 - coefficients.second) * point4.y;
}


void lineToLineIntersection2D(Eigen::Vector2d point1, Eigen::Vector2d point2, Eigen::Vector2d point3,
	Eigen::Vector2d point4, Eigen::Vector2d& intersection, std::pair< double, double > &coefficients)
{

	double delX12 = point1.x() - point2.x();
	double delX34 = point3.x() - point4.x();
	double delX42 = point4.x() - point2.x();
	double delY12 = point1.y() - point2.y();
	double delY34 = point3.y() - point4.y();
	double delY42 = point4.y() - point2.y();

	coefficients.first = (delX42 * delY34 - delX34 * delY42) / (delX12 * delY34 - delY12 * delX34);
	coefficients.second = (delX12 * delY42 - delX42 * delY12) / (delX34 * delY12 - delY34 * delX12);

	intersection.x() = coefficients.second * point3.x() + (1 - coefficients.second) * point4.x();
	intersection.y() = coefficients.second * point3.y() + (1 - coefficients.second) * point4.y();
}




Math2D::Math2D()
{

}

double Math2D::distance(double* p1, double* p2)
{
  double _distance = ( p1[ 0 ] - p2[ 0 ] ) * ( p1[ 0 ] - p2[ 0 ] ) + 
                     ( p1[ 1 ] - p2[ 1 ] ) * ( p1[ 1 ] - p2[ 1 ] );
  
  _distance = sqrt( _distance );
  
  return _distance;
}




float Math2D::distance(cv::Point2f point1, cv::Point2f point2)
{
  float _distance = ( point1.x - point2.x ) * ( point1.x - point2.x ) + 
                    ( point1.y - point2.y ) * ( point1.y - point2.y );
		    
  _distance = sqrt( _distance );		    
		    
  return _distance;		    
}

double Math2D::distance(cv::Point2d point1, cv::Point2d point2)
{
  double _distance = ( point1.x - point2.x ) * ( point1.x - point2.x ) + 
                     ( point1.y - point2.y ) * ( point1.y - point2.y );
		    
  _distance = sqrt( _distance );		    
		    
  return _distance;
}



void Math2D::create_cross_product_matrix(cv::Mat& vec, cv::Mat& product_matrix)
{  	
  assert( vec.rows * vec.cols == 3 );
  
  product_matrix.create( 3 , 3 , CV_64FC1 ); 
  
  double *v = ( double * )vec.data;
  
  double *p = ( double * )product_matrix.data;

  const double a1 = v[ 0 ], a2 = v[ 1 ], a3 = v[ 2 ];

  p[ 0 ] = 0; 
  p[ 1 ] = -a3; 
  p[ 2 ] = a2; 

  p[ 3 ] = a3; 
  p[ 4 ] = 0; 
  p[ 5 ] = -a1; 

  p[ 6 ] = -a2; 
  p[ 7 ] = a1; 
  p[ 8 ] = 0; 
  
}

void Math2D::unitize(cv::Vec3f& vec)
{
  float _mod = vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] + vec[ 2 ] * vec[ 2 ] ; 
  
  _mod = sqrt( _mod );
  
  float _inv_mod = 1.0 / _mod;
  
  vec[ 0 ] *= _inv_mod;
  vec[ 1 ] *= _inv_mod;
  vec[ 2 ] *= _inv_mod;
}


float Math2D::modulus(cv::Vec3f& vec)
{
   float _mod = vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] + vec[ 2 ] * vec[ 2 ] ; 
  
   _mod = sqrt( _mod );
   
   return _mod;
} 

double Math2D::modulus(cv::Vec3d& vec)
{
   double _mod = vec[ 0 ] * vec[ 0 ] + vec[ 1 ] * vec[ 1 ] + vec[ 2 ] * vec[ 2 ] ; 
  
   _mod = sqrt( _mod );
   
   return _mod;
}


cv::Vec4f Math2D::planeEquation(cv::Point3f &pt1, cv::Point3f &pt2, cv::Point3f &pt3)
{
    Eigen::Matrix<float,3,3> matA;
    Eigen::Matrix<float,3,3> matB;
    Eigen::Matrix<float,3,3> matC;
    Eigen::Matrix<float,3,3> matD;

    matA<<1,pt1.y,pt1.z,1,pt2.y,pt2.z,1,pt3.y,pt3.z;
    matB<<pt1.x,1,pt1.z,pt2.x,1,pt2.z,pt3.x,1,pt3.z;
    matC<<pt1.x,pt1.y,1,pt2.x,pt2.y,1,pt3.x,pt3.y,1;
    matD<<pt1.x,pt1.y,pt1.z,pt2.x,pt2.y,pt2.z,pt3.x,pt3.y,pt3.z;
   // std::cout<<"matrix "<<matA<<std::endl;
    cv::Vec4f plane;
    plane[0]= matA.determinant();
    plane[1]= matB.determinant();
    plane[2]= matC.determinant();
    plane[3]= -1*matD.determinant();

   // std::cout<< " plane eq:: "<<plane[0]<<", "<<plane[1]<<", "<<plane[2]<<", "<<plane[3]<<std::endl;
    return plane;
}


cv::Point2f Math2D::weightWrtThreePoints(cv::Point3f &pt1, cv::Point3f &pt2, cv::Point3f &pt3, cv::Point3f &plane_pt)
{
    Eigen::Vector3d v0,v1,v2,p;
    v0(0)=pt1.x;
    v0(1)=pt1.y;
    v0(2)=pt1.z;

    v1(0)=pt2.x;
    v1(1)=pt2.y;
    v1(2)=pt2.z;

    v2(0)=pt3.x;
    v2(1)=pt3.y;
    v2(2)=pt3.z;

    p(0)=plane_pt.x;
    p(1)=plane_pt.y;
    p(2)=plane_pt.z;

    cv::Point2f weight;

//    std::cout<<" (p.dot(v0.cross(v1))) "<<(p.dot(v0.cross(v1)))<<std::endl;
//    std::cout<<" (v2.dot(v0.cross(v1))) "<<(v2.dot(v0.cross(v1)))<<std::endl;

//    std::cout<<"(p.dot(v1.cross(v2))) "<<(p.dot(v1.cross(v2)))<<std::endl;
//    std::cout<<" (v0.dot(v1.cross(v2))) "<<(v0.dot(v1.cross(v2)))<<std::endl;

    //TODO:: if check for denominator =0 is required
    weight.x = (p.dot(v0.cross(v1)))/(v2.dot(v0.cross(v1)));
    weight.y = (p.dot(v1.cross(v2)))/(v0.dot(v1.cross(v2)));

    return weight;
}

cv::Point2f Math2D::parametric_point_wrt_triangle(cv::Point &triangle_point1, cv::Point &triangle_point2, cv::Point &triangle_point3, cv::Point2f &input_point)
{
//  float a = triangle_point1.x - triangle_point3.x;
//  float b = triangle_point2.x - triangle_point3.x;
//  float c = triangle_point3.x - input_point.x;
  
//  float d = triangle_point1.y - triangle_point3.y;
//  float e = triangle_point2.y - triangle_point3.y;
//  float f = triangle_point3.y - input_point.y;
  
  Eigen::Vector2d v0 , v1 , v2;
  
  v0( 0 ) = triangle_point3.x - triangle_point1.x;
  v0( 1 ) = triangle_point3.y - triangle_point1.y;
  
  v1( 0 ) = triangle_point2.x - triangle_point1.x;
  v1( 1 ) = triangle_point2.y - triangle_point1.y;
  
  v2( 0 ) = input_point.x - triangle_point1.x;
  v2( 1 ) = input_point.y - triangle_point1.y;
  
  double dot00 = v0.dot( v0 );
  double dot01 = v0.dot( v1 );
  double dot02 = v0.dot( v2 );
  double dot11 = v1.dot( v1 );
  double dot12 = v1.dot( v2 );
  
  // Compute barycentric coordinates
  double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
  double u = (dot11 * dot02 - dot01 * dot12) * invDenom;
  double v = (dot00 * dot12 - dot01 * dot02) * invDenom;
  
  return cv::Point2f( v , u );
//   cv::Point2f parametric_point;
//   
//   float denom = b * f - c * e;
//   
//   if( a == 0 )
//   {
//     parametric_point.y = - c / b;
//     
//     parametric_point.x = ( -f + parametric_point.y * e ) / d;
//     
//     return parametric_point;
//   }
//   
//   if( b == 0 )
//   {
//     parametric_point.x = - c / a;
//     
//     parametric_point.y = ( -f + parametric_point.x * d ) / e;
//     
//     return parametric_point;
//   }
//   
//   if( d == 0 )
//   {
//     parametric_point.y = - f / e;
//     
//     parametric_point.x = ( -c + parametric_point.y * b ) / a;
//     
//     return parametric_point;
//   }
//   
//   if( e == 0 )
//   {
//     parametric_point.x = - f / d;
//     
//     parametric_point.y = ( -c + parametric_point.x * a ) / b;
//     
//     return parametric_point;
//   }
//   
//   parametric_point.x = ( a * e - d * b ) / denom;
//   parametric_point.y = -( parametric_point.x * a + c ) / b;
  
//   return parametric_point;
}



Math2D::~Math2D()
{

}

}