vcglib/vcg/space/intersection2.h

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 * Visual and Computer Graphics Library                            o     o   *
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 * Copyright(C) 2004                                                \/)\/    *
 * Visual Computing Lab                                            /\/|      *
 * ISTI - Italian National Research Council                           |      *
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 History

$Log: not supported by cvs2svn $
Revision 1.6  2007/05/08 12:11:58  pietroni
added circle-line intersection


****************************************************************************/



#ifndef __VCGLIB_INTERSECTION_2
#define __VCGLIB_INTERSECTION_2
#include <vcg/space/line2.h>
#include <vcg/space/ray2.h>
#include <vcg/space/segment2.h>
#include <vcg/space/point2.h>
#include <vcg/space/triangle2.h>
#include <vcg/space/box2.h>




namespace vcg {
/** \addtogroup space */
/*@{*/
/** 
    Function computing the intersection between couple of geometric primitives in
    2 dimension
*/

/// return true if the algle is convex (right rotation)
template<class SCALAR_TYPE>
    inline bool Convex(const Point2<SCALAR_TYPE> & p0,const Point2<SCALAR_TYPE> & p1,const Point2<SCALAR_TYPE> & p2)
{
  const SCALAR_TYPE EPS= SCALAR_TYPE(1e-8);
  return (((p0-p1)^(p2-p1))<=EPS);
}

///return if exist the intersection point
///between 2 lines in a 2d plane
template<class SCALAR_TYPE>
inline bool LineLineIntersection(const vcg::Line2<SCALAR_TYPE> & l0,
								 const vcg::Line2<SCALAR_TYPE> & l1,
								 Point2<SCALAR_TYPE> &p)
{
	const SCALAR_TYPE Eps= SCALAR_TYPE(1e-8);
	///first line
	SCALAR_TYPE x1=l0.Origin().X();
	SCALAR_TYPE y1=l0.Origin().Y(); 
	SCALAR_TYPE x2=x1+l0.Direction().X();
	SCALAR_TYPE y2=y1+l0.Direction().Y(); 
	
	///second line
	SCALAR_TYPE x3=l1.Origin().X();
	SCALAR_TYPE y3=l1.Origin().Y(); 
	SCALAR_TYPE x4=x3+l1.Direction().X();
	SCALAR_TYPE y4=y3+l1.Direction().Y(); 

	///then  find intersection

	///denominator
	SCALAR_TYPE den=((x1-x2)*(y3-y4))-((y1-y2)*(x3-x4));
	if (fabs(den)<Eps)
		return false;

	SCALAR_TYPE d0=(x1*y2)-(y1*x2);
	SCALAR_TYPE d1=(x3*y4)-(y3*x4);
	SCALAR_TYPE numx=(d0*(x3-x4))-(d1*(x1-x2));
	SCALAR_TYPE numy=(d0*(y3-y4))-(d1*(y1-y2));

	p.X()=numx/den;
	p.Y()=numy/den;
	return true;
}

///return if exist the intersection point
///between 2 lines in a 2d plane
template<class SCALAR_TYPE>
inline bool RayLineIntersection(const vcg::Line2<SCALAR_TYPE> & l,
								const vcg::Ray2<SCALAR_TYPE> & r,
								 Point2<SCALAR_TYPE> &p)
{
	///construct line from ray
	vcg::Line2<SCALAR_TYPE> l_test;
	l_test.Set(r.Origin(),r.Direction());
	if (!LineLineIntersection(l,l_test,p))
		return false;
	Point2<SCALAR_TYPE> dir=p-r.Origin();
	dir.Normalize();
	return (dir*r.Direction()>0);
}


/// interseciton between point and triangle
template<class SCALAR_TYPE>
inline bool RaySegmentIntersection(const vcg::Ray2<SCALAR_TYPE> & r,
									const vcg::Segment2<SCALAR_TYPE> &seg,
									Point2<SCALAR_TYPE> &p_inters)
{
 ///first compute intersection between lines
 vcg::Line2<SCALAR_TYPE> line2;
 line2.SetOrigin(seg.P0());
 vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
 dir.Normalize();
 line2.SetDirection(dir);
 if(!RayLineIntersection<SCALAR_TYPE>(line2,r,p_inters))
	return false;
 ///then test if intersection point is nearest 
 ///to both extremes then lenght of the segment 
 SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
 SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
 SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
 return ((d0<lenght)&&(d1<lenght));
}

/// interseciton between point and triangle
template<class SCALAR_TYPE>
inline bool LineSegmentIntersection(const vcg::Line2<SCALAR_TYPE> & line,
									const vcg::Segment2<SCALAR_TYPE> &seg,
									Point2<SCALAR_TYPE> &p_inters)
{
 ///first compute intersection between lines
 vcg::Line2<SCALAR_TYPE> line2;
 line2.SetOrigin(seg.P0());
 vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
 dir.Normalize();
 line2.SetDirection(dir);
 if(!LineLineIntersection(line,line2,p_inters))
	return false;
 ///then test if intersection point is nearest 
 ///to both extremes then lenght of the segment 
 SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
 SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
 SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
 return ((d0<lenght)&&(d1<lenght));
}

/// interseciton between point and triangle
template<class SCALAR_TYPE>
inline bool SegmentSegmentIntersection(const vcg::Segment2<SCALAR_TYPE> &seg0,
									   const vcg::Segment2<SCALAR_TYPE> &seg1,
									   Point2<SCALAR_TYPE> &p_inters)
{
		vcg::Line2<SCALAR_TYPE> l0,l1;

		l0.SetOrigin(seg0.P0());
		vcg::Point2<SCALAR_TYPE> dir0=seg0.P1()-seg0.P0();
		dir0.Normalize();
		l0.SetDirection(dir0);

		l1.SetOrigin(seg1.P0());
		vcg::Point2<SCALAR_TYPE> dir1=seg1.P1()-seg1.P0();
		dir1.Normalize();
		l1.SetDirection(dir1);
		bool b=LineLineIntersection(l0,l1,p_inters);
		SCALAR_TYPE len0=seg0.Length();
		SCALAR_TYPE len1=seg1.Length();
		SCALAR_TYPE d0=(seg0.P0()-p_inters).Norm();
		SCALAR_TYPE d1=(seg1.P0()-p_inters).Norm();

		if ((d0>len0)||(d1>len1))
			return false;

		vcg::Point2<SCALAR_TYPE> dir2=p_inters-seg0.P0();
		vcg::Point2<SCALAR_TYPE> dir3=p_inters-seg1.P0();
		if (((dir2*dir0)<0)||((dir3*dir1)<0))
			return false;

		return true;

}
/// interseciton between point and triangle
template<class SCALAR_TYPE>
    inline bool IsInsideTrianglePoint( const Triangle2<SCALAR_TYPE> & t,const Point2<SCALAR_TYPE> & p)
{
  Point2<SCALAR_TYPE> p0=t.P0(0);
  Point2<SCALAR_TYPE> p1=t.P0(1);
  Point2<SCALAR_TYPE> p2=t.P0(2);

  ///first test with bounding box
  vcg::Box2<SCALAR_TYPE> b2d;
  b2d.Add(p0);
  b2d.Add(p1);
  b2d.Add(p2);
  if (!b2d.IsIn(p))
	  return false;
  
  ///then text convex
  if (!Convex(p0,p1,p2))
    std::swap<Point2<SCALAR_TYPE> >(p1,p2);
  return((Convex(p,p0,p1))&&(Convex(p,p1,p2))&&(Convex(p,p2,p0)));
  //return((Convex(p,p0,p1))&&(Convex(p,p1,p2))&&(Convex(p,p2,p0)));
}

//intersection between a circle and a line
template<class ScalarType>
	inline bool CircleLineIntersection(const vcg::Line2<ScalarType> & line,
									   const vcg::Point2<ScalarType> &center,
									   const ScalarType &radius,
									   vcg::Point2<ScalarType> &p0,
									   vcg::Point2<ScalarType> &p1)
	{
		///translate with origin on the center
		ScalarType x1,x2,y1,y2;
		x1=line.Origin().X()-center.X();
		y1=line.Origin().Y()-center.Y();
		x2=x1+line.Direction().X();
		y2=y1+line.Direction().Y();

		ScalarType dx,dy,dr,D,delta,sign;
		dx=x2-x1;
		dy=y2-y1;
		dr=sqrt(dx*dx+dy*dy);
		D=x1*y2-x2*y1;
		delta=radius*radius*dr*dr-D*D;
		if (dy>=0)
			sign=1;
		else
			sign=-1;

		if (delta<0.000001)
			return false;///no intersection
		else
		{
			p0.X()=(D*dy+sign*dx*sqrt(delta))/dr*dr;
			p0.Y()=(-D*dx+fabs(dy)*sqrt(delta))/dr*dr;
			p1.X()=(D*dy-sign*dx*sqrt(delta))/dr*dr;
			p1.Y()=(-D*dx-fabs(dy)*sqrt(delta))/dr*dr;
			p0+=center;
			p1+=center;
			return true;
		}
	}
/*@}*/
} // end namespace
#endif