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Added TriangleTriangleIntersect2D function

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Nico Pietroni 2011-04-01 16:13:34 +00:00
parent cf619d282b
commit ed6221e993
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vcg/space/intersection2.h
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/**************************************************************************** /****************************************************************************
* VCGLib o o * * VCGLib o o *
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/**************************************************************************** /****************************************************************************
History History
$Log: not supported by cvs2svn $ $Log: not supported by cvs2svn $
Revision 1.6 2007/05/08 12:11:58 pietroni Revision 1.6 2007/05/08 12:11:58 pietroni
added circle-line intersection added circle-line intersection
****************************************************************************/ ****************************************************************************/
#ifndef __VCGLIB_INTERSECTION_2 #ifndef __VCGLIB_INTERSECTION_2
#define __VCGLIB_INTERSECTION_2 #define __VCGLIB_INTERSECTION_2
#include <vcg/space/line2.h> #include <vcg/space/line2.h>
#include <vcg/space/ray2.h> #include <vcg/space/ray2.h>
#include <vcg/space/segment2.h> #include <vcg/space/segment2.h>
#include <vcg/space/point2.h> #include <vcg/space/point2.h>
#include <vcg/space/triangle2.h> #include <vcg/space/triangle2.h>
#include <vcg/space/box2.h> #include <vcg/space/box2.h>
namespace vcg { namespace vcg {
/** \addtogroup space */ /** \addtogroup space */
/*@{*/ /*@{*/
/** /**
Function computing the intersection between couple of geometric primitives in Function computing the intersection between couple of geometric primitives in
2 dimension 2 dimension
*/ */
/// return true if the algle is convex (right rotation) /// return true if the algle is convex (right rotation)
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool Convex(const Point2<SCALAR_TYPE> & p0,const Point2<SCALAR_TYPE> & p1,const Point2<SCALAR_TYPE> & p2) 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); const SCALAR_TYPE EPS= SCALAR_TYPE(1e-8);
return (((p0-p1)^(p2-p1))<=EPS); return (((p0-p1)^(p2-p1))<=EPS);
} }
///return if exist the intersection point ///return if exist the intersection point
///between 2 lines in a 2d plane ///between 2 lines in a 2d plane
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool LineLineIntersection(const vcg::Line2<SCALAR_TYPE> & l0, inline bool LineLineIntersection(const vcg::Line2<SCALAR_TYPE> & l0,
const vcg::Line2<SCALAR_TYPE> & l1, const vcg::Line2<SCALAR_TYPE> & l1,
Point2<SCALAR_TYPE> &p) Point2<SCALAR_TYPE> &p)
{ {
const SCALAR_TYPE Eps= SCALAR_TYPE(1e-8); const SCALAR_TYPE Eps= SCALAR_TYPE(1e-8);
///first line ///first line
SCALAR_TYPE x1=l0.Origin().X(); SCALAR_TYPE x1=l0.Origin().X();
SCALAR_TYPE y1=l0.Origin().Y(); SCALAR_TYPE y1=l0.Origin().Y();
SCALAR_TYPE x2=x1+l0.Direction().X(); SCALAR_TYPE x2=x1+l0.Direction().X();
SCALAR_TYPE y2=y1+l0.Direction().Y(); SCALAR_TYPE y2=y1+l0.Direction().Y();
///second line ///second line
SCALAR_TYPE x3=l1.Origin().X(); SCALAR_TYPE x3=l1.Origin().X();
SCALAR_TYPE y3=l1.Origin().Y(); SCALAR_TYPE y3=l1.Origin().Y();
SCALAR_TYPE x4=x3+l1.Direction().X(); SCALAR_TYPE x4=x3+l1.Direction().X();
SCALAR_TYPE y4=y3+l1.Direction().Y(); SCALAR_TYPE y4=y3+l1.Direction().Y();
///then find intersection ///then find intersection
///denominator ///denominator
SCALAR_TYPE den=((x1-x2)*(y3-y4))-((y1-y2)*(x3-x4)); SCALAR_TYPE den=((x1-x2)*(y3-y4))-((y1-y2)*(x3-x4));
if (fabs(den)<Eps) if (fabs(den)<Eps)
return false; return false;
SCALAR_TYPE d0=(x1*y2)-(y1*x2); SCALAR_TYPE d0=(x1*y2)-(y1*x2);
SCALAR_TYPE d1=(x3*y4)-(y3*x4); SCALAR_TYPE d1=(x3*y4)-(y3*x4);
SCALAR_TYPE numx=(d0*(x3-x4))-(d1*(x1-x2)); SCALAR_TYPE numx=(d0*(x3-x4))-(d1*(x1-x2));
SCALAR_TYPE numy=(d0*(y3-y4))-(d1*(y1-y2)); SCALAR_TYPE numy=(d0*(y3-y4))-(d1*(y1-y2));
p.X()=numx/den; p.X()=numx/den;
p.Y()=numy/den; p.Y()=numy/den;
return true; return true;
} }
///return if exist the intersection point ///return if exist the intersection point
///between 2 lines in a 2d plane ///between 2 lines in a 2d plane
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool RayLineIntersection(const vcg::Line2<SCALAR_TYPE> & l, inline bool RayLineIntersection(const vcg::Line2<SCALAR_TYPE> & l,
const vcg::Ray2<SCALAR_TYPE> & r, const vcg::Ray2<SCALAR_TYPE> & r,
Point2<SCALAR_TYPE> &p) Point2<SCALAR_TYPE> &p)
{ {
///construct line from ray ///construct line from ray
vcg::Line2<SCALAR_TYPE> l_test; vcg::Line2<SCALAR_TYPE> l_test;
l_test.Set(r.Origin(),r.Direction()); l_test.Set(r.Origin(),r.Direction());
if (!LineLineIntersection(l,l_test,p)) if (!LineLineIntersection(l,l_test,p))
return false; return false;
Point2<SCALAR_TYPE> dir=p-r.Origin(); Point2<SCALAR_TYPE> dir=p-r.Origin();
dir.Normalize(); dir.Normalize();
return (dir*r.Direction()>0); return (dir*r.Direction()>0);
} }
/// interseciton between point and triangle /// interseciton between point and triangle
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool RaySegmentIntersection(const vcg::Ray2<SCALAR_TYPE> & r, inline bool RaySegmentIntersection(const vcg::Ray2<SCALAR_TYPE> & r,
const vcg::Segment2<SCALAR_TYPE> &seg, const vcg::Segment2<SCALAR_TYPE> &seg,
Point2<SCALAR_TYPE> &p_inters) Point2<SCALAR_TYPE> &p_inters)
{ {
///first compute intersection between lines ///first compute intersection between lines
vcg::Line2<SCALAR_TYPE> line2; vcg::Line2<SCALAR_TYPE> line2;
line2.SetOrigin(seg.P0()); line2.SetOrigin(seg.P0());
vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0(); vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
dir.Normalize(); dir.Normalize();
line2.SetDirection(dir); line2.SetDirection(dir);
if(!RayLineIntersection<SCALAR_TYPE>(line2,r,p_inters)) if(!RayLineIntersection<SCALAR_TYPE>(line2,r,p_inters))
return false; return false;
///then test if intersection point is nearest ///then test if intersection point is nearest
///to both extremes then lenght of the segment ///to both extremes then lenght of the segment
SCALAR_TYPE d0=(seg.P1()-p_inters).Norm(); SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
SCALAR_TYPE d1=(seg.P0()-p_inters).Norm(); SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm(); SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
return ((d0<lenght)&&(d1<lenght)); return ((d0<lenght)&&(d1<lenght));
} }
/// interseciton between point and triangle /// interseciton between point and triangle
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool LineSegmentIntersection(const vcg::Line2<SCALAR_TYPE> & line, inline bool LineSegmentIntersection(const vcg::Line2<SCALAR_TYPE> & line,
const vcg::Segment2<SCALAR_TYPE> &seg, const vcg::Segment2<SCALAR_TYPE> &seg,
Point2<SCALAR_TYPE> &p_inters) Point2<SCALAR_TYPE> &p_inters)
{ {
///first compute intersection between lines ///first compute intersection between lines
vcg::Line2<SCALAR_TYPE> line2; vcg::Line2<SCALAR_TYPE> line2;
line2.SetOrigin(seg.P0()); line2.SetOrigin(seg.P0());
vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0(); vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
dir.Normalize(); dir.Normalize();
line2.SetDirection(dir); line2.SetDirection(dir);
if(!LineLineIntersection(line,line2,p_inters)) if(!LineLineIntersection(line,line2,p_inters))
return false; return false;
///then test if intersection point is nearest ///then test if intersection point is nearest
///to both extremes then lenght of the segment ///to both extremes then lenght of the segment
SCALAR_TYPE d0=(seg.P1()-p_inters).Norm(); SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
SCALAR_TYPE d1=(seg.P0()-p_inters).Norm(); SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm(); SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
return ((d0<lenght)&&(d1<lenght)); return ((d0<lenght)&&(d1<lenght));
} }
/// interseciton between point and triangle /// interseciton between point and triangle
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool SegmentSegmentIntersection(const vcg::Segment2<SCALAR_TYPE> &seg0, inline bool SegmentSegmentIntersection(const vcg::Segment2<SCALAR_TYPE> &seg0,
const vcg::Segment2<SCALAR_TYPE> &seg1, const vcg::Segment2<SCALAR_TYPE> &seg1,
Point2<SCALAR_TYPE> &p_inters) Point2<SCALAR_TYPE> &p_inters)
{ {
vcg::Line2<SCALAR_TYPE> l0,l1; vcg::Line2<SCALAR_TYPE> l0,l1;
l0.SetOrigin(seg0.P0()); l0.SetOrigin(seg0.P0());
vcg::Point2<SCALAR_TYPE> dir0=seg0.P1()-seg0.P0(); vcg::Point2<SCALAR_TYPE> dir0=seg0.P1()-seg0.P0();
dir0.Normalize(); dir0.Normalize();
l0.SetDirection(dir0); l0.SetDirection(dir0);
l1.SetOrigin(seg1.P0()); l1.SetOrigin(seg1.P0());
vcg::Point2<SCALAR_TYPE> dir1=seg1.P1()-seg1.P0(); vcg::Point2<SCALAR_TYPE> dir1=seg1.P1()-seg1.P0();
dir1.Normalize(); dir1.Normalize();
l1.SetDirection(dir1); l1.SetDirection(dir1);
LineLineIntersection(l0,l1,p_inters); LineLineIntersection(l0,l1,p_inters);
SCALAR_TYPE len0=seg0.Length(); SCALAR_TYPE len0=seg0.Length();
SCALAR_TYPE len1=seg1.Length(); SCALAR_TYPE len1=seg1.Length();
SCALAR_TYPE d0=(seg0.P0()-p_inters).Norm(); SCALAR_TYPE d0=(seg0.P0()-p_inters).Norm();
SCALAR_TYPE d1=(seg1.P0()-p_inters).Norm(); SCALAR_TYPE d1=(seg1.P0()-p_inters).Norm();
if ((d0>len0)||(d1>len1)) if ((d0>len0)||(d1>len1))
return false; return false;
vcg::Point2<SCALAR_TYPE> dir2=p_inters-seg0.P0(); vcg::Point2<SCALAR_TYPE> dir2=p_inters-seg0.P0();
vcg::Point2<SCALAR_TYPE> dir3=p_inters-seg1.P0(); vcg::Point2<SCALAR_TYPE> dir3=p_inters-seg1.P0();
if (((dir2*dir0)<0)||((dir3*dir1)<0)) if (((dir2*dir0)<0)||((dir3*dir1)<0))
return false; return false;
return true; return true;
} }
/// interseciton between point and triangle /// interseciton between point and triangle
template<class SCALAR_TYPE> template<class SCALAR_TYPE>
inline bool IsInsideTrianglePoint( const Triangle2<SCALAR_TYPE> & t,const Point2<SCALAR_TYPE> & p) inline bool IsInsideTrianglePoint( const Triangle2<SCALAR_TYPE> & t,const Point2<SCALAR_TYPE> & p)
{ {
Point2<SCALAR_TYPE> p0=t.P0(0); Point2<SCALAR_TYPE> p0=t.P0(0);
Point2<SCALAR_TYPE> p1=t.P0(1); Point2<SCALAR_TYPE> p1=t.P0(1);
Point2<SCALAR_TYPE> p2=t.P0(2); Point2<SCALAR_TYPE> p2=t.P0(2);
///first test with bounding box ///first test with bounding box
vcg::Box2<SCALAR_TYPE> b2d; vcg::Box2<SCALAR_TYPE> b2d;
b2d.Add(p0); b2d.Add(p0);
b2d.Add(p1); b2d.Add(p1);
b2d.Add(p2); b2d.Add(p2);
if (!b2d.IsIn(p)) if (!b2d.IsIn(p))
return false; return false;
///then text convex ///then text convex
if (!Convex(p0,p1,p2)) if (!Convex(p0,p1,p2))
std::swap<Point2<SCALAR_TYPE> >(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)));
//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>
template<class ScalarType> bool TriangleTriangleIntersect2D(const vcg::Triangle2<ScalarType> &tr0,
inline bool CircleLineIntersection(const vcg::Line2<ScalarType> & line, const vcg::Triangle2<ScalarType> &tr1)
const vcg::Point2<ScalarType> &center, {
const ScalarType &radius, ///test BBox Intersection
vcg::Point2<ScalarType> &p0, vcg::Box2<ScalarType> bbtr0;
vcg::Point2<ScalarType> &p1) bbtr0.Add(tr0.P(0));
{ bbtr0.Add(tr0.P(1));
///translate with origin on the center bbtr0.Add(tr0.P(2));
ScalarType x1,x2,y1,y2; vcg::Box2<ScalarType> bbtr1;
x1=line.Origin().X()-center.X(); bbtr1.Add(tr1.P(0));
y1=line.Origin().Y()-center.Y(); bbtr1.Add(tr1.P(1));
x2=x1+line.Direction().X(); bbtr1.Add(tr1.P(2));
y2=y1+line.Direction().Y(); if (!bbtr0.Collide(bbtr1)) return false;
///test vertex in face
ScalarType dx,dy,dr,D,delta,sign; for (int i=0;i<3;i++)
dx=x2-x1; {
dy=y2-y1; bool inside0=vcg::IsInsideTrianglePoint(tr0,tr1.P(i));
dr=sqrt(dx*dx+dy*dy); bool inside1=vcg::IsInsideTrianglePoint(tr1,tr0.P(i));
D=x1*y2-x2*y1; if (inside0 || inside1) return true;
delta=radius*radius*dr*dr-D*D; }
if (dy>=0) ///test segment
sign=1; ///to segment intersection
else for (int i=0;i<3;i++)
sign=-1; {
for (int j=0;j<3;j++)
if (delta<0.000001) {
return false;///no intersection if (i>j) continue;
else vcg::Segment2<ScalarType> seg0=vcg::Segment2<ScalarType>(tr0.P(i),tr0.P((i+1)%3));
{ vcg::Segment2<ScalarType> seg1=vcg::Segment2<ScalarType>(tr1.P(j),tr1.P((j+1)%3));
p0.X()=(D*dy+sign*dx*sqrt(delta))/dr*dr; vcg::Point2<ScalarType> p_inters;
p0.Y()=(-D*dx+fabs(dy)*sqrt(delta))/dr*dr; bool intersect=SegmentSegmentIntersection(seg0,seg1,p_inters);
p1.X()=(D*dy-sign*dx*sqrt(delta))/dr*dr; if (intersect) return true;
p1.Y()=(-D*dx-fabs(dy)*sqrt(delta))/dr*dr; }
p0+=center; }
p1+=center; return false;
return true; }
}
} //intersection between a circle and a line
/*@}*/ template<class ScalarType>
} // end namespace inline bool CircleLineIntersection(const vcg::Line2<ScalarType> & line,
#endif 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