339 lines
10 KiB
C++
339 lines
10 KiB
C++
/****************************************************************************
|
|
* VCGLib o o *
|
|
* Visual and Computer Graphics Library o o *
|
|
* _ O _ *
|
|
* Copyright(C) 2004 \/)\/ *
|
|
* Visual Computing Lab /\/| *
|
|
* ISTI - Italian National Research Council | *
|
|
* \ *
|
|
* All rights reserved. *
|
|
* *
|
|
* 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 (http://www.gnu.org/licenses/gpl.txt) *
|
|
* for more details. *
|
|
* *
|
|
****************************************************************************/
|
|
/****************************************************************************
|
|
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 length of the segment
|
|
SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
|
|
SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
|
|
SCALAR_TYPE length=(seg.P0()-seg.P1()).Norm();
|
|
return ((d0<length)&&(d1<length));
|
|
}
|
|
|
|
/// 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 length of the segment
|
|
SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
|
|
SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
|
|
SCALAR_TYPE length=(seg.P0()-seg.P1()).Norm();
|
|
return ((d0<length)&&(d1<length));
|
|
}
|
|
|
|
/// 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);
|
|
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)));
|
|
}
|
|
|
|
template<class ScalarType>
|
|
bool TriangleTriangleIntersect2D(const vcg::Triangle2<ScalarType> &tr0,
|
|
const vcg::Triangle2<ScalarType> &tr1)
|
|
{
|
|
///test BBox Intersection
|
|
vcg::Box2<ScalarType> bbtr0;
|
|
bbtr0.Add(tr0.P(0));
|
|
bbtr0.Add(tr0.P(1));
|
|
bbtr0.Add(tr0.P(2));
|
|
vcg::Box2<ScalarType> bbtr1;
|
|
bbtr1.Add(tr1.P(0));
|
|
bbtr1.Add(tr1.P(1));
|
|
bbtr1.Add(tr1.P(2));
|
|
if (!bbtr0.Collide(bbtr1)) return false;
|
|
///test vertex in face
|
|
for (int i=0;i<3;i++)
|
|
{
|
|
bool inside0=vcg::IsInsideTrianglePoint(tr0,tr1.P(i));
|
|
bool inside1=vcg::IsInsideTrianglePoint(tr1,tr0.P(i));
|
|
if (inside0 || inside1) return true;
|
|
}
|
|
///test segment
|
|
///to segment intersection
|
|
for (int i=0;i<3;i++)
|
|
{
|
|
for (int j=0;j<3;j++)
|
|
{
|
|
if (i>j) continue;
|
|
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));
|
|
vcg::Point2<ScalarType> p_inters;
|
|
bool intersect=SegmentSegmentIntersection(seg0,seg1,p_inters);
|
|
if (intersect) return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
template <class ScalarType>
|
|
bool PointInsidePolygon(vcg::Point2<ScalarType> p,
|
|
const std::vector<vcg::Segment2<ScalarType> > &polygon)
|
|
{
|
|
int n=polygon.size();
|
|
vcg::Box2<ScalarType> BB;
|
|
for (int i=0;i<n;i++)
|
|
{
|
|
BB.Add(polygon[i].P0());
|
|
BB.Add(polygon[i].P1());
|
|
}
|
|
if (!BB.IsIn(p))return false;
|
|
ScalarType size=BB.Diag();
|
|
///take 4 directions
|
|
int inside_test=0;
|
|
for (int dir=0;dir<4;dir++)
|
|
{
|
|
int intersection=0;
|
|
vcg::Ray2<ScalarType> r;
|
|
vcg::Point2<ScalarType> direct=vcg::Point2<ScalarType>(0,0);
|
|
switch (dir)
|
|
{
|
|
case 0 : direct.X()=1;break;
|
|
case 1 : direct.Y()=1;break;
|
|
case 2 : direct.X()=-1; break;
|
|
default :direct.Y()=-1;
|
|
}
|
|
r.SetOrigin(p);
|
|
r.SetDirection(direct);
|
|
for (int i=0;i<n;i++)
|
|
{
|
|
Point2<ScalarType> p_inters;
|
|
if (vcg::RaySegmentIntersection(r,polygon[i],p_inters))intersection++;
|
|
}
|
|
if ((intersection%2)==1)
|
|
inside_test++;
|
|
}
|
|
return(inside_test>2);
|
|
}
|
|
|
|
//intersection between a circle and a line
|
|
template<class ScalarType>
|
|
inline bool CircleLineIntersection(const vcg::Line2<ScalarType> & line,
|
|
const vcg::Point2<ScalarType> ¢er,
|
|
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
|