261 lines
8.2 KiB
C++
261 lines
8.2 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: not supported by cvs2svn $
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Revision 1.6 2007/05/08 12:11:58 pietroni
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added circle-line intersection
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****************************************************************************/
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#ifndef __VCGLIB_INTERSECTION_2
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#define __VCGLIB_INTERSECTION_2
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#include <vcg/space/line2.h>
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#include <vcg/space/ray2.h>
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#include <vcg/space/segment2.h>
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#include <vcg/space/point2.h>
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#include <vcg/space/triangle2.h>
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#include <vcg/space/box2.h>
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namespace vcg {
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/** \addtogroup space */
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/*@{*/
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/**
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Function computing the intersection between couple of geometric primitives in
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2 dimension
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*/
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/// return true if the algle is convex (right rotation)
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template<class SCALAR_TYPE>
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inline bool Convex(const Point2<SCALAR_TYPE> & p0,const Point2<SCALAR_TYPE> & p1,const Point2<SCALAR_TYPE> & p2)
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{
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const SCALAR_TYPE EPS= SCALAR_TYPE(1e-8);
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return (((p0-p1)^(p2-p1))<=EPS);
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}
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///return if exist the intersection point
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///between 2 lines in a 2d plane
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template<class SCALAR_TYPE>
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inline bool LineLineIntersection(const vcg::Line2<SCALAR_TYPE> & l0,
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const vcg::Line2<SCALAR_TYPE> & l1,
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Point2<SCALAR_TYPE> &p)
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{
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const SCALAR_TYPE Eps= SCALAR_TYPE(1e-8);
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///first line
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SCALAR_TYPE x1=l0.Origin().X();
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SCALAR_TYPE y1=l0.Origin().Y();
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SCALAR_TYPE x2=x1+l0.Direction().X();
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SCALAR_TYPE y2=y1+l0.Direction().Y();
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///second line
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SCALAR_TYPE x3=l1.Origin().X();
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SCALAR_TYPE y3=l1.Origin().Y();
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SCALAR_TYPE x4=x3+l1.Direction().X();
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SCALAR_TYPE y4=y3+l1.Direction().Y();
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///then find intersection
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///denominator
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SCALAR_TYPE den=((x1-x2)*(y3-y4))-((y1-y2)*(x3-x4));
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if (fabs(den)<Eps)
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return false;
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SCALAR_TYPE d0=(x1*y2)-(y1*x2);
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SCALAR_TYPE d1=(x3*y4)-(y3*x4);
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SCALAR_TYPE numx=(d0*(x3-x4))-(d1*(x1-x2));
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SCALAR_TYPE numy=(d0*(y3-y4))-(d1*(y1-y2));
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p.X()=numx/den;
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p.Y()=numy/den;
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return true;
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}
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///return if exist the intersection point
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///between 2 lines in a 2d plane
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template<class SCALAR_TYPE>
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inline bool RayLineIntersection(const vcg::Line2<SCALAR_TYPE> & l,
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const vcg::Ray2<SCALAR_TYPE> & r,
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Point2<SCALAR_TYPE> &p)
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{
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///construct line from ray
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vcg::Line2<SCALAR_TYPE> l_test;
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l_test.Set(r.Origin(),r.Direction());
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if (!LineLineIntersection(l,l_test,p))
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return false;
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Point2<SCALAR_TYPE> dir=p-r.Origin();
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dir.Normalize();
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return (dir*r.Direction()>0);
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}
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/// interseciton between point and triangle
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template<class SCALAR_TYPE>
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inline bool RaySegmentIntersection(const vcg::Ray2<SCALAR_TYPE> & r,
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const vcg::Segment2<SCALAR_TYPE> &seg,
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Point2<SCALAR_TYPE> &p_inters)
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{
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///first compute intersection between lines
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vcg::Line2<SCALAR_TYPE> line2;
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line2.SetOrigin(seg.P0());
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vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
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dir.Normalize();
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line2.SetDirection(dir);
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if(!RayLineIntersection<SCALAR_TYPE>(line2,r,p_inters))
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return false;
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///then test if intersection point is nearest
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///to both extremes then lenght of the segment
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SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
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SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
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SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
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return ((d0<lenght)&&(d1<lenght));
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}
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/// interseciton between point and triangle
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template<class SCALAR_TYPE>
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inline bool LineSegmentIntersection(const vcg::Line2<SCALAR_TYPE> & line,
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const vcg::Segment2<SCALAR_TYPE> &seg,
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Point2<SCALAR_TYPE> &p_inters)
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{
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///first compute intersection between lines
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vcg::Line2<SCALAR_TYPE> line2;
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line2.SetOrigin(seg.P0());
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vcg::Point2<SCALAR_TYPE> dir=seg.P1()-seg.P0();
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dir.Normalize();
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line2.SetDirection(dir);
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if(!LineLineIntersection(line,line2,p_inters))
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return false;
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///then test if intersection point is nearest
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///to both extremes then lenght of the segment
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SCALAR_TYPE d0=(seg.P1()-p_inters).Norm();
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SCALAR_TYPE d1=(seg.P0()-p_inters).Norm();
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SCALAR_TYPE lenght=(seg.P0()-seg.P1()).Norm();
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return ((d0<lenght)&&(d1<lenght));
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}
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/// interseciton between point and triangle
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template<class SCALAR_TYPE>
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inline bool SegmentSegmentIntersection(const vcg::Segment2<SCALAR_TYPE> &seg0,
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const vcg::Segment2<SCALAR_TYPE> &seg1,
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Point2<SCALAR_TYPE> &p_inters)
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{
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vcg::Line2<SCALAR_TYPE> l0,l1;
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l0.SetOrigin(seg0.P0());
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vcg::Point2<SCALAR_TYPE> dir0=seg0.P1()-seg0.P0();
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dir0.Normalize();
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l0.SetDirection(dir0);
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l1.SetOrigin(seg1.P0());
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vcg::Point2<SCALAR_TYPE> dir1=seg1.P1()-seg1.P0();
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dir1.Normalize();
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l1.SetDirection(dir1);
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bool b=LineLineIntersection(l0,l1,p_inters);
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SCALAR_TYPE len0=seg0.Length();
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SCALAR_TYPE len1=seg1.Length();
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SCALAR_TYPE d0=(seg0.P0()-p_inters).Norm();
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SCALAR_TYPE d1=(seg1.P0()-p_inters).Norm();
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if ((d0>len0)||(d1>len1))
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return false;
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vcg::Point2<SCALAR_TYPE> dir2=p_inters-seg0.P0();
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vcg::Point2<SCALAR_TYPE> dir3=p_inters-seg1.P0();
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if (((dir2*dir0)<0)||((dir3*dir1)<0))
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return false;
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return true;
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}
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/// interseciton between point and triangle
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template<class SCALAR_TYPE>
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inline bool IsInsideTrianglePoint( const Triangle2<SCALAR_TYPE> & t,const Point2<SCALAR_TYPE> & p)
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{
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Point2<SCALAR_TYPE> p0=t.P0(0);
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Point2<SCALAR_TYPE> p1=t.P0(1);
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Point2<SCALAR_TYPE> p2=t.P0(2);
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///first test with bounding box
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vcg::Box2<SCALAR_TYPE> b2d;
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b2d.Add(p0);
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b2d.Add(p1);
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b2d.Add(p2);
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if (!b2d.IsIn(p))
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return false;
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///then text convex
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if (!Convex(p0,p1,p2))
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std::swap<Point2<SCALAR_TYPE> >(p1,p2);
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return((Convex(p,p0,p1))&&(Convex(p,p1,p2))&&(Convex(p,p2,p0)));
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//return((Convex(p,p0,p1))&&(Convex(p,p1,p2))&&(Convex(p,p2,p0)));
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}
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//intersection between a circle and a line
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template<class ScalarType>
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inline bool CircleLineIntersection(const vcg::Line2<ScalarType> & line,
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const vcg::Point2<ScalarType> ¢er,
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const ScalarType &radius,
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vcg::Point2<ScalarType> &p0,
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vcg::Point2<ScalarType> &p1)
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{
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///translate with origin on the center
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ScalarType x1,x2,y1,y2;
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x1=line.Origin().X()-center.X();
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y1=line.Origin().Y()-center.Y();
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x2=x1+line.Direction().X();
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y2=y1+line.Direction().Y();
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ScalarType dx,dy,dr,D,delta,sign;
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dx=x2-x1;
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dy=y2-y1;
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dr=sqrt(dx*dx+dy*dy);
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D=x1*y2-x2*y1;
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delta=radius*radius*dr*dr-D*D;
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if (dy>=0)
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sign=1;
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else
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sign=-1;
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if (delta<0.000001)
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return false;///no intersection
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else
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{
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p0.X()=(D*dy+sign*dx*sqrt(delta))/dr*dr;
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p0.Y()=(-D*dx+fabs(dy)*sqrt(delta))/dr*dr;
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p1.X()=(D*dy-sign*dx*sqrt(delta))/dr*dr;
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p1.Y()=(-D*dx-fabs(dy)*sqrt(delta))/dr*dr;
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p0+=center;
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p1+=center;
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return true;
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}
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}
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/*@}*/
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} // end namespace
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#endif
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