From 4002b9a706d1c46e762f022d7b87993eafa18d4d Mon Sep 17 00:00:00 2001
From: ganovelli <fabio.ganovelli@isti.cnr.it>
Date: Mon, 27 Oct 2008 16:50:45 +0000
Subject: [PATCH] created as a first working draft. Tessellates a simple
 polygon with the earcut algorithm assuming the polygon is  almost planar

---
 vcg/space/planar_polygon_tessellation.h | 142 ++++++++++++++++++++++++
 1 file changed, 142 insertions(+)
 create mode 100644 vcg/space/planar_polygon_tessellation.h

diff --git a/vcg/space/planar_polygon_tessellation.h b/vcg/space/planar_polygon_tessellation.h
new file mode 100644
index 00000000..7c59abd4
--- /dev/null
+++ b/vcg/space/planar_polygon_tessellation.h
@@ -0,0 +1,142 @@
+/****************************************************************************
+* 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.                                                         *
+*                                                                           *
+****************************************************************************/
+
+#ifndef __VCGLIB_PLANAR_POLYGON_TESSELLATOR
+#define __VCGLIB_PLANAR_POLYGON_TESSELLATOR
+
+#include <assert.h>
+#include <vcg/space/segment2.h>
+#include <vcg/math/random_generator.h>
+
+namespace vcg {
+
+/** \addtogroup space */
+/*@{*/
+    /**
+	A very simple earcut tessellation of planar 2D polygon.
+	Input: a vector or Point2<>
+	Output: a vector of faces as a triple of indices to the input vector
+	*/
+	template <class ScalarType> 
+	bool Cross(	 const Point2<ScalarType> & p00,
+				 const Point2<ScalarType> & p01,
+				 const Point2<ScalarType> & p10,
+				 const Point2<ScalarType> & p11)
+	{
+		Point2<ScalarType> vec0 = p01-p00;
+		Point2<ScalarType> vec1 = p11-p10;
+		if ( ( vec0^ (p11-p00)) *  ( vec0^ (p10 - p00)) >=0) return false;
+		if ( ( vec1^ (p01-p10)) *  ( vec1^ (p00 - p10)) >=0) return false;
+		return true;
+	}
+
+	template <class S>
+	bool Intersect(int cur , int v2, std::vector<int> & next, std::vector<Point2<S> > & points2){
+		for(int i  = 0; i < points2.size();++i)
+			if( (next[i]!=-1) && (i!=cur))
+				if( Cross(points2[cur], points2[v2],points2[i],points2[next[i]]))
+					return true;
+		return false;
+	}
+
+
+	template <class POINT_CONTAINER>
+	void TessellatePlanarPolygon2( POINT_CONTAINER &  points2, std::vector<int> & output){
+		typedef typename POINT_CONTAINER::value_type Point2x;
+		typedef typename Point2x::ScalarType S;
+		// tessellate
+		//  first very inefficient implementation
+		std::vector<int> next,prev;
+		for(int i = 0; i < points2.size(); ++i) next.push_back((i+1)%points2.size());
+		for(int i = 0; i < points2.size(); ++i) prev.push_back((i+points2.size()-1)%points2.size());
+		int v1,v2;
+		// check orientation
+		S orient = 0.0;
+		for(int i = 0 ; i < points2.size(); ++i){
+			v1 =  next[i];
+			v2 =  next[v1];
+			orient+= (points2[v1] - points2[0]) ^ (points2[v2] - points2[0]);
+		}
+		orient = (orient>0)? 1.0:-1.0;
+
+		int cur = 0;
+		int n_faces = 0;
+		while(output.size()<3*(points2.size()-2)){
+			v1 =  next[cur];
+			v2 =  next[v1];
+			if( ( (orient*((points2[v1] - points2[cur]) ^ (points2[v2] - points2[cur]))) >= 0.0) && 
+				  !Intersect(cur, v2,next,points2))
+			{
+				// output the face
+				output.push_back(cur);
+				output.push_back(v1);
+				output.push_back(v2);
+
+				// readjust the topology
+				next[cur] = v2;
+				prev[v2] = cur;
+				prev[v1] = -1;//unnecessary
+				next[v1] = -1;//unnecessary
+			} 
+			else
+				do{cur = (cur+1)%points2.size();} while(next[cur]==-1);
+		}
+	}
+
+    /**
+	A very simple earcut tessellation of planar 2D polygon.
+	Input: a vector or Point3<>
+	Output: a vector of faces as a triple of indices to the input vector
+
+	*/
+
+	template <class POINT_CONTAINER>
+	void TessellatePlanarPolygon3( POINT_CONTAINER &  points, std::vector<int> & output){
+		typedef typename POINT_CONTAINER::value_type Point3x;
+		typedef typename Point3x::ScalarType S;
+		Point3x n;
+
+		math::RandomGenerator rg;
+		int i12[2];
+		S bestsn = -1.0;
+		Point3x bestn,u,v;
+		for(int i  =0; i < points.size();++i){
+			for(int j = 0; j < 2; ++j){ i12[j] = i; while(i12[j]==i) i12[j] = rg(points.size()-1);}
+			n = (points[i12[0]]-points[i])^(points[i12[1]]-points[i]);
+			S sn = n.SquaredNorm();
+			if(sn > bestsn){ bestsn = sn; bestn = n;} 
+		}
+		
+		GetUV(n,u,v);
+		// project the coordinates
+		std::vector<Point2<S> > points2;
+		for(int i = 0; i < points.size(); ++i){
+			Point3x & p = points[i];
+			points2.push_back(Point2<S>(p*u,p*v));
+		}
+		TessellatePlanarPolygon2( points2,output);
+	}
+
+/*@}*/
+} // end namespace
+#endif