added constructors :

-Triangle2()
     -Triangle2(const CoordType &p0,const CoordType &p1,const CoordType &p2)

added functions:
     - InterpolationParameters
     - PointDistance

vcg/space/triangle2.h

@@ -27,8 +27,9 @@
 
 #ifndef __VCG_TRIANGLE2
 #define __VCG_TRIANGLE2
-
+#include <vcg/space/triangle3.h>
-#include <vcg\space\point2.h>
+#include <vcg/space/point2.h>
+#include <float.h>
 
 namespace vcg {
 
@@ -43,18 +44,30 @@ template <class SCALAR_TRIANGLE_TYPE> class Triangle2
 public:
   typedef SCALAR_TRIANGLE_TYPE ScalarTriangleType;
   typedef ScalarTriangleType ScalarType;
-	typedef Point2< ScalarType > CoordType;
+  typedef Point2< ScalarType > CoordType;
-	
+  typedef typename Triangle2<ScalarType> TriangleType;
 
 protected:
 	/// Vector of vertex pointer incident in the face
 	Point2<ScalarType> _v[3];
 public:
 
+	Triangle2()
+	{}
+
+	Triangle2(const CoordType &p0,const CoordType &p1,const CoordType &p2)
+	{
+		P(0)=p0;
+		P(1)=p1;
+		P(2)=p2;
+	}
+
 	/// Shortcut per accedere ai punti delle facce
+	inline CoordType & P( const int j ) { return _v[j];}
 	inline CoordType & P0( const int j ) { return _v[j];}
 	inline CoordType & P1( const int j ) { return _v[(j+1)%3];}
 	inline CoordType & P2( const int j ) { return _v[(j+2)%3];}
+	inline const CoordType &  P( const int j ) const { return _v[j];}
 	inline const CoordType &  P0( const int j ) const { return _v[j];}
 	inline const CoordType &  P1( const int j ) const { return _v[(j+1)%3];}
 	inline const CoordType &  P2( const int j ) const { return _v[(j+2)%3];}
@@ -62,9 +75,66 @@ public:
 	inline const CoordType & cP1( const int j ) const { return _v[(j+1)%3];}
 	inline const CoordType & cP2( const int j ) const { return _v[(j+2)%3];}
 
+/** evaluate barycentric coordinates
+	@param bq Point on the face
+	@param a barycentric value for V(0)
+	@param b barycentric value for V(1)
+	@param c barycentric value for V(2)
+	@return true se bq appartain to the face, false otherwise
+*/
+bool InterpolationParameters(const CoordType & bq, ScalarType &a, ScalarType &b, ScalarType &c ) const
+{	
+	const ScalarType EPSILON = ScalarType(0.0001);
+	ScalarType v_global,v0,v1,v2;
+
+	ScalarType AreaGlobal=(P(1) - P(0)) ^ (P(2) - P(0));
+	ScalarType Area0=(P(2) - P(1)) ^ (bq - P(1));
+	ScalarType Area1=(P(0) - P(2)) ^ (bq - P(2));
+	ScalarType Area2=(P(1) - P(0)) ^ (bq - P(0));
+
+	/*if ((Area0>(AreaGlobal+EPSILON))||(Area1>(AreaGlobal+EPSILON))||(Area2>(AreaGlobal+EPSILON)))
+		return false;*/
+	a=Area0/AreaGlobal;
+	b=Area1/AreaGlobal;
+	c=Area2/AreaGlobal;
+
+	///test inside/outside
+	if((a>(ScalarType)1+EPSILON)||(b>(ScalarType)1+EPSILON)||(c>(ScalarType)1+EPSILON))
+		return false;
+
+	if(a>1)
+		a=(ScalarType)1;
+	if(b>1)
+		b=(ScalarType)1;
+	if(c>1)
+		c=(ScalarType)1;
+
+	return true;
+}
+
+///return the distance to the point q and neighors point p
+void PointDistance(const CoordType & q,
+				   typename ScalarType & dist, 
+				   typename CoordType & p ) const
+{
+	dist=FLT_MAX;
+	///find distance to each segment and take minimum
+	for (int i=0;i<3;i++)
+	{
+		vcg::Segment2<float> s=vcg::Segment2<float>(P(i),P((i+1)%3));
+		CoordType clos=ClosestPoint<ScalarType>(s,q);
+		ScalarType dis_test=(clos-q).Norm();
+		if (dis_test<dist)
+		{
+			dist=dis_test;
+			p=clos;
+		}
+	}
+}
 
 }; //end Class
 
+
 }	 // end namespace
 #endif