CRITICAL CHANGE: the commonly used function Normal() used to compute the normal of a triangle has been changed into TriangleNormal()
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@ -36,26 +36,26 @@ namespace vcg {
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/** \addtogroup space */
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/*@{*/
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/**
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Templated class for storing a generic triangle in a 3D space.
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Templated class for storing a generic triangle in a 3D space.
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Note the relation with the Face class of TriMesh complex, both classes provide the P(i) access functions to their points and therefore they share the algorithms on it (e.g. area, normal etc...)
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*/
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template <class ScalarTriangleType> class Triangle3
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{
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public:
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typedef ScalarTriangleType ScalarType;
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typedef Point3< ScalarType > CoordType;
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/// The bounding box type
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typedef Box3<ScalarType> BoxType;
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typedef Point3< ScalarType > CoordType;
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/// The bounding box type
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typedef Box3<ScalarType> BoxType;
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/*********************************************
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blah
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blah
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**/
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Triangle3(){}
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Triangle3(const CoordType & c0,const CoordType & c1,const CoordType & c2){_v[0]=c0;_v[1]=c1;_v[2]=c2;}
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Triangle3(){}
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Triangle3(const CoordType & c0,const CoordType & c1,const CoordType & c2){_v[0]=c0;_v[1]=c1;_v[2]=c2;}
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protected:
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/// Vector of vertex pointer incident in the face
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Point3<ScalarType> _v[3];
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/// Vector of vertex pointer incident in the face
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Point3<ScalarType> _v[3];
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public:
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/// Shortcut per accedere ai punti delle facce
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@ -79,7 +79,7 @@ public:
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/// Returns the normal to the plane passing through p0,p1,p2
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template<class TriangleType>
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Point3<typename TriangleType::ScalarType> Normal(const TriangleType &t)
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Point3<typename TriangleType::ScalarType> TriangleNormal(const TriangleType &t)
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{
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return (( t.cP(1) - t.cP(0)) ^ (t.cP(2) - t.cP(0)));
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}
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@ -89,20 +89,6 @@ Point3Type Normal( Point3Type const &p0, Point3Type const & p1, Point3Type cons
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return (( p1 - p0) ^ (p2 - p0));
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}
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/// Like the above, it returns the normal to the plane passing through p0,p1,p2, but normalized.
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template<class TriangleType>
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typename TriangleType::CoordType NormalizedNormal(const TriangleType &t)
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{
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return (( t.cP(1) - t.cP(0)) ^ (t.cP(2) - t.cP(0))).Normalize();
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}
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template<class Point3Type>
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Point3Type NormalizedNormal( Point3Type const &p0, Point3Type const & p1, Point3Type const & p2)
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{
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return (( p1 - p0) ^ (p2 - p0)).Normalize();
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}
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/********************** Interpolation **********************/
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// The function to computing barycentric coords of a point inside a triangle.
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@ -120,41 +106,41 @@ Point3Type NormalizedNormal( Point3Type const &p0, Point3Type const & p1, Point
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template<class TriangleType, class ScalarType>
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bool InterpolationParameters(const TriangleType t, const int Axis, const Point3<ScalarType> & P, Point3<ScalarType> & L)
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{
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typedef Point2<ScalarType> P2;
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if(Axis==0) return InterpolationParameters2( P2(t.cP(0)[1],t.cP(0)[2]), P2(t.cP(1)[1],t.cP(1)[2]), P2(t.cP(2)[1],t.cP(2)[2]), P2(P[1],P[2]), L);
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if(Axis==1) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[2]), P2(t.cP(1)[0],t.cP(1)[2]), P2(t.cP(2)[0],t.cP(2)[2]), P2(P[0],P[2]), L);
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if(Axis==2) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[1]), P2(t.cP(1)[0],t.cP(1)[1]), P2(t.cP(2)[0],t.cP(2)[1]), P2(P[0],P[1]), L);
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return false;
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typedef Point2<ScalarType> P2;
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if(Axis==0) return InterpolationParameters2( P2(t.cP(0)[1],t.cP(0)[2]), P2(t.cP(1)[1],t.cP(1)[2]), P2(t.cP(2)[1],t.cP(2)[2]), P2(P[1],P[2]), L);
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if(Axis==1) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[2]), P2(t.cP(1)[0],t.cP(1)[2]), P2(t.cP(2)[0],t.cP(2)[2]), P2(P[0],P[2]), L);
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if(Axis==2) return InterpolationParameters2( P2(t.cP(0)[0],t.cP(0)[1]), P2(t.cP(1)[0],t.cP(1)[1]), P2(t.cP(2)[0],t.cP(2)[1]), P2(P[0],P[1]), L);
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return false;
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}
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/// Handy Wrapper of the above one that uses the passed normal N to choose the right orientation
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template<class TriangleType, class ScalarType>
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bool InterpolationParameters(const TriangleType t, const Point3<ScalarType> & N, const Point3<ScalarType> & P, Point3<ScalarType> & L)
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{
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if(fabs(N[0])>fabs(N[1]))
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{
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{
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if(fabs(N[0])>fabs(N[2]))
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return InterpolationParameters(t,0,P,L); /* 0 > 1 ? 2 */
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else
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return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
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}
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else
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{
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return InterpolationParameters(t,0,P,L); /* 0 > 1 ? 2 */
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else
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return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
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}
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else
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{
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if(fabs(N[1])>fabs(N[2]))
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return InterpolationParameters(t,1,P,L); /* 1 > 0 ? 2 */
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else
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return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
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}
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return InterpolationParameters(t,1,P,L); /* 1 > 0 ? 2 */
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else
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return InterpolationParameters(t,2,P,L); /* 2 > 1 ? 2 */
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}
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}
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// Function that computes the barycentric coords of a 2D triangle.
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template<class ScalarType>
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bool InterpolationParameters2(const Point2<ScalarType> &V1,
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const Point2<ScalarType> &V2,
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const Point2<ScalarType> &V3,
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const Point2<ScalarType> &P, Point3<ScalarType> &L)
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const Point2<ScalarType> &V2,
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const Point2<ScalarType> &V3,
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const Point2<ScalarType> &P, Point3<ScalarType> &L)
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{
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vcg::Triangle2<ScalarType> t2=vcg::Triangle2<ScalarType>(V1,V2,V3);
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return (t2.InterpolationParameters(P,L.X(),L.Y(),L.Z() ));
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vcg::Triangle2<ScalarType> t2=vcg::Triangle2<ScalarType>(V1,V2,V3);
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return (t2.InterpolationParameters(P,L.X(),L.Y(),L.Z() ));
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}
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/// Handy Wrapper of the above one that calculate the normal on the triangle
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@ -175,19 +161,19 @@ bool InterpolationParameters(const TriangleType t, const Point3<ScalarType> & P,
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template<class P3ScalarType>
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P3ScalarType Quality( Point3<P3ScalarType> const &p0, Point3<P3ScalarType> const & p1, Point3<P3ScalarType> const & p2)
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{
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Point3<P3ScalarType> d10=p1-p0;
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Point3<P3ScalarType> d20=p2-p0;
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Point3<P3ScalarType> d12=p1-p2;
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Point3<P3ScalarType> x = d10^d20;
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Point3<P3ScalarType> d10=p1-p0;
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Point3<P3ScalarType> d20=p2-p0;
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Point3<P3ScalarType> d12=p1-p2;
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Point3<P3ScalarType> x = d10^d20;
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P3ScalarType a = Norm( x );
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if(a==0) return 0; // Area zero triangles have surely quality==0;
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P3ScalarType b = SquaredNorm( d10 );
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P3ScalarType a = Norm( x );
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if(a==0) return 0; // Area zero triangles have surely quality==0;
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P3ScalarType b = SquaredNorm( d10 );
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if(b==0) return 0; // Again: area zero triangles have surely quality==0;
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P3ScalarType t = b;
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t = SquaredNorm( d20 ); if ( b<t ) b = t;
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t = SquaredNorm( d12 ); if ( b<t ) b = t;
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return a/b;
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P3ScalarType t = b;
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t = SquaredNorm( d20 ); if ( b<t ) b = t;
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t = SquaredNorm( d12 ); if ( b<t ) b = t;
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return a/b;
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}
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@ -203,19 +189,19 @@ typename TriangleType::ScalarType QualityFace(const TriangleType &t)
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/// e.g. Equilateral triangle 1, halfsquare: 0.81, ... up to a line that has zero quality.
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template<class P3ScalarType>
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P3ScalarType QualityRadii(Point3<P3ScalarType> const &p0,
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Point3<P3ScalarType> const &p1,
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Point3<P3ScalarType> const &p2) {
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Point3<P3ScalarType> const &p1,
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Point3<P3ScalarType> const &p2) {
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P3ScalarType a=(p1-p0).Norm();
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P3ScalarType b=(p2-p0).Norm();
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P3ScalarType c=(p1-p2).Norm();
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P3ScalarType a=(p1-p0).Norm();
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P3ScalarType b=(p2-p0).Norm();
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P3ScalarType c=(p1-p2).Norm();
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P3ScalarType sum = (a + b + c)*0.5;
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P3ScalarType area2 = sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
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if(area2 <= 0) return 0;
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//circumradius: (a*b*c)/(4*sqrt(area2))
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//inradius: (a*b*c)/(4*circumradius*sum) => sqrt(area2)/sum;
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return (8*area2)/(a*b*c*sum);
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P3ScalarType sum = (a + b + c)*0.5;
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P3ScalarType area2 = sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
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if(area2 <= 0) return 0;
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//circumradius: (a*b*c)/(4*sqrt(area2))
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//inradius: (a*b*c)/(4*circumradius*sum) => sqrt(area2)/sum;
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return (8*area2)/(a*b*c*sum);
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}
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/// Compute a shape quality measure of the triangle composed by points p0,p1,p2
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@ -224,16 +210,16 @@ P3ScalarType QualityRadii(Point3<P3ScalarType> const &p0,
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/// the range is range [0, 1]
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template<class P3ScalarType>
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P3ScalarType QualityMeanRatio(Point3<P3ScalarType> const &p0,
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Point3<P3ScalarType> const &p1,
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Point3<P3ScalarType> const &p2) {
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Point3<P3ScalarType> const &p1,
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Point3<P3ScalarType> const &p2) {
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P3ScalarType a=(p1-p0).Norm();
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P3ScalarType b=(p2-p0).Norm();
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P3ScalarType c=(p1-p2).Norm();
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P3ScalarType sum = (a + b + c)*0.5; //semiperimeter
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P3ScalarType area2 = sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
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if(area2 <= 0) return 0;
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return (4.0*sqrt(3.0)*sqrt(area2))/(a*a + b*b + c*c);
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P3ScalarType a=(p1-p0).Norm();
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P3ScalarType b=(p2-p0).Norm();
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P3ScalarType c=(p1-p2).Norm();
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P3ScalarType sum = (a + b + c)*0.5; //semiperimeter
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P3ScalarType area2 = sum*(a+b-sum)*(a+c-sum)*(b+c-sum);
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if(area2 <= 0) return 0;
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return (4.0*sqrt(3.0)*sqrt(area2))/(a*a + b*b + c*c);
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}
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