/*------------------------------------------------------------------------------*/ void GW_TriangularInterpolation_Cubic::SetUpTriangularInterpolation( GW_GeodesicFace& Face ) { /* retrieve vertex and length */ GW_GeodesicVertex* pV0 = (GW_GeodesicVertex*) Face.GetVertex(0); GW_ASSERT( pV0!=NULL ); GW_GeodesicVertex* pV1 = (GW_GeodesicVertex*) Face.GetVertex(1); GW_ASSERT( pV1!=NULL ); GW_GeodesicVertex* pV2 = (GW_GeodesicVertex*) Face.GetVertex(2); GW_ASSERT( pV2!=NULL ); GW_Face* pFace0 = Face.GetFaceNeighbor(0); GW_Face* pFace1 = Face.GetFaceNeighbor(1); GW_Face* pFace2 = Face.GetFaceNeighbor(2); GW_GeodesicVertex *pW0 = NULL, *pW1 = NULL, *pW2 = NULL; if( pFace0!=NULL ) pW0 = (GW_GeodesicVertex*) pFace0->GetVertex( *pV1, *pV2 ); if( pFace1!=NULL ) pW1 = (GW_GeodesicVertex*) pFace1->GetVertex( *pV0, *pV2 ); if( pFace2!=NULL ) pW2 = (GW_GeodesicVertex*) pFace2->GetVertex( *pV0, *pV1 ); GW_Vector3D& V0 = pV0->GetPosition(); GW_Vector3D& V1 = pV1->GetPosition(); GW_Vector3D& V2 = pV2->GetPosition(); GW_Vector3D W0, W1, W2; if( pW0!=NULL ) W0 = pW0->GetPosition(); else W0 = (V1+V2)*0.5; if( pW1!=NULL ) W1 = pW1->GetPosition(); else W1 = (V0+V1)*0.5; if( pW2!=NULL ) W2 = pW2->GetPosition(); else W2 = (V0+V1)*0.5; /* edge of the main triangle */ GW_Vector3D e0 = V0-V2; GW_Vector3D e1 = V1-V2; GW_Vector3D e2 = V1-V0; /* edge of side triangles */ GW_Vector3D s0 = W0 - V2; GW_Vector3D s1 = W1 - V2; GW_Vector3D s2 = W2 - V0; GW_Float l0 = ~e0; GW_Float l1 = ~e1; GW_Float l2 = ~e2; GW_Float m0 = ~s0; GW_Float m1 = ~s1; GW_Float m2 = ~s2; /* compute the orthonormal basis in which the interpolation is performed */ u = e0/l0; v = ( (u^e1)^u ); v.Normalize(); w = V2; // origin /* now compute angles */ GW_Float a = acos( (e0*e1)/(l0*l1) ); GW_Float b = acos( (e1*s0)/(l1*m0) ); GW_Float c = acos( (e0*s1)/(l0*m1) ); GW_Float d = acos(-(e0*e2)/(l0*l2) ); GW_Float e = acos( (e2*s2)/(l2*m2) ); /* compute 2D position of points. Point 0,1,2 are V0,V1,V2 Points 3,4,5 are W0,W1,W2 */ GW_Float Points[6][2]; Points[0][0] = l0; Points[0][1] = 0; Points[1][0] = l1*cos(a); Points[1][1] = l1*sin(a); Points[2][0] = 0; Points[2][1] = 0; Points[3][0] = m0*cos(a+b); Points[3][1] = m0*sin(a+b); Points[4][0] = m1*cos(c); Points[4][1] = -m1*sin(c); Points[5][0] = l0 - m2*cos(d+e); Points[5][1] = m2*sin(d+e); /* compute values */ GW_Float Values[6]; Values[0] = pV0->GetDistance(); Values[1] = pV1->GetDistance(); Values[2] = pV2->GetDistance(); if( pW0!=NULL ) Values[3] = pW0->GetDistance(); else Values[3] = (Values[1]+Values[2])*0.5; if( pW1!=NULL ) Values[4] = pW1->GetDistance(); else Values[4] = (Values[0]+Values[2])*0.5; if( pW2!=NULL ) Values[5] = pW2->GetDistance(); else Values[5] = (Values[0]+Values[1])*0.5; /* compute the coefficients, given in that order : 0->cst, 1->X, 2->Y, 3->XY, 4->X^2, 5->Y^2. */ GW_Maths::Fit2ndOrderPolynomial2D( Points, Values, Coeffs ); }