/*------------------------------------------------------------------------------*/
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 );
}
