/*------------------------------------------------------------------------------*/
void GW_TriangularInterpolation_Cubic::SetLocalGradient( GW_Vector3D& grad, GW_GeodesicFace& Face, GW_GeodesicVertex& Vert )
{
this->ComputeLocalBasis( Face );
GW_I32 nNum = Face.GetEdgeNumber( Vert );
GW_ASSERT( nNum>=0 );
LocalGradient_[nNum][0] = grad*u;
LocalGradient_[nNum][1] = grad*v;
}
/*------------------------------------------------------------------------------*/
void GW_TriangularInterpolation_Cubic::ComputeLocalBasis( GW_GeodesicFace& Face )
{
if( !bIsLocalBasisComputed_ )
{
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_Vector3D& V0 = pV0->GetPosition();
GW_Vector3D& V1 = pV1->GetPosition();
GW_Vector3D& V2 = pV2->GetPosition();
GW_Vector3D e0 = V0-V2;
GW_Vector3D e1 = V1-V2;
GW_Vector3D e2 = V1-V0;
u = e0/e0.Norm();
v = ( (u^e1)^u );
v.Normalize();
w = V2;
}
bIsLocalBasisComputed_ = GW_True;
}
/*------------------------------------------------------------------------------*/
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 );
}
/*------------------------------------------------------------------------------*/
void GW_TriangularInterpolation_Cubic::ComputeLocalGradient( GW_GeodesicVertex& Vert )
{
/* compute the total angle */
GW_Vector3D PrevEdge;
GW_Float rTotalAngle = 0;
for( GW_VertexIterator it=Vert.BeginVertexIterator(); it!=Vert.EndVertexIterator(); ++it )
{
GW_Vertex* pVert = *it;
GW_ASSERT( pVert!=NULL );
if( it==Vert.BeginVertexIterator() )
{
PrevEdge = pVert->GetPosition() - Vert.GetPosition();
PrevEdge.Normalize();
}
else
{
GW_Vector3D NextEdge = pVert->GetPosition() - Vert.GetPosition();
NextEdge.Normalize();
rTotalAngle += acos( NextEdge*PrevEdge );
PrevEdge = NextEdge;
}
}
/* matrix and RHS for least square minimusation */
GW_Float M[2][2] = {{0,0},{0,0}};
GW_Float b[2] = {0,0};
GW_Float rCurAngle = 0;
PrevEdge.SetZero();
for( GW_VertexIterator it=Vert.BeginVertexIterator(); it!=Vert.EndVertexIterator(); ++it )
{
GW_GeodesicVertex* pVert = (GW_GeodesicVertex*) *it;
GW_ASSERT( pVert!=NULL );
GW_Vector3D Edge = pVert->GetPosition() - Vert.GetPosition();
GW_Float a = Edge.Norm();
Edge /= a;
if( it!=Vert.BeginVertexIterator() )
{
/* update the angle */
rCurAngle += acos( Edge*PrevEdge );
}
/* directional gradient estimation */
GW_Float delta = (pVert->GetDistance() - Vert.GetDistance())/a;
/* coordonate of the edge on (u,v) [flatened coords] */
GW_Float eu = a*cos( rCurAngle/rTotalAngle );
GW_Float ev = a*sin( rCurAngle/rTotalAngle );
/* update the matrix */
M[0][0] += eu*eu;
M[0][1] += eu*ev;
M[1][0] += eu*ev;
M[1][1] += ev*ev;
b[0] += delta*eu;
b[1] += delta*ev;
PrevEdge = Edge;
}
/* invert the system */
GW_Float det = M[0][0]*M[1][1] - M[0][1]*M[1][0];
GW_ASSERT( det!=0 );
GW_Float gu = 1/det * ( M[1][1]*b[0] - M[0][1]*b[1] );
GW_Float gv = 1/det * (-M[1][0]*b[0] + M[0][0]*b[1] );
/* set the gradient in local coords for each surrounding face */
rCurAngle = 0;
for( GW_FaceIterator it = Vert.BeginFaceIterator(); it!=Vert.EndFaceIterator(); ++it )
{
GW_GeodesicFace* pFace = (GW_GeodesicFace*) *it;
GW_ASSERT( pFace!=NULL );
GW_Vertex* pVert1 = it.GetLeftVertex(); GW_ASSERT( pVert1!=NULL );
GW_Vertex* pVert2 = it.GetRightVertex(); GW_ASSERT( pVert1!=NULL );
GW_Vector3D e1 = pVert1->GetPosition() - Vert.GetPosition();
GW_Vector3D e2 = pVert2->GetPosition() - Vert.GetPosition();
GW_Float a1 = e1.Norm();
GW_Float a2 = e2.Norm();
e1 /= a1;
e2 /= a2;
GW_Float rInnerAngle = acos( e1*e2 );
/* flattened position of the two vertex */
GW_Float p1[2], p2[2];
p1[0] = cos( rCurAngle );
p1[1] = sin( rCurAngle );
p2[0] = cos( rCurAngle+rInnerAngle );
p2[1] = sin( rCurAngle+rInnerAngle );
/* we have grad = gu*u + gv*v
we are searching for grad = g1*p1 + g2*p2, so:
gu = g1*<p1,u> + g2*<p2,u>
gv = g1*<p1,v> + g2*<p2,v>
i.e.
|p1[0] p2[0]| |g1| |gu|
|p1[1] p2[1]|*|g2| = |gv|
*/
det = p1[0]*p2[1]-p1[1]*p2[0];
GW_ASSERT( det!=0 );
GW_Float g1 = 1/det * ( p2[1]*gu - p2[0]*gv );
GW_Float g2 = 1/det * (-p1[1]*gu + p1[0]*gv );
/* now compute the gradient in world coords */
GW_Vector3D LocGrad = e1*g1 + e2*g2;
GW_TriangularInterpolation_ABC* pInterp = pFace->GetTriangularInterpolation();
if( pInterp==NULL )
{
pInterp = new GW_TriangularInterpolation_Cubic;
pFace->SetTriangularInterpolation( *pInterp );
}
GW_ASSERT( pInterp->GetType()==kCubicTriangulationInterpolation );
((GW_TriangularInterpolation_Cubic*) pInterp)->SetLocalGradient( LocGrad, *pFace, Vert );
rCurAngle += rInnerAngle;
}
}
/*------------------------------------------------------------------------------*/
void GW_GeodesicDisplayer::DisplayPath( GW_GeodesicPath& CurPath, GW_Vector3D& Color, GW_Float rLineWidth )
{
glLineWidth( (GLfloat) rLineWidth );
glPointSize( (GLfloat) rLineWidth );
T_GeodesicPointList& PointList = CurPath.GetPointList();
glDisable( GL_LIGHTING );
glColor( Color );
glBegin( GL_LINE_STRIP );
for( IT_GeodesicPointList it = PointList.begin(); it!=PointList.end(); ++it )
{
GW_GeodesicPoint* pPoint = *it;
GW_ASSERT( pPoint->GetVertex1()!=NULL );
GW_ASSERT( pPoint->GetVertex2()!=NULL );
GW_Vector3D Pos = pPoint->GetVertex1()->GetPosition()*pPoint->GetCoord() +
pPoint->GetVertex2()->GetPosition()*(1-pPoint->GetCoord());
glColor( Color );
glVertex( Pos );
GW_GeodesicFace* pFace = pPoint->GetCurFace();
GW_ASSERT( pFace!=NULL );
T_SubPointVector& SubPointVector = pPoint->GetSubPointVector();
GW_Vector3D& v0 = pPoint->GetVertex1()->GetPosition();
GW_Vector3D& v1 = pPoint->GetVertex2()->GetPosition();
GW_Vertex* pLastVert = pFace->GetVertex( *pPoint->GetVertex1(), *pPoint->GetVertex2() );
GW_ASSERT( pLastVert!=NULL );
GW_Vector3D& v2 = pLastVert->GetPosition();
for( IT_SubPointVector it=SubPointVector.begin(); it!=SubPointVector.end(); ++it )
{
GW_Vector3D& coord = *it;
Pos = v0*coord[0] + v1*coord[1] + v2*coord[2];
glVertex( Pos );
}
}
glEnd();
#if 0
glColor3f( 0,0,0 );
glPointSize(4);
glBegin( GL_POINTS );
for( IT_GeodesicPointList it = PointList.begin(); it!=PointList.end(); ++it )
{
GW_GeodesicPoint* pPoint = *it;
GW_ASSERT( pPoint->GetVertex1()!=NULL );
GW_ASSERT( pPoint->GetVertex2()!=NULL );
GW_Vector3D Pos = pPoint->GetVertex1()->GetPosition()*pPoint->GetCoord() +
pPoint->GetVertex2()->GetPosition()*(1-pPoint->GetCoord());
glVertex( Pos );
GW_GeodesicFace* pFace = pPoint->GetCurFace();
GW_ASSERT( pFace!=NULL );
T_SubPointVector& SubPointVector = pPoint->GetSubPointVector();
GW_Vector3D& v0 = pPoint->GetVertex1()->GetPosition();
GW_Vector3D& v1 = pPoint->GetVertex2()->GetPosition();
GW_Vertex* pLastVert = pFace->GetVertex( *pPoint->GetVertex1(), *pPoint->GetVertex2() );
GW_ASSERT( pLastVert!=NULL );
GW_Vector3D& v2 = pLastVert->GetPosition();
for( IT_SubPointVector it=SubPointVector.begin(); it!=SubPointVector.end(); ++it )
{
GW_Vector3D& coord = *it;
Pos = v0*coord[0] + v1*coord[1] + v2*coord[2];
glVertex( Pos );
}
}
glEnd();
glEnable( GL_LIGHTING );
glLineWidth( 1 );
#endif
}