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found a bug in PrincipaDirections, clean up of the function and better comments (thanks E.Puppo)

This commit is contained in:
ganovelli 2008-10-02 14:25:54 +00:00
parent 4f2be6a4ba
commit a0cdf71abf
1 changed files with 75 additions and 58 deletions
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133
vcg/complex/trimesh/update/curvature.h
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@ -108,87 +108,96 @@ private:
public:
/// \brief Compute principal direction and magniuto of curvature.
/**
Based on the paper <a href="http://mesh.caltech.edu/taubin/publications/taubin-iccv95b.pdf"> <em> "Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation" </em> </a>
/*
Compute principal direction and magniuto of curvature as describe in the paper:
@InProceedings{bb33922,
author = "G. Taubin",
title = "Estimating the Tensor of Curvature of a Surface from a
Polyhedral Approximation",
booktitle = "International Conference on Computer Vision",
year = "1995",
pages = "902--907",
URL = "http://dx.doi.org/10.1109/ICCV.1995.466840",
bibsource = "http://www.visionbib.com/bibliography/describe440.html#TT32253",
*/
static void PrincipalDirections(MeshType &m) {
assert(m.HasVFTopology());
vcg::tri::UpdateNormals<MeshType>::PerVertexNormalized(m);
vcg::tri::UpdateFlags<MeshType>::VertexBorderFromFace(m);
VertexIterator vi;
VertexIterator vi;
for (vi =m.vert.begin(); vi !=m.vert.end(); ++vi) {
if ( ! (*vi).IsD() && (*vi).VFp() != NULL) {
VertexType * central_vertex = &(*vi);
std::vector<float> weights;
std::vector<AdjVertex> vertices_dup,vertices;
std::vector<AdjVertex> vertices;
assert((*vi).VFp() != NULL);
vcg::face::JumpingPos<FaceType> pos((*vi).VFp(), central_vertex);
VertexType* firstV = pos.VFlip();
VertexType* tempV;
float totalDoubleAreaSize = 0.0f;
FaceType * startf = pos.F();
FaceType* tempF;
int hh = 0;
if (((firstV->cP()-central_vertex->cP())^(pos.VFlip()->cP()-central_vertex->cP()))*central_vertex->cN()<=0.0f)
{
pos.Set(central_vertex->VFp(), central_vertex);
pos.FlipE();
firstV = pos.VFlip();
}
else pos.Set(central_vertex->VFp(), central_vertex);
// compute the area of each triangle around the central vertex as well as their total area
do
{ hh++;
{
pos.NextE();
tempV = pos.VFlip();
AdjVertex v;
pos.FlipE();
v.vert = pos.VFlip();
v.doubleArea = vcg::DoubleArea(*pos.F());
vertices_dup.push_back(v);
v.isBorder = pos.IsBorder();
v.vert = tempV;
v.doubleArea = ((pos.F()->V(1)->cP() - pos.F()->V(0)->cP()) ^ (pos.F()->V(2)->cP()- pos.F()->V(0)->cP())).Norm();;
totalDoubleAreaSize += v.doubleArea;
pos.FlipE();
v.vert = pos.VFlip();
v.doubleArea = vcg::DoubleArea(*pos.F());
vertices_dup.push_back(v);
pos.NextFE();
tempF = pos.F();
vertices.push_back(v);
}
while(tempF != startf);
while(tempV != firstV);
AdjVertex v;
for(int i = 1 ; i <= vertices_dup.size(); )
{
v.vert = vertices_dup[(i)%vertices_dup.size()].vert;
v.doubleArea = vertices_dup[i%vertices_dup.size()].doubleArea ;
if( vertices_dup[(i)%vertices_dup.size()].vert == vertices_dup[(i+1)%vertices_dup.size()].vert){
v.doubleArea += vertices_dup[(i+1)%vertices_dup.size()].doubleArea;
i+=2;
}else
++i;
totalDoubleAreaSize+=v.doubleArea;
vertices.push_back(v);
// compute the weights for the formula computing matrix M
for (int i = 0; i < vertices.size(); ++i) {
if (vertices[i].isBorder) {
weights.push_back(vertices[i].doubleArea / totalDoubleAreaSize);
} else {
weights.push_back(0.5f * (vertices[i].doubleArea + vertices[(i-1)%vertices.size()].doubleArea) / totalDoubleAreaSize);
}
assert(weights.back() < 1.0f);
}
for (int i = 0; i < vertices.size(); ++i)
weights.push_back(vertices[i].doubleArea / totalDoubleAreaSize);
// compute I-NN^t to be used for computing the T_i's
Matrix33<ScalarType> Tp;
for (int i = 0; i < 3; ++i)
Tp[i][i] = 1.0f - powf(central_vertex->cN()[i],2);
Tp[0][1] = Tp[1][0] = -1.0f * (central_vertex->cN()[0] * central_vertex->cN()[1]);
Tp[0][1] = Tp[1][0] = -1.0f * (central_vertex->N()[0] * central_vertex->cN()[1]);
Tp[1][2] = Tp[2][1] = -1.0f * (central_vertex->cN()[1] * central_vertex->cN()[2]);
Tp[0][2] = Tp[2][0] = -1.0f * (central_vertex->cN()[0] * central_vertex->cN()[2]);
// for all neighbors vi compute the directional curvatures k_i and the T_i
// compute M by summing all w_i k_i T_i T_i^t
Matrix33<ScalarType> tempMatrix;
Matrix33<ScalarType> M;
M.SetZero();
for (int i = 0; i < vertices.size(); ++i) {
CoordType edge = (central_vertex->cP() - vertices[i].vert->cP());
float curvature = (2.0f * (central_vertex->cN() * edge) ) / edge.SquaredNorm();
CoordType T = (Tp*edge).Normalize()*(-1.0); // -1.0 useless, just to conform the paper
CoordType T = (Tp*edge).Normalize();
tempMatrix.ExternalProduct(T,T);
M += tempMatrix * weights[i] * curvature ;
}
// compute vector W for the Householder matrix
CoordType W;
CoordType e1(1.0f,0.0f,0.0f);
if ((e1 - central_vertex->cN()).SquaredNorm() > (e1 + central_vertex->cN()).SquaredNorm())
@ -197,6 +206,7 @@ public:
W = e1 + central_vertex->cN();
W.Normalize();
// compute the Householder matrix I - 2WW^t
Matrix33<ScalarType> Q;
Q.SetIdentity();
tempMatrix.ExternalProduct(W,W);
@ -204,18 +214,19 @@ public:
Matrix33<ScalarType> Qt(Q);
Qt.Transpose();
// compute matrix Q^t M Q
Matrix33<ScalarType> QtMQ = (Qt * M * Q);
CoordType bl = Q.GetColumn(0);
CoordType T1 = Q.GetColumn(1);
CoordType T2 = Q.GetColumn(2);
// find sin and cos for the Givens rotation
float s,c;
// Gabriel Taubin hint and Valentino Fiorin impementation
float qt21 = QtMQ[2][1];
float qt12 = QtMQ[1][2];
float alpha = QtMQ[1][1]-QtMQ[2][2];
float beta = QtMQ[2][1];
@ -229,7 +240,7 @@ public:
float min_error = std::numeric_limits<ScalarType>::infinity();
for (int i=0; i<2; i++)
{
delta = sqrtf(powf(h[1], 2) + 4.0f);
delta = sqrtf(powf(h[i], 2) + 4.0f);
t[0] = (h[i]+delta) / 2.0f;
t[1] = (h[i]-delta) / 2.0f;
@ -254,35 +265,41 @@ public:
c = best_c;
s = best_s;
vcg::Matrix33<ScalarType> minor22(QtMQ);
// clean up
minor22[0][0] = minor22[0][1] = minor22[0][2] = 0.0;
minor22[0][0] = minor22[1][0] = minor22[2][0] = 0.0;
vcg::ndim::MatrixMNf minor2x2 (2,2);
vcg::ndim::MatrixMNf S (2,2);
vcg::Matrix33<ScalarType> S; S.SetIdentity();
S[1][1] = S[2][2] = c;
S[1][2] = s;
S[2][1] = -1.0f * s;
vcg::Matrix33<ScalarType> St (S);
// diagonalize M
minor2x2[0][0] = QtMQ[1][1];
minor2x2[0][1] = QtMQ[1][2];
minor2x2[1][0] = QtMQ[2][1];
minor2x2[1][1] = QtMQ[2][2];
S[0][0] = S[1][1] = c;
S[0][1] = s;
S[1][0] = -1.0f * s;
vcg::ndim::MatrixMNf St (S);
St.Transpose();
vcg::Matrix33<ScalarType> StMS(St * minor22 * S);
vcg::ndim::MatrixMNf StMS(St * minor2x2 * S);
float Principal_Curvature1 = (3.0f * StMS[1][1]) - StMS[2][2];
float Principal_Curvature2 = (3.0f * StMS[2][2]) - StMS[1][1];
// compute curvatures and curvature directions
float Principal_Curvature1 = (3.0f * StMS[0][0]) - StMS[1][1];
float Principal_Curvature2 = (3.0f * StMS[1][1]) - StMS[0][0];
CoordType Principal_Direction1 = T1 * c - T2 * s;
CoordType Principal_Direction2 = T1 * s + T2 * c;
(*vi).PD1() = Principal_Direction1;
(*vi).PD2() = Principal_Direction2;
(*vi).K1() = Principal_Curvature1;
(*vi).K2() = Principal_Curvature2;
}
(*vi).K1() = Principal_Curvature1;
(*vi).K2() = Principal_Curvature2;
}
}
}
class AreaData