void operator() (const TriMesh *themesh, int v0, vec &c,
float w, int v) const
{
vec ncurv;
proj_curv(themesh->pdir1[v], themesh->pdir2[v],
themesh->curv1[v], 0, themesh->curv2[v],
themesh->pdir1[v0], themesh->pdir2[v0],
ncurv[0], ncurv[1], ncurv[2]);
c += w * ncurv;
}
void Curvature::computePrincipalCurvatures( Surface_mesh * src_mesh )
{
computePointAreas(src_mesh);
uint nv = src_mesh->n_vertices(), nf = src_mesh->n_faces();
curv1.resize(nv);
curv2.resize(nv);
pdir1.resize(nv);
pdir2.resize(nv);
std::vector<double> curv12(nv);
Surface_mesh::Vertex_property<Point> points = src_mesh->vertex_property<Point>("v:point");
Surface_mesh::Vertex_property<Normal> normals = src_mesh->vertex_property<Normal>("v:normal");
Surface_mesh::Face_iterator fit, fend = src_mesh->faces_end();
Surface_mesh::Vertex_around_face_circulator fvit, fvend;
Surface_mesh::Vertex_iterator vit, vend = src_mesh->vertices_end();
//#pragma omp parallel for
for (fit = src_mesh->faces_begin(); fit != fend; ++fit)
{
fvit = src_mesh->vertices(fit);
uint vi0 = ((Vertex)fvit).idx(); Point v0 = points[fvit]; ++fvit;
uint vi1 = ((Vertex)fvit).idx(); Point v1 = points[fvit]; ++fvit;
uint vi2 = ((Vertex)fvit).idx(); Point v2 = points[fvit];
pdir1[vi0] = v1 - v0;
pdir1[vi1] = v2 - v1;
pdir1[vi2] = v0 - v2;
}
//#pragma omp parallel for
for (vit = src_mesh->vertices_begin(); vit != vend; ++vit)
{
uint vi = ((Vertex)vit).idx();
pdir1[vi] = cross(pdir1[vi], normals[vit]);
pdir1[vi].normalize();
pdir2[vi] = cross(normals[vit], pdir1[vi]);
}
// Compute curvature per-face
//#pragma omp parallel for
for (fit = src_mesh->faces_begin(); fit != fend; ++fit)
{
uint i = ((Surface_mesh::Face)fit).idx(); // face index
uint vi[3]; Normal vn[3];
fvit = src_mesh->vertices(fit);
vi[0] = ((Vertex)fvit).idx(); Point v0 = points[fvit]; vn[0] = normals[fvit]; ++fvit;
vi[1] = ((Vertex)fvit).idx(); Point v1 = points[fvit]; vn[1] = normals[fvit]; ++fvit;
vi[2] = ((Vertex)fvit).idx(); Point v2 = points[fvit]; vn[2] = normals[fvit]; ++fvit;
// Edges
Point e[3] = {v2 - v1, v0 - v2, v1 - v0};
// N-T-B coordinate system per face
Point t = e[0];
t.normalize();
Point n = cross(e[0], e[1]);
Point b = cross(n, t);
b.normalize();
// Estimate curvature based on variation of normals
// along edges
double m[3] = { 0, 0, 0 };
double w[3][3] = { {0,0,0}, {0,0,0}, {0,0,0} };
for (int j = 0; j < 3; j++) {
double u = dot(e[j], t);
double v = dot(e[j], b);
w[0][0] += u*u;
w[0][1] += u*v;
//w[1][1] += v*v + u*u;
//w[1][2] += u*v;
w[2][2] += v*v;
Point dn = vn[PREV_Index(j)] - vn[NEXT_Index(j)];
double dnu = dot(dn, t);
double dnv = dot(dn, b);
m[0] += dnu*u;
m[1] += dnu*v + dnv*u;
m[2] += dnv*v;
}
w[1][1] = w[0][0] + w[2][2];
w[1][2] = w[0][1];
// Least squares solution
double diag[3];
if (!ldltdc<double,3>(w, diag)) {
//printf("ldltdc failed!\n");
continue;
}
ldltsl<double,3>(w, diag, m, m);
// Push it back out to the vertices
for (uint j = 0; j < 3; j++)
{
int vj = vi[j];
double c1, c12, c2;
proj_curv(t, b, m[0], m[1], m[2], pdir1[vj], pdir2[vj], c1, c12, c2);
double wt = cornerareas[i][j] / pointareas[vj];
//#pragma omp atomic
curv1[vj] += wt * c1;
//#pragma omp atomic
curv12[vj] += wt * c12;
//#pragma omp atomic
curv2[vj] += wt * c2;
}
}
// Store results into Surface_mesh object
Surface_mesh::Vertex_property<double> my_curv1 = src_mesh->vertex_property<double>("v:curv1");
Surface_mesh::Vertex_property<double> my_curv2 = src_mesh->vertex_property<double>("v:vurv2");
Surface_mesh::Vertex_property<Vec3d> my_pdir1 = src_mesh->vertex_property<Vec3d>("v:pdir1");
Surface_mesh::Vertex_property<Vec3d> my_pdir2 = src_mesh->vertex_property<Vec3d>("v:pdir2");
// Compute principal directions and curvatures at each vertex
//#pragma omp parallel for
for (vit = src_mesh->vertices_begin(); vit != vend; ++vit)
{
uint i = ((Surface_mesh::Vertex)vit).idx();
diagonalize_curv(pdir1[i], pdir2[i],curv1[i], curv12[i], curv2[i], normals[vit], pdir1[i], pdir2[i],curv1[i], curv2[i]);
my_curv1[vit] = curv1[i];
my_curv2[vit] = curv2[i];
my_pdir1[vit] = pdir1[i];
my_pdir2[vit] = pdir2[i];
}
}
// Compute derivatives of curvature
void Curvature::computeDerivativesCurvatures(Surface_mesh * src_mesh)
{
// Compute principal curvatures and directions
computePrincipalCurvatures(src_mesh);
Surface_mesh::Vertex_property<Point> points = src_mesh->vertex_property<Point>("v:point");
Surface_mesh::Vertex_property<Normal> normals = src_mesh->vertex_property<Normal>("v:normal");
Surface_mesh::Face_iterator fit, fend = src_mesh->faces_end();
Surface_mesh::Vertex_around_face_circulator fvit, fvend;
// Resize the arrays we'll be using
uint nv = src_mesh->n_vertices(), nf = src_mesh->n_faces();
dcurv.resize(nv);
// Compute derivatives of curvature per-face
//#pragma omp parallel for
for (fit = src_mesh->faces_begin(); fit != fend; ++fit)
{
uint i = ((Surface_mesh::Face)fit).idx(); // face index
uint vi[3]; Normal vn[3];
fvit = src_mesh->vertices(fit);
vi[0] = ((Vertex)fvit).idx(); Point v0 = points[fvit]; vn[0] = normals[fvit]; ++fvit;
vi[1] = ((Vertex)fvit).idx(); Point v1 = points[fvit]; vn[1] = normals[fvit]; ++fvit;
vi[2] = ((Vertex)fvit).idx(); Point v2 = points[fvit]; vn[2] = normals[fvit]; ++fvit;
// Edges
Point e[3] = {v2 - v1, v0 - v2, v1 - v0};
// N-T-B coordinate system per face
Point t = e[0];
t.normalize();
Point n = cross(e[0], e[1]);
Point b = cross(n, t);
b.normalize();
// Project curvature tensor from each vertex into this
// face's coordinate system
Point fcurv[3];
for (int j = 0; j < 3; j++)
{
int vj = vi[j];
proj_curv(pdir1[vj], pdir2[vj], curv1[vj], 0, curv2[vj],t, b, fcurv[j][0], fcurv[j][1], fcurv[j][2]);
}
// Estimate derivatives of curvature based on variation of curvature along edges
double m[4] = {0,0,0,0};
double w[4][4] = { {0,0,0,0}, {0,0,0,0}, {0,0,0,0}, {0,0,0,0} };
for (int j = 0; j < 3; j++)
{
// Variation of curvature along each edge
Point dfcurv = fcurv[PREV_Index(j)] - fcurv[NEXT_Index(j)];
double u = dot(e[j], t);
double v = dot(e[j], b);
double u2 = u*u, v2 = v*v, uv = u*v;
w[0][0] += u2;
w[0][1] += uv;
//w[1][1] += 2.0f*u2 + v2;
//w[1][2] += 2.0f*uv;
//w[2][2] += u2 + 2.0f*v2;
//w[2][3] += uv;
w[3][3] += v2;
m[0] += u*dfcurv[0];
m[1] += v*dfcurv[0] + 2.0f*u*dfcurv[1];
m[2] += 2.0f*v*dfcurv[1] + u*dfcurv[2];
m[3] += v*dfcurv[2];
}
w[1][1] = 2.0f * w[0][0] + w[3][3];
w[1][2] = 2.0f * w[0][1];
w[2][2] = w[0][0] + 2.0f * w[3][3];
w[2][3] = w[0][1];
// Least squares solution
double d[4];
if (!ldltdc<double,4>(w, d))
{
//printf("ldltdc failed!\n");
continue;
}
ldltsl<double,4>(w, d, m, m);
Vec4d face_dcurv(m[0], m[1], m[2], m[3]);
// Push it back out to each vertex
for (int j = 0; j < 3; j++)
{
int vj = vi[j];
Vec4d this_vert_dcurv;
proj_dcurv(t, b, face_dcurv, pdir1[vj], pdir2[vj], this_vert_dcurv);
double wt = cornerareas[i][j] / pointareas[vj];
dcurv[vj] += wt * this_vert_dcurv;
}
}
Surface_mesh::Vertex_property<Vec4d> my_dcurv = src_mesh->vertex_property<Vec4d>("v:dcurv");
Surface_mesh::Vertex_iterator vit, vend = src_mesh->vertices_end();
for (vit = src_mesh->vertices_begin(); vit != vend; ++vit){
uint i = ((Vertex) vit).idx();
my_dcurv[vit] = dcurv[i];
}
}