File size: 3,036 Bytes
5b89cb9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 | #include <igl/barycenter.h>
#include <igl/cotmatrix.h>
#include <igl/doublearea.h>
#include <igl/grad.h>
#include <igl/jet.h>
#include <igl/massmatrix.h>
#include <igl/per_vertex_normals.h>
#include <igl/readDMAT.h>
#include <igl/readOFF.h>
#include <igl/repdiag.h>
#include <igl/opengl/glfw/Viewer.h>
#include <iostream>
Eigen::MatrixXd V,U;
Eigen::MatrixXi F;
Eigen::SparseMatrix<double> L;
igl::opengl::glfw::Viewer viewer;
int main(int argc, char *argv[])
{
using namespace Eigen;
using namespace std;
// Load a mesh in OFF format
igl::readOFF(TUTORIAL_SHARED_PATH "/cow.off", V, F);
// Compute Laplace-Beltrami operator: #V by #V
igl::cotmatrix(V,F,L);
// Alternative construction of same Laplacian
SparseMatrix<double> G,K;
// Gradient/Divergence
igl::grad(V,F,G);
// Diagonal per-triangle "mass matrix"
VectorXd dblA;
igl::doublearea(V,F,dblA);
// Place areas along diagonal #dim times
const auto & T = 1.*(dblA.replicate(3,1)*0.5).asDiagonal();
// Laplacian K built as discrete divergence of gradient or equivalently
// discrete Dirichelet energy Hessian
K = -G.transpose() * T * G;
cout<<"|K-L|: "<<(K-L).norm()<<endl;
const auto &key_down = [](igl::opengl::glfw::Viewer &viewer,unsigned char key,int mod)->bool
{
switch(key)
{
case 'r':
case 'R':
U = V;
break;
case ' ':
{
// Recompute just mass matrix on each step
SparseMatrix<double> M;
igl::massmatrix(U,F,igl::MASSMATRIX_TYPE_BARYCENTRIC,M);
// Solve (M-delta*L) U = M*U
const auto & S = (M - 0.001*L);
Eigen::SimplicialLLT<Eigen::SparseMatrix<double > > solver(S);
assert(solver.info() == Eigen::Success);
U = solver.solve(M*U).eval();
// Compute centroid and subtract (also important for numerics)
VectorXd dblA;
igl::doublearea(U,F,dblA);
double area = 0.5*dblA.sum();
MatrixXd BC;
igl::barycenter(U,F,BC);
RowVector3d centroid(0,0,0);
for(int i = 0;i<BC.rows();i++)
{
centroid += 0.5*dblA(i)/area*BC.row(i);
}
U.rowwise() -= centroid;
// Normalize to unit surface area (important for numerics)
U.array() /= sqrt(area);
break;
}
default:
return false;
}
// Send new positions, update normals, recenter
viewer.data().set_vertices(U);
viewer.data().compute_normals();
viewer.core().align_camera_center(U,F);
return true;
};
// Use original normals as pseudo-colors
MatrixXd N;
igl::per_vertex_normals(V,F,N);
MatrixXd C = N.rowwise().normalized().array()*0.5+0.5;
// Initialize smoothing with base mesh
U = V;
viewer.data().set_mesh(U, F);
viewer.data().set_colors(C);
viewer.callback_key_down = key_down;
cout<<"Press [space] to smooth."<<endl;;
cout<<"Press [r] to reset."<<endl;;
return viewer.launch();
}
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