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main.cpp
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#include <igl/opengl/glfw/Viewer.h>
#include <igl/triangle/triangulate.h>
#include <Eigen/Sparse>
#include <vector>
#include <igl/boundary_loop.h>
#include <Eigen/Dense>
#include <igl/opengl/glfw/imgui/ImGuiMenu.h>
#include <igl/opengl/glfw/imgui/ImGuiHelpers.h>
#include <imgui/imgui.h>
#include <igl/cotmatrix.h>
double elasticEnergy(const Eigen::VectorXd &q, const Eigen::MatrixXi &F, const Eigen::MatrixXd &origV,
Eigen::VectorXd &deriv, std::vector<Eigen::Triplet<double> > &hess)
{
int nverts = origV.rows();
double result = 0;
deriv.resize(3 * nverts);
deriv.setZero();
hess.clear();
double kstretch = 500.0;
int nfaces = F.rows();
for (int i = 0; i < nfaces; i++)
{
Eigen::Vector3i face = F.row(i);
for (int v1 = 0; v1 < 3; v1++)
{
int v2 = (v1 + 1) % 3;
Eigen::Vector3d op1 = origV.row(face[v1]);
Eigen::Vector3d op2 = origV.row(face[v2]);
double odist = (op1 - op2).norm();
Eigen::Vector3d p1 = q.segment<3>(3 * face[v1]);
Eigen::Vector3d p2 = q.segment<3>(3 * face[v2]);
double dist = (p1 - p2).norm();
if (dist < odist)
continue;
result += 0.5 * kstretch * (dist - odist)*(dist - odist) / odist / odist;
deriv.segment<3>(3 * face[v1]) += kstretch * (dist - odist) * (p1 - p2) / dist / odist / odist;
deriv.segment<3>(3 * face[v2]) -= kstretch * (dist - odist) * (p1 - p2) / dist / odist / odist;
Eigen::Matrix3d I;
I.setIdentity();
Eigen::Matrix3d localH = kstretch*(p1 - p2)*(p1 - p2).transpose() / dist / dist / odist / odist + kstretch * (dist - odist) * (I / dist - (p1 - p2)*(p1 - p2).transpose() / dist / dist / dist) / odist / odist;
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
{
hess.push_back(Eigen::Triplet<double>(3 * face[v1] + j, 3 * face[v1] + k, localH(j, k)));
hess.push_back(Eigen::Triplet<double>(3 * face[v1] + j, 3 * face[v2] + k, -localH(j, k)));
hess.push_back(Eigen::Triplet<double>(3 * face[v2] + j, 3 * face[v1] + k, -localH(j, k)));
hess.push_back(Eigen::Triplet<double>(3 * face[v2] + j, 3 * face[v2] + k, localH(j, k)));
}
}
}
double pressure = 1e-3;
for (int i = 0; i < nfaces; i++)
{
Eigen::Vector3d v0 = q.segment<3>(3 * F(i, 0));
Eigen::Vector3d v1 = q.segment<3>(3 * F(i, 1));
Eigen::Vector3d v2 = q.segment<3>(3 * F(i, 2));
result -= pressure / 6.0 * (v0.cross(v1).dot(v2));
Eigen::Vector3d n = (v1 - v0).cross(v2 - v0);
for (int j = 0; j < 3; j++)
{
deriv.segment<3>(3 * F(i, j)) -= pressure / 6.0 * n;
}
}
return result;
}
void createMesh(double w, double h, double triarea, Eigen::MatrixXd &V, Eigen::MatrixXi &F)
{
Eigen::MatrixXd rectV(4, 2);
Eigen::MatrixXi rectE(4, 2);
Eigen::MatrixXi H(0, 2);
rectV << -w / 2, -h / 2,
w / 2, -h / 2,
w / 2, h / 2,
-w / 2, h / 2;
rectE << 0, 1,
1, 2,
2, 3,
3, 0;
std::stringstream ss;
ss << "a" << triarea << "q";
// Triangulate the interior
igl::triangle::triangulate(rectV, rectE, H, ss.str().c_str(), V, F);
int nverts = V.rows();
V.conservativeResize(nverts, 3);
V.col(2).setZero();
}
double computeVolume(const Eigen::MatrixXd &V, const Eigen::MatrixXi &F)
{
double result = 0.0;
int nfaces = F.rows();
for (int i = 0; i < nfaces; i++)
{
Eigen::Vector3d v0 = V.row(F(i, 0)).transpose();
Eigen::Vector3d v1 = V.row(F(i, 1)).transpose();
Eigen::Vector3d v2 = V.row(F(i, 2)).transpose();
result += 1.0 / 6.0 * (v0.cross(v1)).dot(v2);
}
return result;
}
void takeOneStep(Eigen::MatrixXd &curV, const Eigen::MatrixXd &origV, const Eigen::MatrixXi &F, std::set<int> clamped,
double ®)
{
int nverts = curV.rows();
int freeDOFs = 3 * nverts - clamped.size();
std::vector<Eigen::Triplet<double> > proj;
int row = 0;
for (int i = 0; i < nverts; i++)
{
for (int j = 0; j < 2; j++)
{
proj.push_back(Eigen::Triplet<double>(row, 3 * i + j, 1.0));
row++;
}
if (!clamped.count(i))
{
proj.push_back(Eigen::Triplet<double>(row, 3 * i + 2, 1.0));
row++;
}
}
Eigen::SparseMatrix<double> projM(freeDOFs, 3 * nverts);
projM.setFromTriplets(proj.begin(), proj.end());
while (true)
{
Eigen::VectorXd q(3 * nverts);
for (int i = 0; i < nverts; i++)
{
q.segment<3>(3 * i) = curV.row(i).transpose();
}
Eigen::VectorXd derivative;
std::vector<Eigen::Triplet<double> > hessian;
double energy = elasticEnergy(q, F, origV, derivative, hessian);
Eigen::SparseMatrix<double> H(3 * nverts, 3 * nverts);
H.setFromTriplets(hessian.begin(), hessian.end());
Eigen::VectorXd reducedDeriv = projM * derivative;
Eigen::SparseMatrix<double> reducedH = projM * H * projM.transpose();
Eigen::SparseMatrix<double> I(freeDOFs, freeDOFs);
I.setIdentity();
reducedH += reg * I;
Eigen::SimplicialLDLT<Eigen::SparseMatrix<double> > solver(reducedH);
Eigen::VectorXd descentDir = solver.solve(-reducedDeriv);
std::cout << "Solver residual: " << (reducedH*descentDir + reducedDeriv).norm() << std::endl;
Eigen::VectorXd fullDir = projM.transpose() * descentDir;
Eigen::MatrixXd newPos = curV;
for (int i = 0; i < nverts; i++)
{
newPos.row(i) += fullDir.segment<3>(3 * i);
}
Eigen::VectorXd newq = q + fullDir;
double newenergy = elasticEnergy(newq, F, origV, derivative, hessian);
if (newenergy <= energy)
{
std::cout << "Old energy: " << energy << " new energy: " << newenergy << std::endl;
std::cout << "Volume is " << computeVolume(newPos, F) << std::endl;
curV = newPos;
reg = std::max(1e-6, reg/2.0);
break;
}
else
{
reg *= 2.0;
std::cout << "Old energy: " << energy << " new energy: " << newenergy << " lambda now: " << reg << std::endl;
}
}
}
Eigen::MatrixXd origV;
Eigen::MatrixXd curV;
Eigen::MatrixXi F;
std::set<int> clamped;
void reset()
{
curV = origV;
}
void repaint(igl::opengl::glfw::Viewer &viewer)
{
viewer.data().clear();
viewer.data().set_mesh(curV, F);
}
int main(int argc, char *argv[])
{
createMesh(210, 297, 5.0, origV, F);
curV = origV;
std::vector<std::vector<int> > bdry;
igl::boundary_loop(F, bdry);
assert(bdry.size() == 1);
for (int i : bdry[0])
clamped.insert(i);
// Plot the mesh
igl::opengl::glfw::Viewer viewer;
viewer.data().set_mesh(origV, F);
viewer.data().set_face_based(true);
// Attach a menu plugin
igl::opengl::glfw::imgui::ImGuiMenu menu;
viewer.plugins.push_back(&menu);
// Add content to the default menu window
menu.callback_draw_viewer_menu = [&]()
{
// Draw parent menu content
menu.draw_viewer_menu();
// Add new group
if (ImGui::CollapsingHeader("Optimization", ImGuiTreeNodeFlags_DefaultOpen))
{
if (ImGui::Button("Reset", ImVec2(-1, 0)))
{
reset();
repaint(viewer);
}
if (ImGui::Button("Optimize Some Step", ImVec2(-1, 0)))
{
double reg = 1e-6;
for (int i = 0; i < 100; i++)
{
takeOneStep(curV, origV, F, clamped, reg);
}
repaint(viewer);
}
if (ImGui::Button("Save Meshes", ImVec2(-1, 0)))
{
igl::writeOBJ("rect.obj", origV, F);
igl::writeOBJ("solved.obj", curV, F);
}
}
};
viewer.launch();
}