Checkpoint
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1 changed files with 214 additions and 5 deletions
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@ -2,6 +2,23 @@
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#include <unordered_map>
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#include <utility>
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#include <functional>
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#include <iostream>
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/**
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* @brief Compute the vertices and faces after Catmull-Clark subdivision. Perform one pass of the refinement scheme.
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*
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* Inputs:
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* @param V #V by 3 list of vertex positions
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* @param F #F by 4 list of quad mesh indices into V
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* Outputs:
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* @param SV #SV by 3 list of vertex positions after subdivision
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* @param SF #SF by 4 list of quad mesh indices into SV after subdivision
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*/
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void subdivide_quadmesh_catmullclark(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXi & F,
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Eigen::MatrixXd & SV,
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Eigen::MatrixXi & SF);
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void catmull_clark(
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const Eigen::MatrixXd & V,
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@ -10,9 +27,201 @@ void catmull_clark(
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Eigen::MatrixXd & SV,
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Eigen::MatrixXi & SF)
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{
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////////////////////////////////////////////////////////////////////////////
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// Replace with your code here:
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SV = V;
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SF = F;
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////////////////////////////////////////////////////////////////////////////
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Eigen::MatrixXd SVX = V;
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Eigen::MatrixXi SFX = F;
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for (int i = 0; i < num_iters; i++) {
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subdivide_quadmesh_catmullclark(SVX, SFX, SV, SF);
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SVX = SV;
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SFX = SF;
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}
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}
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/**
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* @brief Compute the centroid of a face.
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*
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* Inputs:
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* @param V #V by 3 list of vertex positions
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* @param f 4 by 1 list of face indices into V
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* Outputs:
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* @return 1 by 3 list of the face centroid
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*/
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Eigen::RowVector3d compute_face_centroid(
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const Eigen::MatrixXd & V,
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const Eigen::RowVector4i & f)
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{
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return (V.row(f[0]) + V.row(f[1]) + V.row(f[2]) + V.row(f[3])) / 4.0;
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}
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/**
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* @brief Compute the average point of an edge.
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*
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* Inputs:
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* @param V #V by 3 list of vertex positions
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* @param F #F by 4 list of quad mesh indices into V
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* @param FC #F by 3 list of face centroids
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* @param e 2 by 1 list of edge indices into V, which make up the edge
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* Outputs:
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* @return 1 by 3 list of the edge average point
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*/
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Eigen::RowVector3d compute_edge_average_point(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXi & F,
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const Eigen::MatrixXd & FC,
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const Eigen::RowVector2i & e)
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{
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/* M + E */
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Eigen::RowVector3d edge_average_point = V.row(e[0]) + V.row(e[1]);
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/* Determine the two faces that share the edge: A + F */
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int counter = 0;
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for (int i = 0; i < F.rows(); i++) {
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for (int j = 0; j < F.cols(); j++) {
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if (F(i, j) == e[0] && (F(i, (j + 1) % 4) == e[1] || F(i, (j + 3) % 4) == e[1])) {
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edge_average_point += FC.row(i);
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counter++;
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}
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}
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}
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if (counter != 2) {
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throw std::runtime_error("An edge should be shared by exactly two faces.");
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}
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/* (A + F + M + E) / 4 */
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return edge_average_point / 4.0;
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}
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/**
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* @brief Compute the vertex position after Catmull-Clark subdivision.
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*
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* Inputs:
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* @param V #V by 3 list of vertex positions
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* @param F #F by 4 list of quad mesh indices into V
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* @param v index of the vertex to be moved
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* Outputs:
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* @return 1 by 3 list of the new vertex position
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*/
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Eigen::RowVector3d compute_vertex_moved_position(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXi & F,
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const Eigen::MatrixXd & FC,
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const int v)
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{
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Eigen::RowVector3d part_F = Eigen::RowVector3d::Zero();
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Eigen::RowVector3d part_R = Eigen::RowVector3d::Zero();
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/* Determine the faces that share the vertex: F */
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int n = 0;
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for (int i = 0; i < F.rows(); i++) {
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for (int j = 0; j < F.cols(); j++) {
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if (F(i, j) == v) {
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part_F += FC.row(i);
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n++;
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}
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}
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}
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if (n == 0) {
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std::cerr << "Error: A vertex should be shared by at least one face, but it is shared by " << n << " faces." << std::endl;
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throw std::runtime_error("A vertex should be shared by at least one face.");
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}
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/* Determine the edges that share the vertex: 2R */
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/* NOTE that the edge midpoint point is computed twice for each edge */
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int m = 0;
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for (int i = 0; i < F.rows(); i++) {
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for (int j = 0; j < F.cols(); j++) {
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if (F(i, j) == v) {
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part_R += (V.row(F(i, (j + 3) % 4)) + V.row(F(i, j))) / 2.0;
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part_R += (V.row(F(i, j)) + V.row(F(i, (j + 1) % 4))) / 2.0;
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m++;
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}
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}
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}
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if (n != m) {
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std::cerr << "Error: A vertex should be shared by exactly two edges, but it is shared by " << m << " edges." << std::endl;
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throw std::runtime_error("A vertex should be shared by exactly two edges.");
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}
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/* (F + 2R + (n - 3)P) / n */
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return (part_F + part_R + (n - 3) * V.row(v)) / n;
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}
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struct RowVector2iHash {
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std::size_t operator()(const Eigen::RowVector2i & v) const {
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return std::hash<int>()(v[0]) ^ std::hash<int>()(v[1]);
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}
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};
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void subdivide_quadmesh_catmullclark(
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const Eigen::MatrixXd & V,
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const Eigen::MatrixXi & F,
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Eigen::MatrixXd & SV,
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Eigen::MatrixXi & SF)
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{
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SV.resize(V.rows() + 3 * F.rows(), 3); // Moved vertices + face centroids + edge average points
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SF.resize(F.rows() * 4, 4);
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std::unordered_map<Eigen::RowVector2i, int, RowVector2iHash> EAP; // Edge average points
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for (int i = 0; i < F.rows(); i++) { /* For each face */
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/* Compute face centroids: FC */
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SV.row(V.rows() + i) = compute_face_centroid(V, F.row(i));
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/* Compute edge average points */
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for (int j = 0; j < F.cols(); j++) { /* For each edge of that face */
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int v1 = std::min(F(i, j), F(i, (j + 1) % 4));
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int v2 = std::max(F(i, j), F(i, (j + 1) % 4));
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/* Check if the edge has been computed before */
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if (EAP.find(Eigen::RowVector2i(v1, v2)) == EAP.end()) {
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SV.row(V.rows() + F.rows() + EAP.size()) = compute_edge_average_point(
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V,
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F,
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SV.block(V.rows(), 0, F.rows(), 3),
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Eigen::RowVector2i(v1, v2));
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EAP[Eigen::RowVector2i(v1, v2)] = V.rows() + F.rows() + EAP.size();
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}
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}
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}
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/* Compute moved vertices: MV */
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/* Vertices get moved but retain their original indices. */
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for (int i = 0; i < V.rows(); i++) {
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SV.row(i) = compute_vertex_moved_position(V, F, SV.block(V.rows(), 0, F.rows(), 3), i);
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}
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/* Compute the faces */
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for (int i = 0; i < F.rows(); i++) { /* For each face */
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int face_centroid = V.rows() + i;
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int edge_average_points[4] = {
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EAP.at(Eigen::RowVector2i(std::min(F(i, 0), F(i, 1)), std::max(F(i, 0), F(i, 1)))),
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EAP.at(Eigen::RowVector2i(std::min(F(i, 1), F(i, 2)), std::max(F(i, 1), F(i, 2)))),
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EAP.at(Eigen::RowVector2i(std::min(F(i, 2), F(i, 3)), std::max(F(i, 2), F(i, 3)))),
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EAP.at(Eigen::RowVector2i(std::min(F(i, 3), F(i, 0)), std::max(F(i, 3), F(i, 0))))
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};
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SF.row(4 * i + 0) = Eigen::RowVector4i(
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F(i, 0),
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edge_average_points[0],
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face_centroid,
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edge_average_points[3]);
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SF.row(4 * i + 1) = Eigen::RowVector4i(
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edge_average_points[0],
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F(i, 1),
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edge_average_points[1],
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face_centroid);
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SF.row(4 * i + 2) = Eigen::RowVector4i(
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face_centroid,
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edge_average_points[1],
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F(i, 2),
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edge_average_points[2]);
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SF.row(4 * i + 3) = Eigen::RowVector4i(
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edge_average_points[3],
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face_centroid,
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edge_average_points[2],
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F(i, 3));
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}
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}
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