biharmonic coordinates tutorial example

Former-commit-id: 82b7b2261a2c5fac216ae941618daafd84405502

tutorial/407_BiharmonicCoordinates/CMakeLists.txt

@@ -0,0 +1,11 @@
+cmake_minimum_required(VERSION 2.6)
+project(407_BiharmonicCoordinates)
+
+include("../CMakeLists.shared")
+
+set(SOURCES
+${PROJECT_SOURCE_DIR}/main.cpp
+)
+
+add_executable(${PROJECT_NAME}_bin ${SOURCES} ${SHARED_SOURCES})
+target_link_libraries(${PROJECT_NAME}_bin ${SHARED_LIBRARIES})

tutorial/407_BiharmonicCoordinates/main.cpp

@@ -0,0 +1,167 @@
+#include <igl/arap.h>
+#include <igl/biharmonic_coordinates.h>
+#include <igl/cat.h>
+#include <igl/cotmatrix.h>
+#include <igl/massmatrix.h>
+#include <igl/matrix_to_list.h>
+#include <igl/parula.h>
+#include <igl/point_mesh_squared_distance.h>
+#include <igl/readDMAT.h>
+#include <igl/readMESH.h>
+#include <igl/remove_unreferenced.h>
+#include <igl/slice.h>
+#include <igl/writeDMAT.h>
+#include <igl/Viewer/viewer.h>
+#include <Eigen/Sparse>
+#include <iostream>
+#include <queue>
+
+struct Mesh
+{
+  Eigen::MatrixXd V,U;
+  Eigen::MatrixXi T,F;
+} low,high,scene;
+
+Eigen::MatrixXd W;
+igl::ARAPData arap_data;
+
+int main(int argc, char * argv[])
+{
+  using namespace Eigen;
+  using namespace std;
+  using namespace igl;
+  if(!readMESH("../shared/octopus-low.mesh",low.V,low.T,low.F))
+  {
+    cout<<"failed to load mesh"<<endl;
+  }
+  if(!readMESH("../shared/octopus-high.mesh",high.V,high.T,high.F))
+  {
+    cout<<"failed to load mesh"<<endl;
+  }
+
+  // Precomputation
+  {
+    Eigen::VectorXi b;
+    {
+      Eigen::VectorXi J = Eigen::VectorXi::LinSpaced(high.V.rows(),0,high.V.rows()-1);
+      Eigen::VectorXd sqrD;
+      Eigen::MatrixXd _2;
+      cout<<"Finding closest points..."<<endl;
+      igl::point_mesh_squared_distance(low.V,high.V,J,sqrD,b,_2);
+      assert(sqrD.minCoeff() < 1e-7 && "low.V should exist in high.V");
+    }
+    // force perfect positioning, rather have popping in low-res than high-res.
+    // The correct/elaborate thing to do is express original low.V in terms of
+    // linear interpolation (or extrapolation) via elements in (high.V,high.F)
+    igl::slice(high.V,b,1,low.V);
+    // list of points --> list of singleton lists
+    std::vector<std::vector<int> > S;
+    igl::matrix_to_list(b,S);
+    cout<<"Computing weights for "<<b.size()<<
+      " handles at "<<high.V.rows()<<" vertices..."<<endl;
+    // Technically k should equal 3 for smooth interpolation in 3d, but 2 is
+    // faster and looks OK
+    const int k = 2;
+    igl::biharmonic_coordinates(high.V,high.T,S,k,W);
+    cout<<"Reindexing..."<<endl;
+    // Throw away interior tet-vertices, keep weights and indices of boundary
+    VectorXi I,J;
+    igl::remove_unreferenced(high.V.rows(),high.F,I,J);
+    for_each(high.F.data(),high.F.data()+high.F.size(),[&I](int & a){a=I(a);});
+    for_each(b.data(),b.data()+b.size(),[&I](int & a){a=I(a);});
+    igl::slice(MatrixXd(high.V),J,1,high.V);
+    igl::slice(MatrixXd(W),J,1,W);
+  }
+
+  // Resize low res (high res will also be resized by affine precision of W)
+  low.V.rowwise() -= low.V.colwise().mean();
+  low.V /= (low.V.maxCoeff()-low.V.minCoeff());
+  low.V.rowwise() += RowVector3d(0,1,0);
+  low.U = low.V;
+  high.U = high.V;
+
+  arap_data.with_dynamics = true;
+  arap_data.max_iter = 10;
+  arap_data.energy = ARAP_ENERGY_TYPE_DEFAULT;
+  arap_data.h = 0.01;
+  arap_data.ym = 0.001;
+  if(!arap_precomputation(low.V,low.T,3,VectorXi(),arap_data))
+  {
+    cerr<<"arap_precomputation failed."<<endl;
+    return EXIT_FAILURE;
+  }
+  // Constant gravitational force
+  Eigen::SparseMatrix<double> M;
+  igl::massmatrix(low.V,low.T,igl::MASSMATRIX_TYPE_DEFAULT,M);
+  const size_t n = low.V.rows();
+  arap_data.f_ext =  M * RowVector3d(0,-9.8,0).replicate(n,1);
+  // Random initial velocities to wiggle things
+  arap_data.vel = MatrixXd::Random(n,3);
+  
+  igl::viewer::Viewer viewer;
+  // Create one huge mesh containing both meshes
+  igl::cat(1,low.U,high.U,scene.U);
+  igl::cat(1,low.F,MatrixXi(high.F.array()+low.V.rows()),scene.F);
+  // Color each mesh
+  viewer.data.set_mesh(scene.U,scene.F);
+  MatrixXd C(scene.F.rows(),3);
+  C<<
+    RowVector3d(0.8,0.5,0.2).replicate(low.F.rows(),1),
+    RowVector3d(0.3,0.4,1.0).replicate(high.F.rows(),1);
+  viewer.data.set_colors(C);
+
+  viewer.callback_key_pressed = 
+    [&](igl::viewer::Viewer & viewer,unsigned int key,int mods)->bool
+  {
+    switch(key)
+    {
+      default: 
+        return false;
+      case ' ':
+        viewer.core.is_animating = !viewer.core.is_animating;
+        return true;
+      case 'r':
+        low.U = low.V;
+        return true;
+    }
+  };
+  viewer.callback_pre_draw = [&](igl::viewer::Viewer & viewer)->bool
+  {
+    glEnable(GL_CULL_FACE);
+    if(viewer.core.is_animating)
+    {
+      arap_solve(MatrixXd(0,3),arap_data,low.U);
+      for(int v = 0;v<low.U.rows();v++)
+      {
+        // collide with y=0 plane
+        const int y = 1;
+        if(low.U(v,y) < 0)
+        {
+          low.U(v,y) = -low.U(v,y);
+          // ~ coefficient of restitution
+          const double cr = 1.1;
+          arap_data.vel(v,y) = - arap_data.vel(v,y) / cr;
+        }
+      }
+
+      scene.U.block(0,0,low.U.rows(),low.U.cols()) = low.U;
+      high.U = W * (low.U.rowwise() + RowVector3d(1,0,0));
+      scene.U.block(low.U.rows(),0,high.U.rows(),high.U.cols()) = high.U;
+
+      viewer.data.set_vertices(scene.U);
+      viewer.data.compute_normals();
+    }
+    return false;
+  };
+  viewer.core.show_lines = false;
+  viewer.core.is_animating = true;
+  viewer.core.animation_max_fps = 30.;
+  viewer.data.set_face_based(true);
+  cout<<R"(
+[space] to toggle animation
+'r'     to reset positions 
+      )";
+  viewer.core.rotation_type = 
+    igl::viewer::ViewerCore::ROTATION_TYPE_TWO_AXIS_VALUATOR_FIXED_UP;
+  viewer.launch();
+}

tutorial/CMakeLists.txt

@@ -86,6 +86,7 @@ add_subdirectory("403_BoundedBiharmonicWeights")
 add_subdirectory("404_DualQuaternionSkinning")
 add_subdirectory("405_AsRigidAsPossible")
 add_subdirectory("406_FastAutomaticSkinningTransformations")
+add_subdirectory("407_BiharmonicCoordinates")
 
 # Chapter 5
 add_subdirectory("501_HarmonicParam")

tutorial/images/octopus-biharmonic-coordinates-physics.gif.REMOVED.git-id

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+7f343ba934cc720eee4bda3fd7115f9c2ce5ea99

tutorial/shared/octopus-high.mesh.REMOVED.git-id

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+8b1bed500bb79187344ba4277f299c4b6d50bd8a

tutorial/shared/octopus-low.mesh

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+MeshVersionFormatted 1
+Dimension 3
+Vertices
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