Merge commit '144c3f008c45a3151c394b74eb511de9b7d6d55f [formerly 807b0e55f5fe13bbfe501076912deed94980aaf0]'

# Conflicts:
#	optional/index.html
#	tutorial/CMakeLists.txt
#	tutorial/tutorial.html


Former-commit-id: 6cdadb0ba827cf7f329ae3658e0c79dbef7d3421

include/igl/shapeup.cpp

@@ -0,0 +1,182 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <igl/shapeup.h>
+#include <igl/min_quad_with_fixed.h>
+#include <igl/igl_inline.h>
+#include <igl/setdiff.h>
+#include <igl/cat.h>
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl
+{
+  
+  template <
+  typename DerivedP,
+  typename DerivedSC,
+  typename DerivedS,
+  typename Derivedw>
+  IGL_INLINE bool shapeup_precomputation(const Eigen::PlainObjectBase<DerivedP>& P,
+                                         const Eigen::PlainObjectBase<DerivedSC>& SC,
+                                         const Eigen::PlainObjectBase<DerivedS>& S,
+                                         const Eigen::PlainObjectBase<DerivedS>& E,
+                                         const Eigen::PlainObjectBase<DerivedSC>& b,
+                                         const Eigen::PlainObjectBase<Derivedw>& wShape,
+                                         const Eigen::PlainObjectBase<Derivedw>& wSmooth,
+                                         ShapeupData & sudata)
+  {
+      using namespace std;
+      using namespace Eigen;
+      sudata.P=P;
+      sudata.SC=SC;
+      sudata.S=S;
+      sudata.b=b;
+      typedef typename DerivedP::Scalar Scalar;
+      
+      //checking for consistency of the input
+      assert(SC.rows()==S.rows());
+      assert(SC.rows()==wShape.rows());
+      assert(E.rows()==wSmooth.rows());
+      assert(b.rows()!=0);  //would lead to matrix becoming SPD
+      
+      sudata.DShape.conservativeResize(SC.sum(), P.rows());  //Shape matrix (integration);
+      sudata.DClose.conservativeResize(b.rows(), P.rows());  //Closeness matrix for positional constraints
+      sudata.DSmooth.conservativeResize(E.rows(), P.rows());  //smoothness matrix
+        
+      //Building shape matrix
+      std::vector<Triplet<Scalar> > DShapeTriplets;
+      int currRow=0;
+      for (int i=0;i<S.rows();i++){
+          Scalar avgCoeff=1.0/(Scalar)SC(i);
+            
+          for (int j=0;j<SC(i);j++){
+            for (int k=0;k<SC(i);k++){
+              if (j==k)
+                DShapeTriplets.push_back(Triplet<Scalar>(currRow+j, S(i,k), (1.0-avgCoeff)));
+              else
+                DShapeTriplets.push_back(Triplet<Scalar>(currRow+j, S(i,k), (-avgCoeff)));
+            }
+          }
+        currRow+=SC(i);
+        
+      }
+ 
+      sudata.DShape.setFromTriplets(DShapeTriplets.begin(), DShapeTriplets.end());
+
+      //Building closeness matrix
+      std::vector<Triplet<Scalar> > DCloseTriplets;
+      for (int i=0;i<b.size();i++)
+        DCloseTriplets.push_back(Triplet<Scalar>(i,b(i), 1.0));
+      
+      sudata.DClose.setFromTriplets(DCloseTriplets.begin(), DCloseTriplets.end());
+      
+      //Building smoothness matrix
+      std::vector<Triplet<Scalar> > DSmoothTriplets;
+      for (int i=0; i<E.rows(); i++) {
+        DSmoothTriplets.push_back(Triplet<Scalar>(i, E(i, 0), -1));
+        DSmoothTriplets.push_back(Triplet<Scalar>(i, E(i, 1), 1));
+      }
+        
+      SparseMatrix<Scalar> tempMat;
+      igl::cat(1, sudata.DShape, sudata.DClose, tempMat);
+      igl::cat(1, tempMat, sudata.DSmooth, sudata.A);
+        
+      //weight matrix
+      vector<Triplet<Scalar> > WTriplets;
+        
+      //one weight per set in S.
+      currRow=0;
+      for (int i=0;i<SC.rows();i++){
+          for (int j=0;j<SC(i);j++)
+              WTriplets.push_back(Triplet<double>(currRow+j,currRow+j,sudata.shapeCoeff*wShape(i)));
+          currRow+=SC(i);
+      }
+        
+      for (int i=0;i<b.size();i++)
+          WTriplets.push_back(Triplet<double>(SC.sum()+i, SC.sum()+i, sudata.closeCoeff));
+        
+      for (int i=0;i<E.rows();i++)
+          WTriplets.push_back(Triplet<double>(SC.sum()+b.size()+i, SC.sum()+b.size()+i, sudata.smoothCoeff*wSmooth(i)));
+        
+      sudata.W.conservativeResize(SC.sum()+b.size()+E.rows(), SC.sum()+b.size()+E.rows());
+      sudata.W.setFromTriplets(WTriplets.begin(), WTriplets.end());
+        
+      sudata.At=sudata.A.transpose();  //for efficieny, as we use the transpose a lot in the iteration
+      sudata.Q=sudata.At*sudata.W*sudata.A;
+
+      return min_quad_with_fixed_precompute(sudata.Q,VectorXi(),SparseMatrix<double>(),true,sudata.solver_data);
+  }
+
+
+  template <
+  typename DerivedP,
+  typename DerivedSC,
+  typename DerivedS>
+  IGL_INLINE bool shapeup_solve(const Eigen::PlainObjectBase<DerivedP>& bc,
+                                const std::function<bool(const Eigen::PlainObjectBase<DerivedP>&, const Eigen::PlainObjectBase<DerivedSC>&, const Eigen::PlainObjectBase<DerivedS>&,  Eigen::PlainObjectBase<DerivedP>&)>& local_projection,
+                                const Eigen::PlainObjectBase<DerivedP>& P0,
+                                const ShapeupData & sudata,
+                                const bool quietIterations,
+                                Eigen::PlainObjectBase<DerivedP>& P)
+  {
+    using namespace Eigen;
+    using namespace std;
+    MatrixXd currP=P0;
+    MatrixXd prevP=P0;
+    MatrixXd projP;
+    
+    assert(bc.rows()==sudata.b.rows());
+    
+		MatrixXd rhs(sudata.A.rows(), 3); rhs.setZero();
+    rhs.block(sudata.DShape.rows(), 0, sudata.b.rows(),3)=bc;  //this stays constant throughout the iterations
+        
+    if (!quietIterations){
+        cout<<"Shapeup Iterations, "<<sudata.DShape.rows()<<" constraints, solution size "<<P0.size()<<endl;
+        cout<<"**********************************************************************************************"<<endl;
+    }
+    projP.conservativeResize(sudata.SC.rows(), 3*sudata.SC.maxCoeff());
+    for (int iter=0;iter<sudata.maxIterations;iter++){
+      
+      local_projection(currP, sudata.SC,sudata.S,projP);
+            
+      //constructing the projection part of the (DShape rows of the) right hand side
+      int currRow=0;
+      for (int i=0;i<sudata.S.rows();i++)
+        for (int j=0;j<sudata.SC(i);j++)
+          rhs.row(currRow++)=projP.block(i, 3*j, 1,3);
+      
+      Eigen::PlainObjectBase<DerivedP> lsrhs=-sudata.At*sudata.W*rhs;
+      MatrixXd Y(0,3), Beq(0,3);  //We do not use the min_quad_solver fixed variables mechanism; they are treated with the closeness energy of ShapeUp.
+      min_quad_with_fixed_solve(sudata.solver_data, lsrhs,Y,Beq,currP);
+      
+      double currChange=(currP-prevP).lpNorm<Infinity>();
+      if (!quietIterations)
+        cout << "Iteration "<<iter<<", integration Linf error: "<<currChange<< endl;
+      prevP=currP;
+      if (currChange<sudata.pTolerance){
+        P=currP;
+        return true;
+      }
+    }
+    
+    P=currP;
+    return false;  //we went over maxIterations
+    
+  }
+}
+
+
+
+
+
+#ifdef IGL_STATIC_LIBRARY
+template bool igl::shapeup_precomputation< typename Eigen::Matrix<double, -1, -1, 0, -1, -1>, typename Eigen::Matrix<int, -1, 1, 0, -1, 1>, typename Eigen::Matrix<int, -1, -1, 0, -1, -1>, typename Eigen::Matrix<double, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, igl::ShapeupData&);
+
+template bool igl::shapeup_solve<typename Eigen::Matrix<double, -1, -1, 0, -1, -1>, typename Eigen::Matrix<int, -1, 1, 0, -1, 1>, typename Eigen::Matrix<int, -1, -1, 0, -1, -1> >(const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& bc, const std::function<bool(const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, const Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, const Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&,  Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& ) >& local_projection, const Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& P0, const igl::ShapeupData & sudata, const bool quietIterations, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >& P);
+#endif

include/igl/shapeup.h

@@ -0,0 +1,113 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_SHAPEUP_H
+#define IGL_SHAPEUP_H
+
+#include <igl/shapeup_local_projections.h>
+#include <igl/min_quad_with_fixed.h>
+#include <igl/igl_inline.h>
+#include <igl/setdiff.h>
+#include <igl/cat.h>
+#include <Eigen/Core>
+#include <vector>
+
+
+//This file implements the following algorithm:
+
+//Boaziz et al.
+//Shape-Up: Shaping Discrete Geometry with Projections
+//Computer Graphics Forum (Proc. SGP) 31(5), 2012
+
+namespace igl
+{
+  struct ShapeupData{
+    //input data
+    Eigen::MatrixXd P;
+    Eigen::VectorXi SC;
+    Eigen::MatrixXi S;
+    Eigen::VectorXi b;
+    int maxIterations; //referring to number of local-global pairs.
+    double pTolerance;   //algorithm stops when max(|P_k-P_{k-1}|)<pTolerance.
+    double shapeCoeff, closeCoeff, smoothCoeff;
+          
+    //Internally-used matrices
+    Eigen::SparseMatrix<double> DShape, DClose, DSmooth, Q, A, At, W;
+          
+    min_quad_with_fixed_data<double> solver_data;
+          
+    ShapeupData():
+    maxIterations(50),
+    pTolerance(10e-6),
+    shapeCoeff(1.0),
+    closeCoeff(100.0),
+    smoothCoeff(0.0){}
+  };
+      
+    
+    
+  //This function precomputation the necessary matrices for the ShapeUp process, and prefactorizes them.
+    
+  //input:
+  //  P   #P by 3             point positions
+  //  SC  #Set by 1           cardinalities of sets in S
+  //  S   #Sets by max(SC)    independent sets where the local projection applies. Values beyond column SC(i)-1 in row S(i,:) are "don't care"
+  //  E   #E by 2             the "edges" of the set P; used for the smoothness energy.
+  //  b   #b by 1             boundary (fixed) vertices from P.
+  //  wShape,   #Set by 1
+  //  wSmooth   #b by 1       weights for constraints from S and positional constraints (used in the global step)
+
+  // Output:
+  //  sudata struct ShapeupData     the data necessary to solve the system in shapeup_solve
+
+  template <
+  typename DerivedP,
+  typename DerivedSC,
+  typename DerivedS,
+  typename Derivedw>
+  IGL_INLINE bool shapeup_precomputation(const Eigen::PlainObjectBase<DerivedP>& P,
+                                         const Eigen::PlainObjectBase<DerivedSC>& SC,
+                                         const Eigen::PlainObjectBase<DerivedS>& S,
+                                         const Eigen::PlainObjectBase<DerivedS>& E,
+                                         const Eigen::PlainObjectBase<DerivedSC>& b,
+                                         const Eigen::PlainObjectBase<Derivedw>& wShape,
+                                         const Eigen::PlainObjectBase<Derivedw>& wSmooth,
+                                         ShapeupData & sudata);
+    
+    
+    
+  //This function solve the shapeup project optimization. shapeup_precompute must be called before with the same sudata, or results are unpredictable
+    
+  //Input:
+  //bc                #b by 3 fixed point values corresonding to "b" in sudata
+  //local_projection  function pointer taking (P,SC,S,projP),
+  // where the first three parameters are as defined, and "projP" is the output, as a #S by 3*max(SC) function in format xyzxyzxyz, and where it returns the projected points corresponding to each set in S in the same order.
+  //NOTE: the input values in P0 don't need to correspond to prescribed values in bc; the iterations will project them automatically (by design).
+  //P0                #P by 3 initial solution (point positions)
+  //sudata            the ShapeUpData structure computed in shapeup_precomputation()
+  //quietIterations   flagging if to output iteration information.
+
+  //Output:
+  //P                 the solution to the problem, indices corresponding to P0.
+  template <
+  typename DerivedP,
+  typename DerivedSC,
+  typename DerivedS>
+  IGL_INLINE bool shapeup_solve(const Eigen::PlainObjectBase<DerivedP>& bc,
+                                const std::function<bool(const Eigen::PlainObjectBase<DerivedP>&, const Eigen::PlainObjectBase<DerivedSC>&, const Eigen::PlainObjectBase<DerivedS>&,  Eigen::PlainObjectBase<DerivedP>&)>& local_projection,
+                                const Eigen::PlainObjectBase<DerivedP>& P0,
+                                const ShapeupData & sudata,
+                                const bool quietIterations,
+                                Eigen::PlainObjectBase<DerivedP>& P);
+  
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "shapeup.cpp"
+#endif
+
+#endif

include/igl/shapeup_local_projections.cpp

@@ -0,0 +1,78 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <igl/shapeup_local_projections.h>
+#include <igl/igl_inline.h>
+#include <igl/setdiff.h>
+#include <igl/cat.h>
+#include <Eigen/Core>
+#include <vector>
+
+
+//This file implements several basic local projection functions for the shapeup algorithm in shapeup.h
+
+namespace igl
+{
+  
+  //This projection does nothing but render points into projP. Mostly used for "echoing" the global step
+  IGL_INLINE bool shapeup_identity_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S,  Eigen::PlainObjectBase<Eigen::MatrixXd>& projP){
+    projP.conservativeResize(SC.rows(), 3*SC.maxCoeff());
+    for (int i=0;i<S.rows();i++){
+      Eigen::RowVector3d avgCurrP=Eigen::RowVector3d::Zero();
+      for (int j=0;j<SC(i);j++)
+        avgCurrP+=P.row(S(i,j))/(double)(SC(i));
+  
+      for (int j=0;j<SC(i);j++)
+        projP.block(i,3*j,1,3)=P.row(S(i,j))-avgCurrP;
+    }
+    return true;
+  }
+  
+  
+  //the projection assumes that the sets are vertices of polygons in order
+  IGL_INLINE bool shapeup_regular_face_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S,  Eigen::PlainObjectBase<Eigen::MatrixXd>& projP){
+    projP.conservativeResize(SC.rows(), 3*SC.maxCoeff());
+    for (int currRow=0;currRow<SC.rows();currRow++){
+    //computing average
+      int N=SC(currRow);
+      const Eigen::RowVectorXi SRow=S.row(currRow);
+      Eigen::RowVector3d avgCurrP=Eigen::RowVector3d::Zero();
+      Eigen::MatrixXd targetPolygon(N, 3);
+      Eigen::MatrixXd sourcePolygon(N, 3);
+      for (int j=0;j<N;j++)
+        avgCurrP+=P.row(SRow(j))/(double)(N);
+  
+      for (int j=0;j<N;j++)
+        targetPolygon.row(j)=P.row(SRow(j))-avgCurrP;
+  
+      //creating perfectly regular source polygon
+      for (int j=0;j<N;j++)
+        sourcePolygon.row(j)<<cos(2*M_PI*(double)j/(double(N))), sin(2*M_PI*(double)j/(double(N))),0.0;
+  
+      //finding closest similarity transformation between source and target
+      Eigen::MatrixXd corrMat=sourcePolygon.transpose()*targetPolygon;
+      Eigen::JacobiSVD<Eigen::Matrix3d> svd(corrMat, Eigen::ComputeFullU | Eigen::ComputeFullV);
+      Eigen::MatrixXd R=svd.matrixU()*svd.matrixV().transpose();
+      //getting scale by edge length change average. TODO: by singular values
+      Eigen::VectorXd sourceEdgeLengths(N);
+      Eigen::VectorXd targetEdgeLengths(N);
+      for (int j=0;j<N;j++){
+        sourceEdgeLengths(j)=(sourcePolygon.row((j+1)%N)-sourcePolygon.row(j)).norm();
+        targetEdgeLengths(j)=(targetPolygon.row((j+1)%N)-targetPolygon.row(j)).norm();
+      }
+      double scale=(targetEdgeLengths.cwiseQuotient(sourceEdgeLengths)).mean();
+  
+      for (int j=0;j<N;j++)
+        projP.block(currRow,3*j,1,3)=sourcePolygon.row(j)*R*scale;
+    }
+  
+    return true;
+  }
+
+}
+

include/igl/shapeup_local_projections.h

@@ -0,0 +1,46 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_SHAPEUP_LOCAL_PROJECTIONS_H
+#define IGL_SHAPEUP_LOCAL_PROJECTIONS_H
+
+#include <igl/igl_inline.h>
+#include <igl/setdiff.h>
+#include <igl/cat.h>
+#include <Eigen/Core>
+#include <vector>
+
+
+
+
+namespace igl
+{
+
+	//Every function here defines a local projection for ShapeUp, and must have the following structure to qualify:
+	//Input:
+	//	P		#P by 3				the set of points, either the initial solution, or from previous iteration.
+	//  SC		#Set by 1           cardinalities of sets in S
+	//  S		#Sets by max(SC)    independent sets where the local projection applies. Values beyond column SC(i)-1 in row S(i,:) are "don't care"
+	//Output:
+	//	projP	#S by 3*max(SC) in format xyzxyzxyz,  where the projected points correspond to each set in S in the same order.
+	typedef std::function<bool(const Eigen::PlainObjectBase<Eigen::MatrixXd>&, const Eigen::PlainObjectBase<Eigen::VectorXi>&, const Eigen::PlainObjectBase<Eigen::MatrixXi>&, Eigen::PlainObjectBase<Eigen::MatrixXd>&)> shapeup_projection_function;
+
+  
+  //This projection does nothing but render points into projP. Mostly used for "echoing" the global step
+  IGL_INLINE bool shapeup_identity_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S,  Eigen::PlainObjectBase<Eigen::MatrixXd>& projP);
+  
+  //the projection assumes that the sets are vertices of polygons in cyclic order
+  IGL_INLINE bool shapeup_regular_face_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S,  Eigen::PlainObjectBase<Eigen::MatrixXd>& projP);
+  
+ 
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "shapeup_local_projections.cpp"
+#endif
+
+#endif

tutorial/713_ShapeUp/CMakeLists.txt

@@ -0,0 +1,5 @@
+cmake_minimum_required(VERSION 2.8.12)
+project(713_ShapeUp)
+
+add_executable(${PROJECT_NAME}_bin main.cpp)
+target_link_libraries(${PROJECT_NAME}_bin igl::core igl::opengl igl::opengl_glfw tutorials)

tutorial/713_ShapeUp/main.cpp

@@ -0,0 +1,156 @@
+#include <igl/avg_edge_length.h>
+#include <igl/barycenter.h>
+#include <igl/jet.h>
+#include <igl/shapeup.h>
+#include <igl/shapeup_local_projections.h>
+#include <igl/quad_planarity.h>
+#include <igl/readDMAT.h>
+#include <igl/readOFF.h>
+#include <igl/slice.h>
+#include <igl/opengl/glfw/Viewer.h>
+#include <igl/PI.h>
+#include <vector>
+#include <cstdlib>
+
+#include "tutorial_shared_path.h"
+
+// Quad mesh loaded
+Eigen::MatrixXd VQC;
+Eigen::MatrixXi FQC;
+Eigen::MatrixXi E;
+Eigen::MatrixXi FQCtri;
+Eigen::MatrixXd PQC0, PQC1, PQC2, PQC3;
+// Euclidean-regular quad mesh
+Eigen::MatrixXd VQCregular;
+Eigen::MatrixXi FQCtriregular;
+Eigen::MatrixXd PQC0regular, PQC1regular, PQC2regular, PQC3regular;
+
+igl::ShapeupData su_data;
+
+
+
+// Scale for visualizing the fields
+double global_scale; //TODO: not used
+
+void quadAngleRegularity(const Eigen::MatrixXd& V, const Eigen::MatrixXi& Q, Eigen::VectorXd& angleRegularity)
+{
+  angleRegularity.conservativeResize(Q.rows());
+  angleRegularity.setZero();
+  for (int i=0;i<Q.rows();i++){
+    for (int j=0;j<4;j++){
+      Eigen::RowVectorXd v21=(V.row(Q(i,j))-V.row(Q(i,(j+1)%4))).normalized();
+      Eigen::RowVectorXd v23=(V.row(Q(i,(j+2)%4))-V.row(Q(i,(j+1)%4))).normalized();
+  
+      angleRegularity(i)+=(abs(acos(v21.dot(v23))-igl::PI/2.0)/(igl::PI/2.0))/4.0;
+    }
+  }
+}
+
+
+bool key_down(igl::opengl::glfw::Viewer& viewer, unsigned char key, int modifier)
+{
+  using namespace std;
+  using namespace Eigen;
+
+  // Plot the original quad mesh
+  
+  if (key == '1')
+  {
+    viewer.data().clear();
+    // Draw the triangulated quad mesh
+    viewer.data().set_mesh(VQC, FQCtri);
+
+    // Assign a color to each quad that corresponds to the average deviation of each angle from pi/2
+    VectorXd angleRegularity(FQC.rows());
+    quadAngleRegularity( VQC, FQC, angleRegularity);
+    MatrixXd Ct;
+    igl::jet(angleRegularity, 0.0, 0.05, Ct);
+    MatrixXd C(FQCtri.rows(),3);
+    C << Ct, Ct;
+    viewer.data().set_colors(C);
+
+    // Plot a line for each edge of the quad mesh
+    viewer.data().add_edges(PQC0, PQC1, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC1, PQC2, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC2, PQC3, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC3, PQC0, Eigen::RowVector3d(0,0,0));
+  }
+
+  // Plot the planarized quad mesh
+  if (key == '2')
+  {
+    viewer.data().clear();
+    // Draw the triangulated quad mesh
+    viewer.data().set_mesh(VQCregular, FQCtri);
+
+    // Assign a color to each quad that corresponds to its planarity
+    VectorXd angleRegularity(FQC.rows());
+    quadAngleRegularity( VQCregular, FQC, angleRegularity);
+    MatrixXd Ct;
+    igl::jet(angleRegularity, 0, 0.05, Ct);
+    MatrixXd C(FQCtri.rows(),3);
+    C << Ct, Ct;
+    viewer.data().set_colors(C);
+
+    // Plot a line for each edge of the quad mesh
+    viewer.data().add_edges(PQC0regular, PQC1regular, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC1regular, PQC2regular, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC2regular, PQC3regular, Eigen::RowVector3d(0,0,0));
+    viewer.data().add_edges(PQC3regular, PQC0regular, Eigen::RowVector3d(0,0,0));
+  }
+
+  return false;
+}
+
+int main(int argc, char *argv[])
+{
+  using namespace Eigen;
+  using namespace std;
+
+  // Load a quad mesh
+  igl::readOFF(TUTORIAL_SHARED_PATH "/halftunnel.off", VQC, FQC);
+
+  // Convert it in a triangle mesh
+  FQCtri.resize(2*FQC.rows(), 3);
+  FQCtri <<  FQC.col(0),FQC.col(1),FQC.col(2),
+             FQC.col(2),FQC.col(3),FQC.col(0);
+  igl::slice( VQC, FQC.col(0).eval(), 1, PQC0);
+  igl::slice( VQC, FQC.col(1).eval(), 1, PQC1);
+  igl::slice( VQC, FQC.col(2).eval(), 1, PQC2);
+  igl::slice( VQC, FQC.col(3).eval(), 1, PQC3);
+
+  // Create a planar version with ShapeUp
+  //igl::planarize_quad_mesh(VQC, FQC, 100, 0.005, VQCregular);
+  
+  E.resize(FQC.size(),2);
+  E.col(0)<<FQC.col(0),FQC.col(1),FQC.col(2),FQC.col(3);
+  E.col(1)<<FQC.col(1),FQC.col(2),FQC.col(3),FQC.col(0);
+  
+  VectorXi b(1); b(0)=0;  //setting the first vertex to be the same.
+  
+  VectorXd wShape=VectorXd::Constant(FQC.rows(),1.0);
+  VectorXd wSmooth=VectorXd::Constant(E.rows(),1.0);
+  MatrixXd bc(1,3); bc<<VQC.row(0);
+  
+  VectorXi array_of_fours=VectorXi::Constant(FQC.rows(),4);
+  igl::shapeup_projection_function localFunction(igl::shapeup_regular_face_projection);
+  
+  su_data.maxIterations=200;
+  shapeup_precomputation(VQC, array_of_fours,FQC,E,b,wShape, wSmooth,su_data);
+  shapeup_solve(bc,localFunction, VQC,su_data, false,VQCregular);
+  
+
+  // Convert the planarized mesh to triangles
+  igl::slice( VQCregular, FQC.col(0).eval(), 1, PQC0regular);
+  igl::slice( VQCregular, FQC.col(1).eval(), 1, PQC1regular);
+  igl::slice( VQCregular, FQC.col(2).eval(), 1, PQC2regular);
+  igl::slice( VQCregular, FQC.col(3).eval(), 1, PQC3regular);
+
+  // Launch the viewer
+  igl::opengl::glfw::Viewer viewer;
+  key_down(viewer,'1',0);
+  viewer.data().invert_normals = true;
+  viewer.data().show_lines = false;
+  viewer.callback_key_down = &key_down;
+  viewer.launch();
+}

tutorial/CMakeLists.txt

@@ -147,4 +147,7 @@ if(TUTORIALS_CHAPTER7)
   add_subdirectory("710_SLIM")
   add_subdirectory("711_Subdivision")
   add_subdirectory("712_DataSmoothing")
+  add_subdirectory("713_ShapeUp")
 endif()
+
+

tutorial/images/713_ShapeUp.png.REMOVED.git-id

@@ -0,0 +1 @@
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