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+// This file is part of libigl, a simple c++ geometry processing library.
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+//
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+// Copyright (C) 2013 Olga Diamanti, 2015 Alec Jacobson
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+//
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+// This Source Code Form is subject to the terms of the Mozilla Public License
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+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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+// obtain one at http://mozilla.org/MPL/2.0/.
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+#ifndef IGL_CONJUGATE_FF_SOLVER_DATA_H
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+#define IGL_CONJUGATE_FF_SOLVER_DATA_H
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+#include "igl_inline.h"
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+#include <Eigen/Core>
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+#include <Eigen/Sparse>
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+
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+namespace igl {
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+ template <typename DerivedV, typename DerivedF>
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+ class ConjugateFFSolverData
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+ {
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+ public:
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+ const Eigen::PlainObjectBase<DerivedV> &V; int numV;
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+ const Eigen::PlainObjectBase<DerivedF> &F; int numF;
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+
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+ Eigen::MatrixXi EV; int numE;
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+ Eigen::MatrixXi F2E;
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+ Eigen::MatrixXi E2F;
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+ Eigen::VectorXd K;
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+
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+ Eigen::VectorXi isBorderEdge;
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+ int numInteriorEdges;
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+ Eigen::Matrix<int,Eigen::Dynamic,2> E2F_int;
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+ Eigen::VectorXi indInteriorToFull;
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+ Eigen::VectorXi indFullToInterior;
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+
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+ Eigen::PlainObjectBase<DerivedV> B1, B2, FN;
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+
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic,1> kmin, kmax;
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+ Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic,2> dmin, dmax;
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+ Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic,3> dmin3, dmax3;
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+
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+ Eigen::VectorXd nonPlanarityMeasure;
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+ Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > planarityWeight;
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+
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+ //conjugacy matrix
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+ std::vector<Eigen::Matrix<typename DerivedV::Scalar, 4,4> > H;
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+
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+ //conjugacy matrix eigenvectors and (scaled) eigenvalues
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+ std::vector<Eigen::Matrix<typename DerivedV::Scalar, 4,4> > UH;
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+ std::vector<Eigen::Matrix<typename DerivedV::Scalar, 4,1> > s;
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+
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+ //laplacians
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+ Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>> DDA, DDB;
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+
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+ private:
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+ IGL_INLINE void computeCurvatureAndPrincipals();
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+ IGL_INLINE void precomputeConjugacyStuff();
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+ IGL_INLINE void computeLaplacians();
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+ IGL_INLINE void computek();
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+ IGL_INLINE void computeCoefficientLaplacian(int n, Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &D);
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+
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+ IGL_INLINE void precomputeInteriorEdges();
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+
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+public:
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+ IGL_INLINE ConjugateFFSolverData(const Eigen::PlainObjectBase<DerivedV> &_V,
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+ const Eigen::PlainObjectBase<DerivedF> &_F);
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+ IGL_INLINE void evaluateConjugacy(const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> &pvU,
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+ const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> &pvV,
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+ Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 1> &conjValues) const ;
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+ };
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+}
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+
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+#include <igl/colon.h>
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+#include <igl/edge_topology.h>
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+#include <igl/false_barycentric_subdivision.h>
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+#include <igl/local_basis.h>
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+#include <igl/principal_curvature.h>
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+#include <igl/sparse.h>
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+
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+template <typename DerivedV, typename DerivedF>
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+IGL_INLINE igl::ConjugateFFSolverData<DerivedV, DerivedF>::
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+ConjugateFFSolverData(const Eigen::PlainObjectBase<DerivedV> &_V,
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+ const Eigen::PlainObjectBase<DerivedF> &_F):
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+V(_V),
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+numV(_V.rows()),
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+F(_F),
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+numF(_F.rows())
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+{
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+ igl::edge_topology(V,F,EV,F2E,E2F);
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+ numE = EV.rows();
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+
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+ precomputeInteriorEdges();
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+
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+ igl::local_basis(V,F,B1,B2,FN);
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+
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+ computek();
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+
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+ computeLaplacians();
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+
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+ computeCurvatureAndPrincipals();
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+ precomputeConjugacyStuff();
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+
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+};
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+
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+
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+template <typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::computeCurvatureAndPrincipals()
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+{
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+ Eigen::MatrixXd VCBary;
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+ Eigen::MatrixXi FCBary;
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+
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+ VCBary.setZero(numV+numF,3);
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+ FCBary.setZero(3*numF,3);
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+ igl::false_barycentric_subdivision(V, F, VCBary, FCBary);
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+
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+ Eigen::MatrixXd dmax3_,dmin3_;
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+ igl::principal_curvature(VCBary, FCBary, dmax3_, dmin3_, kmax, kmin, 5,true);
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+
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+ dmax3 = dmax3_.bottomRows(numF);
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+ dmin3 = dmin3_.bottomRows(numF);
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+
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+ kmax = kmax.bottomRows(numF);
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+ kmin = kmin.bottomRows(numF);
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+
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+ // kmax = dmax3.rowwise().norm();
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+ // kmin = dmin3.rowwise().norm();
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+
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+ dmin3.rowwise().normalize();
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+ dmax3.rowwise().normalize();
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+ dmax.setZero(numF,2);
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+ dmin.setZero(numF,2);
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+ for (int i= 0; i <numF; ++i)
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+ {
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+ if(kmin[i] != kmin[i] || kmax[i] != kmax[i] || (dmin3.row(i).array() != dmin3.row(i).array()).any() || (dmax3.row(i).array() != dmax3.row(i).array()).any())
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+ {
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+ kmin[i] = 0;
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+ kmax[i] = 0;
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+ dmin3.row(i) = B1.row(i);
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+ dmax3.row(i) = B2.row(i);
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+ }
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+ else
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+ {
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+ dmax3.row(i) = (dmax3.row(i) - (dmax3.row(i).dot(FN.row(i)))*FN.row(i)).normalized();
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+ dmin3.row(i) = dmin3.row(i) - (dmin3.row(i).dot(FN.row(i)))*FN.row(i);
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+ dmin3.row(i) = (dmin3.row(i) - (dmin3.row(i).dot(dmax3.row(i)))*dmax3.row(i)).normalized();
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+ if ((dmin3.row(i).cross(dmax3.row(i))).dot(FN.row(i))<0)
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+ dmin3.row(i) = -dmin3.row(i);
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+ }
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+ dmax.row(i) << dmax3.row(i).dot(B1.row(i)), dmax3.row(i).dot(B2.row(i));
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+ dmax.row(i).normalize();
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+ dmin.row(i) << dmin3.row(i).dot(B1.row(i)), dmin3.row(i).dot(B2.row(i));
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+ dmin.row(i).normalize();
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+
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+ }
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+
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+ nonPlanarityMeasure = kmax.cwiseAbs().array()*kmin.cwiseAbs().array();
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+ typename DerivedV::Scalar minP = nonPlanarityMeasure.minCoeff();
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+ typename DerivedV::Scalar maxP = nonPlanarityMeasure.maxCoeff();
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+ nonPlanarityMeasure = (nonPlanarityMeasure.array()-minP)/(maxP-minP);
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+ Eigen::VectorXi I = igl::colon<typename DerivedF::Scalar>(0, numF-1);
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+ igl::sparse(I, I, nonPlanarityMeasure, numF, numF, planarityWeight);
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+
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+}
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+
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+template <typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::precomputeConjugacyStuff()
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+{
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+ H.resize(numF);
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+ UH.resize(numF);
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+ s.resize(numF);
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+
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+ for (int i = 0; i<numF; ++i)
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+ {
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+ //compute conjugacy matrix
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+ typename DerivedV::Scalar e1x = dmin(i,0), e1y = dmin(i,1), e2x = dmax(i,0), e2y = dmax(i,1), k1 = kmin[i], k2 = kmax[i];
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+
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+ H[i]<<
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+ 0, 0, k1*e1x*e1x, k1*e1x*e1y,
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+ 0, 0, k1*e1x*e1y, k1*e1y*e1y,
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+ k2*e2x*e2x, k2*e2x*e2y, 0, 0,
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+ k2*e2x*e2y, k2*e2y*e2y, 0, 0;
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+ Eigen::Matrix<typename DerivedV::Scalar, 4, 4> Ht = H[i].transpose();
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+ H[i] = .5*(H[i]+Ht);
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+
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+ Eigen::EigenSolver<Eigen::Matrix<typename DerivedV::Scalar, 4, 4> > es(H[i]);
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+ s[i] = es.eigenvalues().real();//ok to do this because H symmetric
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+ //scale
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+ s[i] = s[i]/(s[i].cwiseAbs().minCoeff());
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+ UH[i] = es.eigenvectors().real();
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+
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+
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+ }
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+}
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+
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+
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+template <typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::computeLaplacians()
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+{
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+ computeCoefficientLaplacian(2, DDA);
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+
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+ computeCoefficientLaplacian(4, DDB);
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+}
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+
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+template<typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::
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+precomputeInteriorEdges()
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+{
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+ // Flag border edges
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+ numInteriorEdges = 0;
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+ isBorderEdge.setZero(numE,1);
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+ indFullToInterior = -1.*Eigen::VectorXi::Ones(numE,1);
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+
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+ for(unsigned i=0; i<numE; ++i)
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+ {
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+ if ((E2F(i,0) == -1) || ((E2F(i,1) == -1)))
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+ isBorderEdge[i] = 1;
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+ else
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+ {
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+ indFullToInterior[i] = numInteriorEdges;
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+ numInteriorEdges++;
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+ }
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+ }
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+
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+ E2F_int.resize(numInteriorEdges, 2);
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+ indInteriorToFull.setZero(numInteriorEdges,1);
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+ int ii = 0;
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+ for (int k=0; k<numE; ++k)
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+ {
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+ if (isBorderEdge[k])
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+ continue;
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+ E2F_int.row(ii) = E2F.row(k);
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+ indInteriorToFull[ii] = k;
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+ ii++;
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+ }
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+
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+}
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+
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+
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+
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+template<typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::
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+computeCoefficientLaplacian(int n, Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &D)
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+{
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+ std::vector<Eigen::Triplet<std::complex<typename DerivedV::Scalar> >> tripletList;
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+
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+ // For every non-border edge
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+ for (unsigned eid=0; eid<numE; ++eid)
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+ {
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+ if (!isBorderEdge[eid])
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+ {
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+ int fid0 = E2F(eid,0);
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+ int fid1 = E2F(eid,1);
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+
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+ tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
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+ fid0,
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+ std::complex<typename DerivedV::Scalar>(1.)));
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+ tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
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+ fid1,
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+ std::complex<typename DerivedV::Scalar>(1.)));
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+ tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
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+ fid1,
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+ -1.*std::polar(1.,-1.*n*K[eid])));
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+ tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
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+ fid0,
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+ -1.*std::polar(1.,1.*n*K[eid])));
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+
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+ }
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+ }
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+ D.resize(numF,numF);
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+ D.setFromTriplets(tripletList.begin(), tripletList.end());
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+
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+
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+}
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+
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+template<typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::
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+computek()
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+{
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+ K.setZero(numE);
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+ // For every non-border edge
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+ for (unsigned eid=0; eid<numE; ++eid)
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+ {
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+ if (!isBorderEdge[eid])
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+ {
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+ int fid0 = E2F(eid,0);
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+ int fid1 = E2F(eid,1);
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N0 = FN.row(fid0);
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N1 = FN.row(fid1);
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+
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+ // find common edge on triangle 0 and 1
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+ int fid0_vc = -1;
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+ int fid1_vc = -1;
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+ for (unsigned i=0;i<3;++i)
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+ {
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+ if (F2E(fid0,i) == eid)
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+ fid0_vc = i;
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+ if (F2E(fid1,i) == eid)
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+ fid1_vc = i;
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+ }
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+ assert(fid0_vc != -1);
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+ assert(fid1_vc != -1);
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> common_edge = V.row(F(fid0,(fid0_vc+1)%3)) - V.row(F(fid0,fid0_vc));
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+ common_edge.normalize();
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+
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+ // Map the two triangles in a new space where the common edge is the x axis and the N0 the z axis
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+ Eigen::Matrix<typename DerivedV::Scalar, 3, 3> P;
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> o = V.row(F(fid0,fid0_vc));
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> tmp = -N0.cross(common_edge);
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+ P << common_edge, tmp, N0;
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+ // P.transposeInPlace();
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+
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V0;
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+ V0.row(0) = V.row(F(fid0,0)) -o;
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+ V0.row(1) = V.row(F(fid0,1)) -o;
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+ V0.row(2) = V.row(F(fid0,2)) -o;
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+
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+ V0 = (P*V0.transpose()).transpose();
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V1;
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+ V1.row(0) = V.row(F(fid1,0)) -o;
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+ V1.row(1) = V.row(F(fid1,1)) -o;
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+ V1.row(2) = V.row(F(fid1,2)) -o;
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+ V1 = (P*V1.transpose()).transpose();
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+
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+ // compute rotation R such that R * N1 = N0
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+ // i.e. map both triangles to the same plane
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+ double alpha = -atan2(V1((fid1_vc+2)%3,2),V1((fid1_vc+2)%3,1));
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 3, 3> R;
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+ R << 1, 0, 0,
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+ 0, cos(alpha), -sin(alpha) ,
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+ 0, sin(alpha), cos(alpha);
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+ V1 = (R*V1.transpose()).transpose();
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+
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+ // measure the angle between the reference frames
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+ // k_ij is the angle between the triangle on the left and the one on the right
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref0 = V0.row(1) - V0.row(0);
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref1 = V1.row(1) - V1.row(0);
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+
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+ ref0.normalize();
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+ ref1.normalize();
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+
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+ double ktemp = atan2(ref1(1),ref1(0)) - atan2(ref0(1),ref0(0));
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+
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+ // just to be sure, rotate ref0 using angle ktemp...
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+ Eigen::Matrix<typename DerivedV::Scalar, 2, 2> R2;
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+ R2 << cos(ktemp), -sin(ktemp), sin(ktemp), cos(ktemp);
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+
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+ Eigen::Matrix<typename DerivedV::Scalar, 1, 2> tmp1 = R2*(ref0.head(2)).transpose();
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+
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+ K[eid] = ktemp;
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+ }
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+ }
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+
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+}
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+
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+template<typename DerivedV, typename DerivedF>
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+IGL_INLINE void igl::ConjugateFFSolverData<DerivedV, DerivedF>::
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+evaluateConjugacy(const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> &pvU,
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+ const Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 2> &pvV,
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+ Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 1> &conjValues) const
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|
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+{
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+ conjValues.resize(numF,1);
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+ for (int j =0; j<numF; ++j)
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+ {
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+ Eigen::Matrix<typename DerivedV::Scalar, 4, 1> x; x<<pvU.row(j).transpose(), pvV.row(j).transpose();
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+ conjValues[j] = x.transpose()*H[j]*x;
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+ }
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+}
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+
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+#endif
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