129 lines
4.6 KiB
C++
129 lines
4.6 KiB
C++
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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) 2016 Alec Jacobson <alecjacobson@gmail.com>
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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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#include <igl/parallel_transport_angles.h>
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#include <Eigen/Geometry>
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template <typename DerivedV, typename DerivedF, typename DerivedK>
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IGL_INLINE void igl::parallel_transport_angles(
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const Eigen::PlainObjectBase<DerivedV>& V,
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const Eigen::PlainObjectBase<DerivedF>& F,
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const Eigen::PlainObjectBase<DerivedV>& FN,
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const Eigen::MatrixXi &E2F,
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const Eigen::MatrixXi &F2E,
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Eigen::PlainObjectBase<DerivedK> &K)
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{
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int numE = E2F.rows();
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Eigen::VectorXi isBorderEdge;
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isBorderEdge.setZero(numE,1);
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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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}
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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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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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// 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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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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// 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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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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V0 = (P*V0.transpose()).transpose();
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// assert(V0(0,2) < 1e-10);
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// assert(V0(1,2) < 1e-10);
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// assert(V0(2,2) < 1e-10);
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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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// assert(V1(fid1_vc,2) < 10e-10);
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// assert(V1((fid1_vc+1)%3,2) < 10e-10);
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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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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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// assert(V1(0,2) < 1e-10);
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// assert(V1(1,2) < 1e-10);
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// assert(V1(2,2) < 1e-10);
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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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ref0.normalize();
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ref1.normalize();
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double ktemp = atan2(ref1(1),ref1(0)) - atan2(ref0(1),ref0(0));
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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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// Eigen::Matrix<typename DerivedV::Scalar, 1, 2> tmp1 = R2*(ref0.head(2)).transpose();
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// assert(tmp1(0) - ref1(0) < 1e-10);
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// assert(tmp1(1) - ref1(1) < 1e-10);
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K[eid] = ktemp;
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}
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}
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template void igl::parallel_transport_angles<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, 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<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
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#endif
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