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- # This file is part of libigl, a simple c++ geometry processing library.
- #
- # Copyright (C) 2017 Sebastian Koch <s.koch@tu-berlin.de> and Daniele Panozzo <daniele.panozzo@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/.
- import sys, os
- # Add the igl library to the modules search path
- sys.path.insert(0, os.getcwd() + "/../")
- import pyigl as igl
- from shared import TUTORIAL_SHARED_PATH, check_dependencies
- dependencies = ["viewer"]
- check_dependencies(dependencies)
- V = igl.eigen.MatrixXd()
- F = igl.eigen.MatrixXi()
- igl.readOFF(TUTORIAL_SHARED_PATH + "camelhead.off", V, F)
- # Find boundary edges
- E = igl.eigen.MatrixXi()
- igl.boundary_facets(F, E)
- # Find boundary vertices
- b = igl.eigen.MatrixXi()
- IA = igl.eigen.MatrixXi()
- IC = igl.eigen.MatrixXi()
- igl.unique(E, b, IA, IC)
- # List of all vertex indices
- vall = igl.eigen.MatrixXi()
- vin = igl.eigen.MatrixXi()
- igl.coloni(0, V.rows() - 1, vall)
- # List of interior indices
- igl.setdiff(vall, b, vin, IA)
- # Construct and slice up Laplacian
- L = igl.eigen.SparseMatrixd()
- L_in_in = igl.eigen.SparseMatrixd()
- L_in_b = igl.eigen.SparseMatrixd()
- igl.cotmatrix(V, F, L)
- igl.slice(L, vin, vin, L_in_in)
- igl.slice(L, vin, b, L_in_b)
- # Dirichlet boundary conditions from z-coordinate
- bc = igl.eigen.MatrixXd()
- Z = V.col(2)
- igl.slice(Z, b, bc)
- # Solve PDE
- solver = igl.eigen.SimplicialLLTsparse(-L_in_in)
- Z_in = solver.solve(L_in_b * bc)
- # slice into solution
- igl.slice_into(Z_in, vin, Z)
- # Alternative, short hand
- mqwf = igl.min_quad_with_fixed_data()
- # Linear term is 0
- B = igl.eigen.MatrixXd()
- B.setZero(V.rows(), 1)
- # Empty constraints
- Beq = igl.eigen.MatrixXd()
- Aeq = igl.eigen.SparseMatrixd()
- # Our cotmatrix is _negative_ definite, so flip sign
- igl.min_quad_with_fixed_precompute(-L, b, Aeq, True, mqwf)
- igl.min_quad_with_fixed_solve(mqwf, B, bc, Beq, Z)
- # Pseudo-color based on solution
- C = igl.eigen.MatrixXd()
- igl.jet(Z, True, C)
- # Plot the mesh with pseudocolors
- viewer = igl.viewer.Viewer()
- viewer.data.set_mesh(V, F)
- viewer.core.show_lines = False
- viewer.data.set_colors(C)
- viewer.launch()
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