libigl_Martin/python/tutorial/303_LaplaceEquation.py

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()