Toolbox Graph

A toolbox to perform computations on graph.

Description

Graph theory toolbox
Copyright (c) 2007 Gabriel Peyre

This toolbox contains useful functions to deal with graph and triangulation.

The basic representation of a graph of n vertices is the adjacency matrix A where A(i,j)=1 if vertex i is linked to vertex j. A graph often comes with a geometric realization in R^d which an (d,n) matrix where vertex(:,i) is the position of the ith vertex.

A triangulation of m faces and n vertex is represented through:
* a set of faces which is a (3,m) matrix where face(:,i) are the vertices indexes of the ith face.
* a set of vertex which is a (d,n) matrix.
The toolbox contains function to deal more easily with a triangulation data structure, and allows to retrieve vertex and face 1-ring and switch from adjacency to faces.

The graph part of the toolbox contains function to creates synthetic graph and compute shortest path (dijkstra and isomap algorithm).

This toolbox contains a lot of function to deal with spectral theory of triangulation. You can load triangulations from files and then display the resulting mesh. It allows to compute various laplacian operator, and the to compute parameterization using spectral decomposition, harmonic mapping, free boundary harmonic mapping, and isomap.

• MATLAB release: MATLAB 7 (R14)
• Published M Files: Toolbox graph - A toolbox to process graph and triangulated meshes
• HTML Files: __MACOSX/toolbox_graph/._html,; __MACOSX/toolbox_graph/html/._content.html

Other Files

__MACOSX/._toolbox_graph,
__MACOSX/toolbox_graph/._.DS_Store,
__MACOSX/toolbox_graph/._adjacency2incidence.m,
__MACOSX/toolbox_graph/._adjmatrix2list.m,
__MACOSX/toolbox_graph/._batch_levelsets_meshes.m,
__MACOSX/toolbox_graph/._build_euclidean_weight_matrix.m,
__MACOSX/toolbox_graph/._build_graph_from_image.m,
__MACOSX/toolbox_graph/._bunny.gim.jpg,
__MACOSX/toolbox_graph/._check_face_vertex.m,
__MACOSX/toolbox_graph/._check_incircle.m,
__MACOSX/toolbox_graph/._check_incircle.m~,
__MACOSX/toolbox_graph/._check_incircle_edge.m,
__MACOSX/toolbox_graph/._compile_mex.m,
__MACOSX/toolbox_graph/._compute_boundary.m,
__MACOSX/toolbox_graph/._compute_combinatorial_laplacian.m,
__MACOSX/toolbox_graph/._compute_curvature.m,
__MACOSX/toolbox_graph/._compute_delaunay.m,
__MACOSX/toolbox_graph/._compute_diffusion_geometry.m,
__MACOSX/toolbox_graph/._compute_diffusion_kernel.m,
__MACOSX/toolbox_graph/._compute_distance_graph.m,
__MACOSX/toolbox_graph/._compute_dual_graph.m,
__MACOSX/toolbox_graph/._compute_edge_face_ring.m,
__MACOSX/toolbox_graph/._compute_edges.m,
__MACOSX/toolbox_graph/._compute_face_ring.m,
__MACOSX/toolbox_graph/._compute_geometric_laplacian.m,
__MACOSX/toolbox_graph/._compute_laplacian_curve.m,
__MACOSX/toolbox_graph/._compute_levelset_mesh.m,
__MACOSX/toolbox_graph/._compute_mesh_gradient.m,
__MACOSX/toolbox_graph/._compute_mesh_laplacian.m,
__MACOSX/toolbox_graph/._compute_mesh_local_covariance.m,
__MACOSX/toolbox_graph/._compute_mesh_weight.m,
__MACOSX/toolbox_graph/._compute_normal.m,
__MACOSX/toolbox_graph/._compute_orthocenter.m,
__MACOSX/toolbox_graph/._compute_orthoproj_triangulation.m,
__MACOSX/toolbox_graph/._compute_orthoproj_triangulation.m~,
__MACOSX/toolbox_graph/._compute_parameterization.m,
__MACOSX/toolbox_graph/._compute_rotation.m,
__MACOSX/toolbox_graph/._compute_semidual_graph.m,
__MACOSX/toolbox_graph/._compute_traveling_salesman.m,
__MACOSX/toolbox_graph/._compute_triangulation_angles.m,
__MACOSX/toolbox_graph/._compute_vertex_face_ring.m,
__MACOSX/toolbox_graph/._compute_vertex_ring.m,
__MACOSX/toolbox_graph/._compute_voronoi_mesh.m,
__MACOSX/toolbox_graph/._content.m,
__MACOSX/toolbox_graph/._convert_gim2mesh.m,
__MACOSX/toolbox_graph/._griddata_arbitrary.m,
__MACOSX/toolbox_graph/._griddata_arbitrary.m~,
__MACOSX/toolbox_graph/._incidence2adjacency.m,
__MACOSX/toolbox_graph/._load_gim.m,
__MACOSX/toolbox_graph/._load_graph.m,
__MACOSX/toolbox_graph/._mesh.exe,
__MACOSX/toolbox_graph/._mesh_flip_faces.m,
__MACOSX/toolbox_graph/._mesh_previewer.m,
__MACOSX/toolbox_graph/._mesh_wrapper.m,
__MACOSX/toolbox_graph/._metro.exe,
__MACOSX/toolbox_graph/._metro_wrapper.m,
__MACOSX/toolbox_graph/._mex,
__MACOSX/toolbox_graph/._off,
__MACOSX/toolbox_graph/._pawn.wrl,
__MACOSX/toolbox_graph/._perform_delaunay_flipping.m,
__MACOSX/toolbox_graph/._perform_dijkstra.m,
__MACOSX/toolbox_graph/._perform_dijkstra_fast.dll,
__MACOSX/toolbox_graph/._perform_dijkstra_fast.mexmaci,
__MACOSX/toolbox_graph/._perform_dijkstra_path_extraction.m,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation.dll,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation.m,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation.mexglx,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation.mexmaci,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation_old.m,
__MACOSX/toolbox_graph/._perform_dijkstra_propagation_slow.m,
__MACOSX/toolbox_graph/._perform_faces_reorientation.m,
__MACOSX/toolbox_graph/._perform_floyd_algorithm.m,
__MACOSX/toolbox_graph/._perform_lloyd_iteration.m,
__MACOSX/toolbox_graph/._perform_mesh_heat_diffusion.m,
__MACOSX/toolbox_graph/._perform_mesh_simplification.m,
__MACOSX/toolbox_graph/._perform_mesh_smoothing.m,
__MACOSX/toolbox_graph/._perform_normal_displacement.m,
__MACOSX/toolbox_graph/._perform_point_picking.m,
__MACOSX/toolbox_graph/._perform_saturation.m,
__MACOSX/toolbox_graph/._perform_triangle_flipping.m,
__MACOSX/toolbox_graph/._plot_dijkstra.m,
__MACOSX/toolbox_graph/._plot_edges.m,
__MACOSX/toolbox_graph/._plot_geometry_image.m,
__MACOSX/toolbox_graph/._plot_graph.m,
__MACOSX/toolbox_graph/._plot_mesh.m,
__MACOSX/toolbox_graph/._plot_silouhette.m,
__MACOSX/toolbox_graph/._plot_spherical_triangulation.m,
__MACOSX/toolbox_graph/._progressive_mesh.m,
__MACOSX/toolbox_graph/._publish_html.m,
__MACOSX/toolbox_graph/._qslim.m,
__MACOSX/toolbox_graph/._read_gim.m,
__MACOSX/toolbox_graph/._read_mesh.m,
__MACOSX/toolbox_graph/._read_mfile.m,
__MACOSX/toolbox_graph/._read_obj.m,
__MACOSX/toolbox_graph/._read_off.m,
__MACOSX/toolbox_graph/._read_ply.m,
__MACOSX/toolbox_graph/._read_smf.m,
__MACOSX/toolbox_graph/._read_tet.m,
__MACOSX/toolbox_graph/._read_vtk.m,
__MACOSX/toolbox_graph/._read_wrl.m,
__MACOSX/toolbox_graph/._reverse_orientation.m,
__MACOSX/toolbox_graph/._select3d.m,
__MACOSX/toolbox_graph/._tests,
__MACOSX/toolbox_graph/._tet2tri.m,
__MACOSX/toolbox_graph/._toolbox,
__MACOSX/toolbox_graph/._toolbox_graph.m,
__MACOSX/toolbox_graph/._triangle.exe,
__MACOSX/toolbox_graph/._triangulate.m,
__MACOSX/toolbox_graph/._triangulation2adjacency.m,
__MACOSX/toolbox_graph/._triangulation_isequal.m,
__MACOSX/toolbox_graph/._write_gim.m,
__MACOSX/toolbox_graph/._write_mesh.m,
__MACOSX/toolbox_graph/._write_obj.m,
__MACOSX/toolbox_graph/._write_off.m,
__MACOSX/toolbox_graph/._write_ply.m,
__MACOSX/toolbox_graph/._write_smf.m,
__MACOSX/toolbox_graph/._write_wrl.m,
__MACOSX/toolbox_graph/html/._content.png,
__MACOSX/toolbox_graph/html/._content_01.png,
__MACOSX/toolbox_graph/html/._content_02.png,
__MACOSX/toolbox_graph/html/._content_03.png,
__MACOSX/toolbox_graph/html/._content_04.png,
__MACOSX/toolbox_graph/html/._content_05.png,
__MACOSX/toolbox_graph/html/._content_06.png,
__MACOSX/toolbox_graph/html/._content_07.png,
__MACOSX/toolbox_graph/html/._content_08.png,
__MACOSX/toolbox_graph/html/._content_09.png,
__MACOSX/toolbox_graph/html/._content_10.png,
__MACOSX/toolbox_graph/html/._content_11.png,
__MACOSX/toolbox_graph/html/._content_12.png,
__MACOSX/toolbox_graph/html/._gpeyre.xsl,
__MACOSX/toolbox_graph/html/._style.css,
__MACOSX/toolbox_graph/mex/._config.h,
__MACOSX/toolbox_graph/mex/._dijkstra.cpp,
__MACOSX/toolbox_graph/mex/._fheap,
__MACOSX/toolbox_graph/mex/._fibheap.h,
__MACOSX/toolbox_graph/mex/._perform_dijkstra_propagation.cpp,
__MACOSX/toolbox_graph/mex/._perform_dijkstra_propagation.def,
__MACOSX/toolbox_graph/mex/._perform_dijkstra_propagation.vcproj,
__MACOSX/toolbox_graph/mex/._toolbox_graph.sln,
__MACOSX/toolbox_graph/mex/fheap/._.svn,
__MACOSX/toolbox_graph/mex/fheap/._fib.cpp,
__MACOSX/toolbox_graph/mex/fheap/._fib.h,
__MACOSX/toolbox_graph/mex/fheap/._fibpriv.h,
__MACOSX/toolbox_graph/mex/fheap/._fibtest.c,
__MACOSX/toolbox_graph/mex/fheap/._fibtest2.c,
__MACOSX/toolbox_graph/mex/fheap/._tt.c,
__MACOSX/toolbox_graph/mex/fheap/._use.c,
__MACOSX/toolbox_graph/mex/fheap/.svn/._all-wcprops,
__MACOSX/toolbox_graph/mex/fheap/.svn/._entries,
__MACOSX/toolbox_graph/mex/fheap/.svn/._format,
__MACOSX/toolbox_graph/mex/fheap/.svn/._prop-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/._props,
__MACOSX/toolbox_graph/mex/fheap/.svn/._text-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/._tmp,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._fib.cpp.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._fib.h.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._fibpriv.h.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._fibtest.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._fibtest2.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._tt.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/prop-base/._use.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._fib.cpp.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._fib.h.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._fibpriv.h.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._fibtest.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._fibtest2.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._tt.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/text-base/._use.c.svn-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/tmp/._prop-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/tmp/._props,
__MACOSX/toolbox_graph/mex/fheap/.svn/tmp/._text-base,
__MACOSX/toolbox_graph/mex/fheap/.svn/tmp/._wcprops,
__MACOSX/toolbox_graph/off/._.svn,
__MACOSX/toolbox_graph/off/._beetle.off,
__MACOSX/toolbox_graph/off/._cube.off,
__MACOSX/toolbox_graph/off/._cube_oversampled.off,
__MACOSX/toolbox_graph/off/._cylinder.off,
__MACOSX/toolbox_graph/off/._elephant-50kv.off,
__MACOSX/toolbox_graph/off/._hhh.off,
__MACOSX/toolbox_graph/off/._hole_sphere1.off,
__MACOSX/toolbox_graph/off/._hole_sphere2.off,
__MACOSX/toolbox_graph/off/._hole_sphere3.off,
__MACOSX/toolbox_graph/off/._hole_sphere4.off,
__MACOSX/toolbox_graph/off/._hole_sphere5.off,
__MACOSX/toolbox_graph/off/._hole_sphere6.off,
__MACOSX/toolbox_graph/off/._hypersheet.off,
__MACOSX/toolbox_graph/off/._mannequin.off,
__MACOSX/toolbox_graph/off/._mushroom.off,
__MACOSX/toolbox_graph/off/._nefertiti-entire.off,
__MACOSX/toolbox_graph/off/._nefertiti.off,
__MACOSX/toolbox_graph/off/._pipes.off,
__MACOSX/toolbox_graph/off/._tre_twist.off,
__MACOSX/toolbox_graph/off/._venus.off,
__MACOSX/toolbox_graph/off/.svn/._all-wcprops,
__MACOSX/toolbox_graph/off/.svn/._entries,
__MACOSX/toolbox_graph/off/.svn/._format,
__MACOSX/toolbox_graph/off/.svn/._prop-base,
__MACOSX/toolbox_graph/off/.svn/._props,
__MACOSX/toolbox_graph/off/.svn/._text-base,
__MACOSX/toolbox_graph/off/.svn/._tmp,
__MACOSX/toolbox_graph/off/.svn/prop-base/._beetle.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._cube.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._cube_oversampled.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._cylinder.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._elephant-50kv.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._hhh.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._hole_sphere1.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._hole_sphere2.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/prop-base/._hole_sphere3.off.svn-base,
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__MACOSX/toolbox_graph/off/.svn/text-base/._beetle.off.svn-base,
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__MACOSX/toolbox_graph/off/.svn/text-base/._cube_oversampled.off.svn-base,
__MACOSX/toolbox_graph/off/.svn/text-base/._cylinder.off.svn-base,
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__MACOSX/toolbox_graph/tests/._test_compression_fixed.m,
__MACOSX/toolbox_graph/tests/._test_constrained_delaunay.m,
__MACOSX/toolbox_graph/tests/._test_curvature.m,
__MACOSX/toolbox_graph/tests/._test_diffusion_wavelets.m,
__MACOSX/toolbox_graph/tests/._test_dijkstra.m,
__MACOSX/toolbox_graph/tests/._test_dijkstra_astar.m,
__MACOSX/toolbox_graph/tests/._test_drawing.m,
__MACOSX/toolbox_graph/tests/._test_duality.m,
__MACOSX/toolbox_graph/tests/._test_face_reorientation.m,
__MACOSX/toolbox_graph/tests/._test_filling_holes.m,
__MACOSX/toolbox_graph/tests/._test_flattening.m,
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__MACOSX/toolbox_graph/tests/._test_grid_data.m,
__MACOSX/toolbox_graph/tests/._test_image_approx_refinement.m,
__MACOSX/toolbox_graph/tests/._test_image_approx_thining.m,
__MACOSX/toolbox_graph/tests/._test_laplacian_curve.m,
__MACOSX/toolbox_graph/tests/._test_levelset_mesh.m,
__MACOSX/toolbox_graph/tests/._test_lloyd.m,
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[[e-mail] lo]

Perfect

[Attila Altay Yavuz]

Very useful

[Khaled Khairy]

 

[Edo urra]

good

[Will Liu]

 

[Ben abdallah youssef]

Very helpful toolbox!!

[bahram gh]

very useful

[anup vibhute]

very useful

[David S]

Very useful, except for a bug in the compute_curvature function:

compute_curvature will generate an error on line 75 ("dp = sum( normal(:,E(:,1)) .* normal(:,E(:,2)), 1 );") for SOME surfaces. The error stems from E containing indices that are out of range which is caused by line 48 ("A = sparse(double(i),double(j),s,n,n);") where A's values eventually entirely make up the E matrix. The problem occurs when the i and j vectors create the same ordered pair twice in which case the sparse function adds the two s vector elements together for that matrix location resulting in a value that is too large to be used as an index on line 75. For example, if i = [1 1] and j = [2 2] and s = [3 4] then A(1,2) will equal 3 + 4 = 7.

The i and j vectors are created here:
i = [face(1,:) face(2,:) face(3,:)];
j = [face(2,:) face(3,:) face(1,:)];

The fact that your code seems to depend on the order of the vertices in the faces matrix worries me because the curvature should be the same regardless of the order, obviously. To be fair, I don't completely understand how your code works so perhaps the way it is written it works out to not matter except that it does certainly matter when it results in an index out of bounds error as previously described.

[David S]

Just wanted to add that the error I mentioned is caused by the flipping of the sign of the surface normal of just one face by rearranging the order of the vertices in the face matrix

[Axel zheng]

Cool!!!

[Ofra]

Very useful.
Is there a Matlab 2008b version ?

[europe lee]

test_diffusion_wavelet.m file did not work!
Because it miss some functions, such as MakeDiffusion function.
Although I download and install diffusion wavelet code from MAURO MAGGIONI, I find that MakeDiffusion in his code is different from yours,like parameter called 'gauss' in your MakeDiffusion was not included in Mauro's MakeDiffusion.

[YUANCHUN WANG]

Very useful.

But I have a question: when I tried to use the function "perform_mesh_simplification" to make the simplificatino for mesh. Matlab said that QSlim is not a command. And here is the command where situates the problem: "system(['QSlim tmp.smf -o tmp1.smf -s ' num2str(nface)]);"

I'm afraid this is because the qslim.exe was missed?

thanks for your explaination!

[Raymond Cheng]

Thanks for your sharing.

[kamel]

Very useful
compute_curvature will generate an error on line 75 ("dp = sum( normal(:,E(:,1)) .* normal(:,E(:,2)), 1 );") for SOME surfaces.
what's the solution of this bug
thanks

[Peter]

 

[Ged Ridgway]

Looks really useful. However, isomap seems to fail:
>> xy = isomap(dat);
??? Undefined command/function 'compute_nn_graph'.
Error in ==> isomap at 85
    D = compute_nn_graph(X,options);