authors: Keenan Crane, Peter Schröder

This code is a reference implementation of the paper

Felix Knöppel, Keenan Crane, Ulrich Pinkall, Peter Schröder
"Globally Optimal Direction Fields"
SIGGRAPH 2013

This version carefully implements the finite element connection Laplacian as described in the paper, using Chebyshev expansions to ensure good numerics. It also supports some sophisticated features, such as holomorphic/anti-holomorphic energy, alignment with principal curvature directions, and alignment with the boundary.

The code itself is somewhat messy research code with a very basic user interface. Several other implementations are available, which use a less sophisticated discretization of the connection Laplacian and do not support some of the features mentioned above. However, they may be useful for certain tasks, or in different build settings. In particular:

• The stripes code provides a simple version of the algorithm, as well as editing of singularities and generation of a field- aligned parameterization:

  http://www.cs.cmu.edu/~kmcrane/Projects/StripePatterns/code.zip

• There is an implementaiton in Directional, which is built on top of libigl and Eigen, and is hence header-only:

  https://github.com/avaxman/Directional

Note that fieldgen and stripes are both built on top of the CHOLMOD sparse direct solver, whereas Directional is built on top of Eigen. The latter can be easier to install (since it is header only) but can be significantly slower, since the Eigen Cholseky solver is much less mature than CHOLMOD. See also below for easy install instructions for CHOLMOD.

• 0.01 (Sep 1, 2013) — Initial release
• 0.02 (Jun 4, 2019) — Added boundary alignment

fieldgen depends on SuiteSparse, which you can obtain from

http://faculty.cse.tamu.edu/davis/suitesparse.html

On most platforms, SuiteSparse can be installed via standard package managers. On Mac OS X / HomeBrew, it can be installed via

brew install homebrew/science/suite-sparse

To build, you will have to edit the Makefile and set the include/lib paths accordingly. Some examples are provided. Once these paths have been set, simply type

make

which (barring any compilation/linker errors) should build an executable called kvec.

Once built, you should be able to run the executable by typing

./kvec data/bunny.obj

(or specifying a path to any mesh file in OBJ format). You should see a window showing the mesh and some information in the upper-left corner.

Hitting spacebar will generate the smoothest field on the surface.

Other commands can be accessed via the keyboard:

Note: curvature alignment works only when the symmetry degree of the field is 2 or 4.

Currently there is no built-in functionality for writing direction fields to disk, since there is no standard file format for fields and each user likely has different needs. The best place to look is at the code that draws the field (in Viewer.cpp); one can also write the mesh itself using methods in MeshIO.cpp.

Much of the source code in this archive is just there to support basic stuff like loading a mesh, solving a linear system, etc. The key routines are all in

Mesh.h/Mesh.cpp SectionIntegrals.h/SectionIntegrals.cpp

The main routines are

• Mesh::InitKVecDirData() — setup
• Mesh::ComputeSmoothest() — computes smoothest field
• Mesh::SmoothestCurvatureAlignment() — computes curvature-aligned field

An example of how these routines should be called is found in Viewer::mSmoothField().

This code is covered by a standard MIT license.

Copyright (c) 2013 Keenan Crane and Peter Schröder.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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