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QuadriFlow: A Scalable and Robust Method for Quadrangulation

Source code for the paper:

Jingwei Huang, Yichao Zhou, Matthias Niessner, Jonathan Shewchuk and Leonidas Guibas. QuadriFlow: A Scalable and Robust Method for Quadrangulation, The Eurographics Symposium on Geometry Processing (SGP) 2018.

QuadriFlow Results

WebGL Application

Our 3D WebGL Apps for QuadriFlow are online! Without any installation, you are able to

Desktop Software

The software supports cmake build for Linux/Mac/Windows systems. For linux and mac users, run sh to build and try the QuadriFlow example, which converts examples/Gargoyle_input.obj to examples/Gargoyle_quadriflow.obj.


git clone git://
cd quadriflow
mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=release
make -j

QuadriFlow Software

We take a manifold triangle mesh input.obj and generate a manifold quad mesh output.obj. The face number increases linearly with the resolution controled by the user.

./quadriflow -i input.obj -o output.obj -f [resolution]

Here, the resolution is the desired number of faces in the quad mesh.

Advanced Functions

Min-cost Flow

By default, quadriflow uses the Boykov maximum flow solver from boost because it is faster. To enable the adaptive network simplex minimum-cost flow solver, you can enable the -mcf option:

./quadriflow -mcf -i input.obj -o output.obj -f [resolution]

Sharp Preserving

By default, quadriflow does not explicitly detect and preserve the sharp edges in the model. To enable this feature, uses

./quadriflow -sharp -i input.obj -o output.obj -f [resolution]

SAT Flip Removal (Unix Only)

By default, quadriflow does not use the SAT solver to remove the flips in the integer offsets map. To remove the flips and guarantee a watertight result mesh, you can enable the SAT solver. First, make sure that minisat and timeout is properly installed under your ${PATH}. The former can be done by building 3rd/MapleCOMSPS_LRB/CMakeLists.txt and copying minisat to /usr/bin. In addition, timeout is included in coreutils. If you are using Mac, you can install it using homebrew:

brew install coreutils
export PATH="/usr/local/opt/coreutils/libexec/gnubin:$PATH"

You can verify if those binaries are properly installed by executing

which minisat
which timeout

After that, you can enable SAT flip removal procedure by executing

./quadriflow -sat -i input.obj -o output.obj -f [resolution]

When using the SAT flip removal, we also suggest you enabling the verbose logging to understand what is going on. You can build quadriflow with the following options:


GUROBI Support (For Benchmark Purpose)

To use the Gurobi integer programming to solve the integer offset problem, you can build QuadriFlow with


This override other solvers and should only be used for benchmark purpose.

External Dependencies

  • Boost
  • Eigen
  • OpenMP (optional in CMake)
  • TBB (optional in CMake)
  • GUROBI (for benchmark purpose only)


QuadriFlow is released under MIT License. For 3rd dependencies,

  • Boost and Lemon are released under Boost Software License
  • Most part of Eigen is released under MPL2
    • Sparse Cholesky Decomposition algorithms are released under LGPL
    • To replace it using Sparse LU decomposition with a more permissive MPL2 license (a little slower), enable BUILD_FREE_LICENSE in CMake (e.g., -DBUILD_FREE_LICENSE=ON).
  • pcg32.h is released under the Apache License, Version 2.0
  • parallel_stable_sort.h is released under the MIT License


© 2018 Jingwei Huang and Yichao Zhou All Rights Reserved

IMPORTANT: If you use this software please cite the following in any resulting publication:

@article {10.1111:cgf.13498,
    journal = {Computer Graphics Forum},
    title = {{QuadriFlow: A Scalable and Robust Method for Quadrangulation}},
    author = {Huang, Jingwei and Zhou, Yichao and Niessner, Matthias and Shewchuk, Jonathan Richard and Guibas, Leonidas J.},
    year = {2018},
    publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/cgf.13498}

Triangle Manifold

In case you are dealing with a triangle mesh that is not a manifold, we implemented the software that converts any triangle mesh to watertight manifold. Please visit for details.