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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](http://stanford.edu/~jingweih/papers/quadriflow/quadriflow.pdf), The Eurographics Symposium on Geometry Processing (SGP) 2018.

				<!-- ## Processing Result -->
				![QuadriFlow Results](https://github.com/hjwdzh/quadriflow/raw/master/img/result.jpg)

				## WebGL Application
				Our 3D WebGL Apps for QuadriFlow are online! Without any installation, you are able to
				* [Compare](https://yichaozhou.com/publication/1805quadriflow/#demo) QuadriFlow with previous methods;
				* [Quadrangulate](https://yichaozhou.com/publication/1805quadriflow/#tool) your own meshes and
				download the result!

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

				### Install

				```
				git clone git://github.com/hjwdzh/quadriflow
				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 becuase 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 perserve 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:
				```
				cmake .. -DCMAKE_BUILD_TYPE=release -DBUILD_LOG=ON
				```

				### GUROBI Support (For Benchmark Purpose)

				To use the Gurobi integer programming to solve the integer offset problem, you can build QuadriFlow with
				```
				cmake .. -DCMAKE_BUILD_TYPE=release -DBUILD_GUROBI=ON -DBUILD_LOG=ON
				```
				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)

				## Licenses

				QuadriFlow is released under [MIT License](LICENSE.txt).
				For 3rd dependencies,
				* Boost and Lemon are released under [Boost Software License](https://lemon.cs.elte.hu/trac/lemon/wiki/License)
				* Most part of Eigen is released under [MPL2](https://www.mozilla.org/en-US/MPL/2.0/FAQ/)
				* 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

				## Authors
				- [Jingwei Huang](mailto:jingweih@stanford.edu)
				- [Yichao Zhou](mailto:zyc@berkeley.edu)

				© 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 https://github.com/hjwdzh/Manifold for details.