AlphaContours

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A reference implementation of the Alpha Contours algorithm

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This is a reference implementation of the 'Differential Operators on Sketches via Alpha Contours' by Mariia Myronova, William Neveu, and Mikhail Bessmeltsev, ACM Transactions on Graphics (SIGGRAPH 2023).

Structure of the repository:

```
AlphaContours/ -- C++ code of the main algorithm
SGP21_discreteOptimization-main/ -- a few files from https://github.com/llorz/SGP21_discreteOptimization with a minor change in their energy
algoB/ -- python code to compare with StrokeAggregator
paper/ -- Matlab scripts to reproduce figures in the paper
svg_to_matlab/ -- a Windows binary to convert .svg -> .m
```

# Main algorithm
Command line: 
```AlphaContours drawing.m [alpha]```

Drawing.m is a vector drawing in a vector format (see the inputs folder). You can convert your own svg to .m using the binary in the 'svg_to_matlab' folder.

Alpha is the radius; when not specified, it is computed automatically.

The binary produces two files, all in Matlab format:
- drawing_segments.m -- the segments added to the drawing
- drawing_contours.m -- the Alpha Contours. This file contains three Matlab variables: 
  - cppContour, a cell array containing exterior contours
  - cppContourInner, a cell array containing interior contours
  - seedPts, an array containing an arbitrary point inside each interior contour.

These variables can then be fed into Triangle library to triangulate the interior of the sketch shape, if necessary.

# Dependencies
CGAL (tested with 5.5)

Eigen3 (tested with 3.4.0)

CMake

# Building
We have only tried building under Windows, but the binary can be succefully run with wine under Mac. To build the C++ code
```cd AlphaContours
mkdir build
cd build
cmake ../
```

Then build the visual studio project as usual. Then move the binary, together with mpfr-6.dll and gmp-10.dll into AlphaContours/bin.

# Reference Binary
If you don't want to compile anything, [here](http://www-labs.iro.umontreal.ca/~bmpix/AlphaContours/AlphaContoursBinary.zip) is the reference binary for Windows. Unzip it into AlphaContours/bin. After that, you should be able to run reproduce all the figures by running the scripts in the paper/ folder, except for Fig.16 that requires installation of [StrokeStrip](https://github.com/davepagurek/StrokeStrip) and [StrokeAggregator](https://www.cs.ubc.ca/labs/imager/tr/2018/StrokeAggregator/).

# External code
To compute functional maps on our domains, we use the implementation of "Discrete Optimization for Shape Matching" by Jing Ren, Simone Melzi, Peter Wonka, and Maks Ovsjanikov from [here](https://github.com/llorz/SGP21_discreteOptimization). We have slightly modified their function compute_fmap.m.

To triangulate, we use the Triangle library by Jonathan Richard Shewchuk from [here](https://www.cs.cmu.edu/~quake/triangle.html). It is 'triangle.exe' in our repository.

# Citation
When using the code, please reference the following paper:
```
@article{AlphaContours,
author = {Myronova, Mariia and Neveu, William and Bessmeltsev, Mikhail},
title = {Differential Operators on Sketches via Alpha Contours},
year = {2023},
issue_date = {August 2023},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {42},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3592420},
doi = {10.1145/3592420},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {69},
numpages = {15},
keywords = {differential operators, vector graphics, sketch processing}
}
```

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