Algebraic Smooth Occluding Contours

Ryan Capouellez¹, Jiacheng Dai¹, Aaron Hertzmann², Denis Zorin¹

¹New York University, ²Adobe Research

Implementation of Algebraic Smooth Occluding Contours.

This algorithm takes an input mesh and camera viewpoint, approximates the mesh with a smooth piecewise-quadratic surface, and computes the occluding contours of this approximating surface in closed form. These contours are piecewise-rational curves in image-space, and they are computed with consistent visibility much more efficiently than previous methods.

Installation

To install this project on a Unix-based system, use the following standard CMake build procedure:

git clone https://github.com/rjc8237/algebraic-contours.git
cd algebraic-contours
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make -j 8

Usage

The core contour generation pipeline is bin/generate_algebraic_contours. This executable takes the following arguments:

flag	description
-i, --input	Mesh filepath
-o, --output	Output directory
-c, --camera	Camera filepath (uses default camera if none provided)
--log_level	Level of logging
--invisibility_method	Method for invisibility tests of contours
--svg_mode	Output mode for SVG contours
-w, --weight	Fitting weight for the quadratic surface approximation
--trim	Trimming for contour intersection checks
--pad	Padding for contour chaining checks
--show_nodes	Show important nodes in the contours

Supported parameter values for log_level, invisibility_method, and svg_mode are listed by bin/generate_algebraic_contours --help.

The input mesh must be a manifold surface with texture coordinates describing a parameterization with isolated cone vertices; such a parameterization can be generated using the method of Efficient and Robust Discrete Conformal Equivalence with Boundary. The camera file must be a comma separated 4 by 4 projective transformation matrix.

We also include a viewer executable bin/view_quadratic_spline for the piecewise-quadratic spline approximation, which supports the following arguments:

flag	description
-i, --input	Mesh filepath
--log_level	Level of logging
-w, --weight	Fitting weight for the quadratic surface approximation
--num_subdivisions	Number of subdivisions for triangulation

Figure Reproduction

Scripts to generate the figures of Algebraic Smooth Occluding Contours are included in figures.

The models (with parameterizations) and cameras used in Algebraic Smooth Occluding Contours necessary for these scripts can be downloaded here; they must be copied to data/meshes and data/cameras respectively.

The figure scripts can be run independently or in batch with the command

bash fig-all.sh

We also provide scripts to generate animation frames for the supplementary videos. These can be run with the commands

bash anim-rotation.sh
bash anim-approximation-error.sh

Citation

@inproceedings{capouellez:2023:algebraic,
  author = {Capouellez, Ryan and Dai, Jiacheng and Hertzmann, Aaron and Zorin, Denis},
  title = {Algebraic Smooth Occluding Contours},
  year = {2023},
  isbn = {9798400701597},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  url = {https://doi.org/10.1145/3588432.3591547},
  doi = {10.1145/3588432.3591547},
  booktitle = {ACM SIGGRAPH 2023 Conference Proceedings},
  articleno = {39},
  numpages = {10},
  keywords = {non-photorealistic rendering, contours, visibility, piecewise-quadratic surface},
  location = {Los Angeles, CA, USA},
  series = {SIGGRAPH '23}
}