Algebraic Smooth Occluding Contours

Ryan Capouellez1, Jiacheng Dai1, Aaron Hertzmann2, Denis Zorin1
1New York University, 2Adobe Research


Computing occluding contours is a key step in 3D non-photorealistic rendering, but producing smooth contours with consistent visibility has been a notoriously-challenging open problem. This paper describes the first general-purpose smooth surface construction for which the occluding contours can be computed in closed form. Given an input mesh and camera viewpoint, we show how to approximate the mesh with a piecewise-quadratic surface, for which the occluding contours are piecewise-rational curves in image-space. We show that this method produces smooth contours with consistent visibility much more efficiently than the state-of-the-art.




Examples of contour line sets obtained using our method on models from the modified dataset of [Liu et al. 2023]. (Fertility courtesy UU from AIM@SHAPE-VISIONAIR Shape Repository. Public domain Bob model by Keenan Crane. Killeroo ©


  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 = {},
  doi = {10.1145/3588432.3591547},
  booktitle = {ACM SIGGRAPH 2023 Conference Proceedings},
  articleno = {39},
  numpages = {10},
  keywords = {visibility, contours, non-photorealistic rendering, piecewise-quadratic surface},
  location = {Los Angeles, CA, USA},
  series = {SIGGRAPH '23}