Computational Design of Shape-Aware Sieves

SIGGRAPH Asia 2025

David Cha, University of Southern California

Oded Stein, University of Southern California

Given a shape \(A\) that should pass through a sieve, and shapes \(B_1, B_2, B_3\) that should be blocked by it, we compute a sieve hole that admits \(A\) and blocks the \(B\)s. A \(\textcolor{teal}{\checkmark}\) means the sieve lets the shape pass, and a \(\textcolor{red}{\times}\) means the shape does not fit. We fabricate the sieves to verify their properties (cf. supplemental video). Our method can also handle multiple \(A_i\)s and accounts for various fabrication considerations.

Abstract

We introduce mathematical tools to describe the geometric problem of sieves, two-dimensional holes that admit certain three-dimensional objects to pass through them, but block others. This is achieved by formulating the sieve design problem as a two-player game where both players (the one that wants to pass, and the one that wants to block) try to find a set of rigid transformations to achieve their objective. We also introduce an algorithm for solving this game by solving a global optimization problem employing both differentiable rendering with gradient-based optimization as well as particle swarm optimization. Our procedure accounts for real-world manufacturing concerns, and we fabricate a variety of examples demonstrating the practical viability of our sieves. Our implementation takes advantage of GPUs and does not rely on any clean or manifold input geometry as long as it is a triangle mesh. We can produce intricate sieves that block an arbitrary set of shapes \(\mathcal{B}\) but admit another arbitrary set of shapes \(\mathcal{A}\) (if finding a solution is possible for our method).

Links

Acknowledgements

We thank Jernej Barbič, Huanyu Chen, Silvia Sellán, Ryan Mei, Bingjian Huang, and the USC Maker Space team for helping with 3D prints. We thank Silvia Sellán, Yingying (Samara) Ren, and Eitan Grinspun for scientific discussions. We thank Pranav Jain for insight on finding interesting combinations of meshes by suggesting the aliens and machine parts examples. We are grateful to Leticia Mattos Da Silva, Dylan Rowe, Pranav Jain, Letao Chen, and Alice Wei for proofreading. USC's Geometry and Graphics Group is supported by NSF grant 2335493 and a gift by Adobe Inc. We thank the creators of all assets used in the article.