MiSo: A DSL for Robust and Efficient Solve and MInimize Problems

• Published in: ACM transactions on graphics Vol. 44; no. 4; pp. 1 - 18
• Main Authors: Sichetti, Federico, Puppo, Enrico, Huang, Zizhou, Attene, Marco, Zorin, Denis, Panozzo, Daniele
• Format: Journal Article
• Language: English
• Published: New York, NY, USA ACM 01.08.2025
• Subjects: Animation; Compilers; Computer graphics; Computing methodologies; Context specific languages; Continuous optimization; Design and analysis of algorithms; Domain specific languages; Interval arithmetic; Mathematical analysis; Mathematical optimization; Mathematics of computing; Mesh geometry models; Nonconvex optimization; Nonlinear equations; Numerical analysis; Physical simulation; Shape modeling; Software and its engineering; Software notations and tools; Source code generation; Theory of computation
• ISSN: 0730-0301; 1557-7368; 1557-7368
• DOI: 10.1145/3731207

Many problems in computer graphics can be formulated as finding the global minimum of a function subject to a set of non-linear constraints (Minimize), or finding all solutions of a system of non-linear constraints (Solve). We introduce MiSo, a domain-specific language and compiler for generating efficient C++ code for low-dimensional Minimize and Solve problems, that uses interval methods to guarantee conservative results while using floating point arithmetic. We demonstrate that MiSo-generated code shows competitive performance compared to hand-optimized codes for several computer graphics problems, including high-order collision detection with non-linear trajectories, surface-surface intersection, and geometrical validity checks for finite element simulation.