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

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 ef...

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Published inACM 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
LanguageEnglish
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
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Abstract 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.
AbstractList 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.
ArticleNumber 120
Author Sichetti, Federico
Puppo, Enrico
Huang, Zizhou
Panozzo, Daniele
Zorin, Denis
Attene, Marco
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  organization: New York University, New York, NY, USA
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Snippet 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...
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SubjectTerms 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
SubjectTermsDisplay Computing methodologies -- Computer graphics -- Animation -- Physical simulation
Computing methodologies -- Computer graphics -- Shape modeling -- Mesh geometry models
Mathematics of computing -- Mathematical analysis -- Nonlinear equations
Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Interval arithmetic
Software and its engineering -- Software notations and tools -- Compilers -- Source code generation
Software and its engineering -- Software notations and tools -- Context specific languages -- Domain specific languages
Theory of computation -- Design and analysis of algorithms -- Mathematical optimization -- Continuous optimization -- Nonconvex optimization
Title MiSo: A DSL for Robust and Efficient Solve and MInimize Problems
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Volume 44
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