Sound and Robust Solid Modeling via Exact Real Arithmetic and Continuity
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3341703.pdf
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Author(s)
Sherman, Benjamin
Michel, Jesse
Carbin, Michael
Date Issued
July 26, 2019
Journal
Proceedings of the ACM on Programming Languages
Publisher
Association for Computing Machinery
Citation
Benjamin Sherman, Jesse Michel, and Michael Carbin. 2019. Sound and robust solid modeling via exact real arithmetic and continuity. Proc. ACM Program. Lang. 3, ICFP, Article 99 (August 2019), 29 pages.
Version
Final published version
Abstract
Algorithms for solid modeling, i.e., Computer-Aided Design (CAD) and computer graphics, are often specified on real numbers and then implemented with finite-precision arithmetic, such as floating-point. The result is that these implementations do not soundly compute the results that are expected from their specifications.
We present a new library, StoneWorks, that provides sound and robust solid modeling primitives. We implement StoneWorks in MarshallB, a pure functional programming language for exact real arithmetic in which types denote topological spaces and functions denote continuous maps, ensuring that all programs are sound and robust. We developed MarshallB as an extension of the Marshall language.
We also define a new shape representation, compact representation (K-rep), that enables constructions such as Minkowski sum and analyses such as Hausdorff distance that are not possible with traditional representations. K-rep is a nondeterminism monad for describing all the points in a shape.
With our library, language, and representation together, we show that short StoneWorks programs can specify and execute sound and robust solid modeling algorithms and tasks.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1145/3341703
