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.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
