Sound and robust solid modeling via exact real arithmetic and continuity
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 have implemented this library in MarshallB, a language we have developed as an extension of Marshall. Marshall is a 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 also define a new shape representation, compact representation (K-rep), that enables a user of our library to perform constructions such as Minkowski sum and analyses such as Hausdorff distance that are not possible with traditional representations.
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.
Conference DayTue 20 AugDisplayed time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change
13:30 - 15:00
|Demystifying Differentiable Programming: Shift/Reset the Penultimate Backpropagator|
Fei Wang, Dan ZhengPurdue University, Google Brain, James Decker, Xilun WuPurdue University, Gregory EssertelPurdue University, Tiark RompfPurdue UniversityPre-print
|Efficient Differentiable Programming in a Functional Array-Processing Language|
|From high-level inference algorithms to efficient code|
Rajan WaliaIndiana University, Praveen NarayananIndiana University, USA, Jacques CaretteMcMaster University, Sam Tobin-HochstadtIndiana University, Chung-chieh ShanIndiana University, USAPre-print
|Sound and robust solid modeling via exact real arithmetic and continuityDistinguished Paper|
Benjamin ShermanMassachusetts Institute of Technology, USA, Jesse MichelMassachusetts Institute of Technology, Michael CarbinMassachusetts Institute of TechnologyDOI Pre-print Media Attached