Composable Language Extensions for Computational Geometry: A Case Study

This paper demonstrates how two different sets of powerful domain specific language features can be specified and deployed as composable language extensions. These extensions incorporate analyses and transformations that simplify the process of writing efficient and robust computational geometry programs and can be automatically added to a host language and used simultaneously. This is not possible in domain-specific language and library-based implementations of these features. One extension relies on characteristics of geometric algorithms to implement efficient exact-precision integers; the other employs a technique that symbolically perturbs geometric coordinates to safely and automatically handle degeneracies in the input data. These language extensions are implemented in an extensible language framework based on higher-order attribute grammars and forwarding. Attribute evaluation on the new language extension constructs is used to implement the static analysis and code transformations that enable the generation of efficient code.