Snap together mathematics
Abstract
Large numbers of applications involve building complicated mathematical models out of predefined functions and repeatedly evaluating the combined function and its derivatives. For interactive applications it is important that the evaluations be efficient and that the model can be altered dynamically. Snap Together Mathematics is a facility that provides this functionality. Primitive functions are defined at compile time and can be composed dynamically to create larger models. Evaluation of both the composed function and its derivatives is accomplished by traversal of the expression graph. The sparse derivative matrix of a subset of a model’s outputs with respect to any set of its inputs can be computed efficiently. Snap Together Mathematics is implemented as a set of class definitions that provide a base for application specific objects. Among the applications we have developed are interactive systems for geometric modelling, constrained optimization, and constrained dynamics.
BibTeX
@workshop{Gleicher-1990-15806,author = {Michael Gleicher and Andrew Witkin},
title = {Snap together mathematics},
booktitle = {Proceedings of EUROGRAPHICS '90 Workshop on Object Oriented Graphics},
year = {1990},
month = {December},
editor = {Edwin Blake and Peter Weisskirchen},
pages = {21 - 34},
publisher = {Springer Verlag},
}