Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
ACM Transactions on Mathematical Software (TOMS)
Fast Triangulation of Simple Polygons
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Modeling of the 2001 lava flow at Etna volcano by a Cellular Automata approach
Environmental Modelling & Software
A kinetic framework for computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
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To quantify the flow of particles over a heterogeneous area, some models require the integration of a pointwise dispersal function over source and target polygons. This calculation is a non-trivial task and may require a great deal of computing time. In this paper, an efficient and accurate algorithm is presented to integrate general individual dispersal functions between pairs of convex or non-convex polygons. Geometric calculations are performed using standard tools from computational geometry. Numerical integration is then performed either by a grid method or by an adaptive cubature method. The procedure is illustrated with a case study. It is shown that the cubature method is much more efficient than the grid method and that its error estimates are accurate. The algorithm is implemented in a C++ program, Califlopp.