Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
Graph-based approach for solving geometric constraint problems
Graph-based approach for solving geometric constraint problems
Solving spatial basic geometric constraint configurations with locus intersection
Proceedings of the seventh ACM symposium on Solid modeling and applications
Solving Geometric Constraints By Homotopy
IEEE Transactions on Visualization and Computer Graphics
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
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The paper presents a method for multivariate root finding that uses adaptive search space decomposition by generalised quad-trees and non-linear Lagrange polynomials to interpolate the function inside the tree nodes. The method applies randomisation to achieve robustness. Selection of start points for the Newton-Raphson like search is based on a heuristic rating of the decomposition cells. The algorithm tunes out found roots to find all solutions. Although aimed at geometric constraint solving, where functions are only partially defined and no derivatives are available, the root finding method is applicable to a wider range of problems.