Solving geometric constraints by iterative projections and backprojections

F. Thomas
2004 IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004  
Most geometric constraint problems can be reduced to give coordinates to a set of points from a subset of their pairwise distances. By exploiting this fact, this paper presents an algorithm that solves geometric constraint systems by iteratively reducing and expanding the dimension of the problem. In general, these projection/backprojection iterations permit tightening the ranges for the possible solutions but, if at a given point no progress is made, the algorithm bisects the search space and
more » ... roceeds recursively for both subproblems. This branch-and-prune strategy is shown to converge to all solutions.
doi:10.1109/robot.2004.1308083 dblp:conf/icra/Thomas04 fatcat:yswb5it3cjdmnn7gwcf3i3afui