The Reachability Problem in Constructive Geometric Constraint Solving Based Dynamic Geometry

Abstract

An important issue in dynamic geometry is the reachability problem that asks whether there is a continuos path that, from a given starting geometric configuration, continuously leads to an ending configuration. In this work we report on a technique to compute a continuous evaluation path, if one exists, that solves the reachability problem for geometric constructions with one variant parameter. The technique is developed in the framework of a constructive geometric constraint-based dynamic geometry system, uses the A * algorithm and minimizes the variant parameter arc length.

Variational geometric modeling with black box constraints and DAGs

“…When updating the intersection point o 1 ∩ o 2 between times t i and t i+1 , the ambiguity is typically solved with a continuity argument, i.e., selecting at time t i+1 the solution which is the closest to the intersection point at time t i . A well-known problem in dynamic geometry occurs when two curves no more intersect [21][22][23]. This problem also occurs in our approach and is related to the Persistent Naming Problem discussed in Section 6.…”

h-graphs: A new representation for tree decompositions of graphs

“…[5,6,23]. In these fields, knowing beforehand which is the set of values for λ such that the geometric construction can actually be built plays a central role.…”

“…The method was formalized in [5,6] where a correctness proof along with specific implementation details were given.…”

“…The method was formalized by Hidalgo and Joan-Arinyo in [5,6] where a correctness proof along with specific implementation details were given. This approach heavily relies on identifying the set of construction steps in the solution to the constraint problem the actual construction of which depend on the current value assigned to the variant parameter.…”

“…The h-graph captures the relations between construction steps that dependences natu-rally define in the description of the solution to the geometric constraint problem. Computing parameter ranges where the solution is feasible using h-graphs improves over the method described by Hidalgo and Joan-Arinyo in [5,6].…”