Problem 52328. ICFP2021 Hole-In-Wall: Figure Validation with Segment Crossing Check
The contest folds the figure in Red to fit within the hole shown in light grey
This Challenge is to evaluate the complete Figure validation defined in the Specification when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole. The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.
Valid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)<= epsilon/1000000. Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.
Valid=check_figureS(hxy, pxy, mseg, epsilon, npxy)
Crossing Segments appears in Cody 1720 but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.
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