Forsch, Kemna, Langetepe and Haunert – MORPHING OF SCHEMATIZED POLYGONS FOR ANIMATED TRAVEL-TIME MAPS 2019

Description

The paper presents an algorithm to compute animated morphs between schematized travel-time isochrones—polygonal outlines of equal travel time that vary strongly with start time—aiming to keep schematic properties (e.g., octilinearity) during transitions. The authors reduce polygon morphing to polyline morphing by splitting outlines, then model point movement as constant-velocity vertex matchings. Three basic operations (match, insert, delete) plus multi-insert/multi-delete composite operations handle differing segment sampling; auxiliary vertices may be inserted on a segment while preserving order to maintain schematization. Matches are constrained to segments of identical orientation so all intermediate polylines remain schematic. Different scoring functions (point distances, segment similarity) evaluate morph quality, and a dynamic programming method (extending Nöllenburg et al.) finds optimal morphs under the orientation constraint. Future work addresses matching corresponding rings when isochrones contain multiple polygonal rings and extending polygon correspondence techniques for broader application.