Exploded View Diagrams of Mathematical Surfaces

, , , and . IEEE Transactions on Visualization and Computer Graphics 16 (6): 1311--1318 (November 2010)


We present a technique for visualizing complicated mathematical surfaces that is inspired by hand-designed topologicalillustrations.Our approach generates exploded views that exposethe internal structure of such a surface by partitioning it intoparallel slices, which are separated from each other along a singlelinear explosion axis.Our contributions include a set of simple,prescriptive design rules for choosing an explosion axis and placingcutting planes, as well as automatic algorithms for applying theserules.First we analyze the input shape to select the explosionaxis based on the detected rotational and reflective symmetries ofthe input model.We then partition the shape into slices that aredesigned to help viewers better understand how the shape of thesurface and its cross-sections vary along the explosion axis.Our algorithms work directly ontriangle meshes, and do not dependon any specific parameterization of the surface.We generateexploded views for a variety of mathematical surfaces using oursystem.


Exploded View Diagrams of Mathematical Surfaces

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