Last update: Jan. 20, 2004

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3D Shape Representation based on Shocks - Transitions

Benjamin B. Kimia, Frederic F. Leymarie and Ming-Ching Chang, Brown University

Peter J. Giblin, Liverpool University

A_1 A_3-I Transition - Protrusion-like event

A_1A_3-I Transition
(after Bogaevski)

Illustration

We illustrate the transition between two planar patches, where we "pull" out an elongated Gaussian-like bump from one of the two planes, leading to the creation of a new vertical sheet bounded above by an A_3 ridge-like shock curve, and below by an A_1^3 axial-like shock curve (Gaussian bump sets made of 3200 point generators).

Initially, a slight bump on the top surface start rising up the
MA sheet (before transition point)

Soon after transition, the loop structure appears.

More surface pull brings up the loop bounding a new MA sheet.

Even more pull accentuates the loop upward pull.
Here we also emphasize the junction points
(a pairs of A_1 A_3's shown as small spheres).

Recovered Surfaces

The "surface scaffold" (i.e., the less significant part of the shock scaffold) gives us back a meshing of the input data. Thus, we can re-build connectivity on the input samples automatically.


Recovered surfaces for the 4th dataset above.

 


Combined surface mesh and scaffold.

More details here (old page)

F.F.Leymarie

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