Last update: May 22, 2002

BACK

3D Shape Representation based on Shocks - Transitions

Frederic F. Leymarie and Benjamin B. Kimia, Brown

Peter J. Giblin, Liverpool

A_1 A_3 - I Transition - Gaussian bump

A_1 A_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.

First two steps: (i) Two flat planes; (ii) a Gaussian perturbation is initiated on the top plane. Top row: Sketch; Bottom: Simulation

Two more steps: (iii) Gaussian perturbation becomes a small bump; (iv) Gaussian bump. Top row: Sketch; Bottom: Simulation

Inputs

We illustrate, in greater detail, the final stage of 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.

We run this expriment on two data-sets: one where we uniformly sample each surface, and one where we randomly sample them.

Inputs

Uniform sampling

Random sampling

Gaussian bump sets: 3200 pts.  

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.

Surface Meshes

Uniform sampling

Random sampling

 

Recovered "Internal" Medial Axis description

Internal MA (3 views for each set) - Distance to source flow field as rainbow colormap (red is far, blue is close)

Unifrom sampling

Random sampling

Last updated: May 22, 2002

F.F.Leymarie

BACK