Last update: May 14, 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


Transitions

The 26 topologically different perestroikas of the momentary shock waves are shown by arrows (after Bogaevski).
Those relevant to the Medial Axis are indicated by a double-arrow.
Single lines indicate the (exterior) boundary of the shock illustration.
Double lines indicate rims where shock sheets are limited by surface ridges, i.e., they correspond to A_3 shock curves.
Triple lines indicate intercepts of shock sheets, i.e., they correspond to A_1^3 shock curves.
Concentric circles indicate an overlap of medial points.

3D Transistions relevant for the Medial Axis:

  1. A_1 A_3 - I (protrusion-like event)
  2. A_1 A_3 - II (pulling apart-like event)
  3. A_1^5 (squashed prism)
  4. A_1^4 (squeezed tube)
  5. A_5 (tube with ridges)
  6. A_1^2 A_3 - I (protrusion near axis)
  7. A_1^2 A_3 - II (protrusion thru axis)


F.F.Leymarie

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