May 2001
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Shock Scaffold
Definitions
Order of contact : Giblin & Kimia
A_k^n
:
k+1
degree of contact at
n
distinct points
Only "odd" orders of contacts (
i.e.
, k = 1, 3) can contribute to the MA
In 3D, this leads to FIVE principal types of shocks :
A_1^2 : SHEETS
A_1^3 : Axial CURVES
A_3 : Boundary CURVES (
e.g.
, Ridges)
A_1^4 : Voronoi NODES
A_1 A_3 : Surface NODES (
e.g.
, end of ridges)
Shock Flow : Leymarie & Kimia
Flow along curves
Flow at nodes
Flow on surfaces
Scaffold of Tetrahedron
Truncated tetrahedron
Close Relationship with Voronoi Diagrams
A_1^4 shock points are the Voronoi nodes
Additional structure in the Scaffold: Initial points of flow on sheets and curves
Conjecture 1 : The Scaffold includes the Voronoi diagram
Conjecture 2 : The Scaffold includes the CW-complex (or Molecular graph)
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