April 2001
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Shock Scaffold
Definitions
Order of contact : Giblin & Kimia
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A_k^n : k+1
degree of contact at n distinct points
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Only "odd" orders of contacts (i.e.,
k = 1, 3) can contribute to the MA
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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
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Scaffold of Tetrahedron
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Truncated tetrahedron
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Computations : Shockwaves and Bisectors
Pairs of "sources" and their bisectors (the Full Symmetry
Set).
The (trimmed) MA and its shock flows.
Close Relationship with Voronoi Diagrams
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A_1^4 shock points are the Voronoi nodes
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Additional structure in the Scaffold: Initial points
of flow on sheets and curves
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Conjecture 1 : The Scaffold includes the Voronoi
diagram
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Conjecture 2 : The Scaffold includes the CW-complex
(or Molecular graph)
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