Post on 18-Dec-2015
Martin Isenburg
University of North Carolina
at Chapel Hill
Craig Gotsman
Technion - Israel Instituteof Technology
Stefan Gumhold
University of Tübingen
Connectivity Shapes
Overview
• Shape from Connectivity• Connectivity from Shape• Hierarchical Methods• Applications
– Graph Drawing– Compression– Connectivity Creatures
• Discussion
Connectivity Shape
Given a connectivity graph C = ( V, E )consisting of a list vertices
V = ( v1 , v2 , ... , vn )and a set undirected edges
E = { e1 , e2 , ... , em } : ej = ( i1 , i2 )
The connectivity shape CS ( C ) of C is alist of vectors ( x1 , x2 , x3 , ... , xn ) : xi R3
that satisfy some “natural” property.
Some “Natural” Property
“all edges have unit length”
Equilibrium state of spring system.
The connectivity shape is the solution to a set of m equations of the form
|| xi - xj || = 1 ( i , j ) E
The number of unknowns is determined by Euler’s relation m = n + f + 2g - 1
Meshing / Re-meshing
objective:
generate a faithful approximation of a given shape, but use only edges of unit length
we customized Turk method