SLIDE 1
Parameterization
- f
Meshes
CS 176 Winter 2011
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Meshes
2-Manifold
What makes for a smooth manifold?
locally looks like Euclidian space collection of charts
ll ibl
CS 176 Winter 2011
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mutually compatible
- n their overlaps
form an atlas
Parameterizations are key
Parameterizations
What is a parameterization?
function from some region ⊂ R2
to the embedded surface M⊂ R3
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Image from Sander et al. 2002
Task
Find map from mesh to R2
identify region on mesh and find
map to R2
n et al. 2002
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what’s different?
existence of solutions when mapping
to convex region
Image from Desbrun
Applications
texture mapping
piecewise linear
interpolation of
Parameterizations
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interpolation of attributes across mesh
resampling simulation
needs surface as function
First Attempt
Tutte, 1963
make planar vertex the barycenter
- f its neighbors
fix boundary
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fix boundary
convex!
- riginal
centroid mapping