Scientific Visualization

Data and Geometry Processing for Scientific Visualization

CS 5630 / 6630August 28, 2007

Recap: The Vis Pipeline

Recap: The Vis Pipeline

Processsing the data

Smoothing Image smoothing resampling

Reconstruction Meshing Mesh smoothing

Simplification Mesh “resampling”

(VisTrails Demo)

(Edge detection with noise) (Resampling high-res image)

Processing Regular Data

Spatial domain filtering Frequency domain filtering

Spatial Filtering

Convolution

Edge detection

Edge detection

Derivative of convolution is convolution with derivative

Frequency Domain Filtering

Convolution in the spatial domain is multiplication in the frequency domain Much faster if kernel is wide

Things make more mathematical sense in the frequency domain More intuitive filter design

Frequency Domain Filtering

Frequency Domain Filtering

(VisTrails Demo)

(Triangle meshes to approximate function)

Unstructured grid challenges

Shape of the elements becomes critical for quality and performance of simulation and visualization

Not all meshes are created equal!

J. Shewchuk. What is a good linear element?

Triangle Meshes

Node spacing roughly corresponds to mesh quality Only to zeroth order

Mesh filtering

Laplacian smoothing Move vertices to centroid of neighborhood

“Filtering” because it looks like spatial filtering you can actually find a Fourier transform if

you squint hard enough

(VisTrails Demo)

(Smoothing triangle meshes to improve triangles)

Issues

What happened to boundary? Volume? What if that was your kneecap?

Tetrahedral Meshes

Even when vertices are nicely apart from one another, there can be degenerate tetrahedra (!)

http://www.ics.uci.edu/~eppstein/junkyard/tetraqual.gif

Mesh Simplification

Vertex clustering Edge collapse

Vertex Clustering

Start with any mesh

Vertex Clustering

Start with any mesh

Overlay a grid

Vertex Clustering

Start with any mesh

Overlay a grid If more than one

vertex in a cell, merge them

Edge Collapse

Start with any mesh

Edge Collapse

Start with any mesh

Pick some edge and join it repeat

Edge Collapse

Start with any mesh

Pick some edge and join it repeat

(VisTrails Demo)

Simplification