1. Scientific Visualization Data and Geometry Processing for Scientific Visualization CS 5630 / 6630 August 28, 2007

2. Recap: The Vis Pipeline

4. Processsing the data Smoothing  Image smoothing  resampling Reconstruction  Meshing  Mesh smoothing Simplification  Mesh “resampling”

5. (VisTrails Demo)‏ (Edge detection with noise)‏ (Resampling high-res image)‏

6. Processing Regular Data Spatial domain filtering Frequency domain filtering

7. Spatial Filtering Convolution

10. Edge detection

11. Derivative of convolution is convolution with derivative

12. 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

13. Frequency Domain Filtering

15. (VisTrails Demo)‏ (Triangle meshes to approximate function)‏

16. Unstructured grid challenges Shape of the elements becomes critical for quality and performance of simulation and visualization

17. Not all meshes are created equal! J. Shewchuk. What is a good linear element?

18. Triangle Meshes Node spacing roughly corresponds to mesh quality  Only to zeroth order

19. 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

20. (VisTrails Demo)‏ (Smoothing triangle meshes to improve triangles)‏

21. Issues What happened to boundary? Volume? What if that was your kneecap?

22. 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

23. Mesh Simplification Vertex clustering Edge collapse

24. Vertex Clustering Start with any mesh

25. Vertex Clustering Start with any mesh Overlay a grid

26. Vertex Clustering Start with any mesh Overlay a grid If more than one vertex in a cell, merge them

27. Edge Collapse Start with any mesh

28. Edge Collapse Start with any mesh Pick some edge and join it  repeat

29. Edge Collapse Start with any mesh Pick some edge and join it  repeat

30. (VisTrails Demo)‏ Simplification