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Accelerated Isosurface Extraction Approach

Introducing a novel representation called Span Space to expedite isosurface extraction, reducing processing time for both structured and unstructured grids. The approach includes geometric and interval search methods, lattice subdivision, implementation details, and a parallel algorithm for efficient extraction. Incorporating a Kd-tree for point organization, this course presents new techniques in isosurface extraction.

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Accelerated Isosurface Extraction Approach

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  1. Accelerated Isosurface Extraction Approach Course: Visualization Modelling Presents Alex Levin International University Bremen International University Bremen 2006

  2. Introduction International University Bremen 2006

  3. Introduction New representation, called Span Space will reduce the running time to for both structured and unstructured grids. International University Bremen 2006

  4. Span Space International University Bremen 2006

  5. Isosurface Extraction We deal with Accelerated Isosurface Extraction Approach [remember?] International University Bremen 2006

  6. Isosurface Extraction International University Bremen 2006

  7. Isosurface Extraction International University Bremen 2006

  8. Isosurface Extraction 1. 2. International University Bremen 2006

  9. Isosurface Extraction International University Bremen 2006

  10. Isosurface Extraction [Geometric Search Approach] International University Bremen 2006

  11. Isosurface Extraction [Geometric Search Approach] International University Bremen 2006

  12. Isosurface Extraction[Interval Search Approach] International University Bremen 2006

  13. Isosurface Extraction[Span Space] • There is a better approach International University Bremen 2006

  14. Isosurface Extraction[Span Space] International University Bremen 2006

  15. Lattice (net) Subdivision International University Bremen 2006

  16. Search Approach International University Bremen 2006

  17. Searching Approach International University Bremen 2006

  18. Searching Approach International University Bremen 2006

  19. Searching Approach International University Bremen 2006

  20. Searching Approach International University Bremen 2006

  21. Searching Approach International University Bremen 2006

  22. Searching Approach International University Bremen 2006

  23. Searching Approach International University Bremen 2006

  24. Searching Approach International University Bremen 2006

  25. Implementation Details • How determine the dividing points {di}? • What happen with sparse dataset?-- avoid visiting empty lattice elements International University Bremen 2006

  26. Implementation Details International University Bremen 2006

  27. Implementation Details International University Bremen 2006

  28. Implementation Details International University Bremen 2006

  29. Implementation Details • To avoid this, we find di in such a way that the number of data points at each interval approximately the same. How to do it? International University Bremen 2006

  30. Implementation Details • Sort all data points into a list and divide the list into L sub-lists having approximately the same lengths. • Problem!!More sub-division we have->larger number of empty lattice elements are possible. International University Bremen 2006

  31. Implementation Details • What we do is: as we pre-process the data field and distribute the cells into the lattice, the non-empty lattice element are marked and connected with pointers. International University Bremen 2006

  32. Parallel Algorithm Three steps: • Cell distribution phase: cells are partitioned into several sub-sets and distributed to Processing Elements [PE]. • Initialization phase: each PE build lattice, based on local data • Isosurface Extraction phase: each PE locally employs searching algorithm to extract the isosurface. International University Bremen 2006

  33. Parallel Algorithm • Example: we have 3 Processing Elements: 0,1,2. After distribution  each PE has its field of processing International University Bremen 2006

  34. Kd –tree search • Remember Interval Method->min and max values?! • Min & Max -> maintaining two lists • May we combine 2 lists in one? Yes, using Kd-tree International University Bremen 2006

  35. Kd-tree Introduction • A kd-tree (short for k-dimensional tree) is a space-partitioningdata structure for organizing points in a k-dimensional space International University Bremen 2006

  36. Kd-tree Introduction • Example:point list = [(2,3), (5,4), (9,6), (4,7), (8,1), (7,2)] International University Bremen 2006

  37. Kd-tree Introduction International University Bremen 2006

  38. Kd-tree International University Bremen 2006

  39. Construction of Kd-tree International University Bremen 2006

  40. Summary • We showed that there is possibility to implement new approaches in for Extracting Span Space. International University Bremen 2006

  41. References • Han-Wei Shen, Charles D. Hansen, Yarden Livnat, Christopher R. Johnson, Isosurfacing in Span Space with Utmost Efficiency (ISSUE); • Yarden Livnat, Han-Wei Shen, Christopher R. Johnson, A Near Optimal Isosurface Extraction Algorithm Using the Span Space • Johnson/Hnsen, The Visualization Handbook, chapter 2: Accelerated Isosurface Extraction Approaches International University Bremen 2006

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