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Isosurfacing (Part 2 )

Isosurfacing (Part 2 ). Hank Childs, University of Oregon. October 25th, 2013. Announcements. Final project Pre-defined project: Volume rendering Finding data http://sciviscontest.ieeevis.org / Talk with me I may delay Nov 1 st quiz to Nov 6 th (stay tuned)

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Isosurfacing (Part 2 )

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  1. Isosurfacing (Part 2) Hank Childs, University of Oregon October 25th, 2013

  2. Announcements • Final project • Pre-defined project: Volume rendering • Finding data • http://sciviscontest.ieeevis.org/ • Talk with me • I may delay Nov 1st quiz to Nov 6th (stay tuned) • OH: Fri 12-1 is a bad time • How would Thurs 2-3 be?

  3. Project 5 • What is the ground truth?

  4. Height field over a terrain

  5. IsolinesvsIsosurfaces • Isolines: • Input: scalar field over 2D space • Output: lines • Isosurfaces: • Input: scalar field over 3D space • Output: surface • Commonalities: • Reduce topological dimension by 1 • Produce output where scalar field is constant

  6. Iterating Over Cells • For isosurface/isoline calculation, we can iterate over the cells. • At the end, we take the results from each cell and put them into a single scene.

  7. Reality Check: context for isolines • We have millions of cells • If one cell can produce tens or hundreds of lines, then the isolines could take much more memory than the input data set

  8. Big picture: what do we want from our isosurface? • Tractable computation • Can’t create 100s or 1000s of line segments per cell for super-accurate representation • Continuous surface • Triangles (or lines for an isosurface) need to connect up … no gaps.

  9. Big idea #1: approximate the isolines / isosurface • Isolines: represent them with a minimal # of segments • Isosurface: represent them with a minimal # of triangles

  10. Quiz: how to approximate our “quarter circle”?

  11. Big picture: what do we want from our isosurface? • Tractable computation • Can’t create 100s or 1000s of line segments per cell for super-accurate representation • Quiz: did we accomplish this? • Yes: very few per cell • Continuous surface • Triangles (or lines for an isosurface) need to connect up … no gaps. • Quiz: did we accomplish this? Answer: we got the answer exactly right at the edge of the cell … hence no gaps. 

  12. The 16 cases Case 0 Case 1-5 Case 6-10 Case 11-15

  13. Big idea #2: do pre-computation to make it fast If you knew which case you had, then you would know how to proceed • Pre-compute correct answers for all 16 cases and store them in a lookup table • For each cell, identify which case it is in • Then use corresponding lookup table to generate isosurface

  14. Big idea #2: pre-computation of all possible cases If you knew which case you had, then you would know how to proceed • Pre-compute correct answers for all 16 cases and store them in a lookup table • For each cell, identify which case it is in • Then use corresponding lookup table to generate isosurface

  15. Pre-compute correct answers for all 16 cases and store them in a lookup table • Observations about correct answers for a case: • It contains one or two line segments • The ends of the line segments are always along edges.

  16. Pre-compute correct answers for all 16 cases and store them in a lookup table Edge 2 • The ends of the line segments are always along edges. • We will need to number the edges Edge 1 Edge 3 Edge 0

  17. Big idea #2: do pre-computation to make it fast If you knew which case you had, then you would know how to proceed • Pre-compute correct answers for all 16 cases and store them in a lookup table • For each cell, identify which case it is in • Then use corresponding lookup table to generate isosurface

  18. For each cell, identify which case it is in Vertex 2 Vertex 3 • 4 vertices • Each has one of 2 possible classification values • Lower than isovalue • Call this “0” • Higher than isovalue • Call this “1” • (ignore equality case) 1 1 1 0 Vertex 1 Vertex 0

  19. For each cell, identify which case it is in Vertex 2 Vertex 3 • Goal: turn classification values into a number • Number should be between 0 and 15 • Idea: use binary numbers • V3V2V1V0  1 1 1 0  14 1 1 1 0 Vertex 1 Vertex 0 This is case 14

  20. The 16 cases 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 Case 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 Case 1-5 Case 6-10 Case 11-15

  21. Big idea #2: do pre-computation to make it fast If you knew which case you had, then you would know how to proceed • Pre-compute correct answers for all 16 cases and store them in a lookup table • For each cell, identify which case it is in • Then use corresponding lookup table to generate isosurface

  22. Then use corresponding lookup table to generate isosurface intnumSegments[16]; numSegments[0] = 0; ... numSegments[6] = 2; ... numSegments[14] = 1; numSegments[15] = 0;

  23. Then use corresponding lookup table to generate isosurface intlup[16][4]; // lup == lookup lup[0][0] = lup[0][1] = lup[0][2] = lup[0][3] = -1; ... lup[6][0] = 0; lup[6][1] = 1; lup[6][2]=2; lup[6][3] = 3; … lup[14][0] = 0; lup[14][1] = 3; lup[14][2] = lup[14][3] = -1; lup[15][0] = lup[15][1] = lup[15][2] = lup[15][3] = -1;

  24. Then use corresponding lookup table to generate isosurface inticase = IdentifyCase(cell); // case is a reserved word in C++ intnsegments = numSegments[icase]; for (inti = 0 ; i < nsegments ; i++) { int edge1 = lup[icase][2*i]; float pt1[2] = // Interpolate position along edge1 int edge2 = lup[icase][2*i+1]; float pt2[2] = // Interpolate position along edge2 AddLineSegmentToOutput(pt1, pt2); }

  25. Isosurfacing • Will follow a very similar game plan. • Pre-compute correct answers for all cases and store them in a lookup table • For each cell, identify which case it is in • Then use corresponding lookup table to generate isosurface

  26. Isosurfacing 0 0 1 0 Quiz: where should the isosurface go? 0 0 0 0

  27. Isosurfacing 0 0 1 0 Quiz: where should the isosurface go? 0 0 0 0

  28. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 1

  29. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 0 0 0 1

  30. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 0

  31. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 0

  32. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 0

  33. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 0

  34. Isosurfacing 1 0 1 0 Quiz: where should the isosurface go? 1 0 0 0

  35. Isosurfacing V6 V7 V4 V5 We need conventions! V2 V3 V1 V0 Z Y X

  36. Isosurfacing V6 V7 V4 V5 We need conventions! E2 E3 V2 V3 E1 V1 V0 E0 Z Y X

  37. Isosurfacing V6 E6 V7 E7 V4 V5 E5 We need conventions! E4 V2 V3 V1 V0 Z Y X

  38. Isosurfacing V6 V7 V4 V5 We need conventions! E11 E10 E9 E8 V2 V3 V1 V0 Z Y X

  39. Isosurfacing V6 V7 V4 V5 static int edges[12][2] = { {0,1}, {1,3}, {2,3}, {0,2}, {4,5}, {5,7}, {6,7}, {4,6}, {0,4}, {1,5}, {2,6}, {3,7} }; V2 V3 V1 V0 Z Y X

  40. Different cell types • We know how to contour cubes • How do we do tetrahedrons? Prisms? Wedges?

  41. Our isosurface approximation is improved by computer graphics

  42. Project 6 • 6A: implement marching quads (Weds lecture), including all 16 cases • 6B: implement marching cubes, but only a subset of the cases • We will use SVN to share our cases • There will be a case checker • Ambiguities are hard • Everyone does 6A, some do 6B • Please email if you want to do 6B

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