PWLSF - 3/2016 - Gilbert Bernstein on Marching Cubes

Gilbert Bernstein on Marching Cubes (http://www.eecs.berkeley.edu/~jrs/meshpapers/LorensenCline.pdf )

Marching Cubes is one of the most important geometry algorithms for 3D volume visualization, 3D scanning/reconstruction, etc. It has the distinction of being the most cited graphics paper ever. And it's also definitely not the best algorithm you could implement for the problem it solves. Intriguing?

Gilbert's Bio

Gilbert Bernstein is a Ph.D. student in the department of Computer Science at Stanford University. His work focuses on a range of topics across Computer Graphics, HCI and Programming Languages, including Domain-Specific (Programming) Languages, Visual Tools for Artists and Designers, Geometry and Topology. He’s gotten some awards in the past that you don’t really care about. The only song Gilbert can rap at karaoke is “Amish Paradise."

Meetup: http://www.meetup.com/papers-we-love-too/events/228340935/

Video: https://www.youtube.com/watch?v=7dc4Tl5ZHRg

Transcript

1. Marching Cubes
2. Hey Gilbert, could you give a talk thing at this thing that we are at right now? that would be awesome
3. Uhhh, sure!
4. ?
5. ‘pooter Time!
8. What does Marching Cubes do?
9. Topographic Map map by Brian Stokle @urbanlifesigns
10. Topographic Map map by Brian Stokle @urbanlifesigns
11. Iso-contour 100 ft elevation map by Brian Stokle @urbanlifesigns
12. Marching Cubes extracts Iso-Surfaces
13. CT & MRI Machines Perform Scan in Slices images: wikipedia
14. slices vs. iso-surface images: wikipedia
15. movies: LBNL - http:/ /vis.lbl.gov/Events/SC05/Incite4/ Visualization of Magneto-rotational instability and turbulent angular momentum transport
16. level-set diagram from http:/ /cmcs.epfl.ch/ methodologies/freesurface videos from Ron Fedkiw’s website Level-Set Simulation
17. 3d Sculpting this is a program called 3d Coat
18. Poisson Surface Reconstruction, by Kazhdan et al. Symposium on Geometry Processing 2006 Standard 3d Scanning Pipeline
19. Poisson Surface Reconstruction, by Kazhdan et al. Symposium on Geometry Processing 2006 1. scan object, producing point-cloud Standard 3d Scanning Pipeline
20. Poisson Surface Reconstruction, by Kazhdan et al. Symposium on Geometry Processing 2006 1. scan object, producing point-cloud 2. use points to compute a signed- distance function Standard 3d Scanning Pipeline
21. Poisson Surface Reconstruction, by Kazhdan et al. Symposium on Geometry Processing 2006 1. scan object, producing point-cloud 3. extract surface as 0-value isocontour 2. use points to compute a signed- distance function Standard 3d Scanning Pipeline
23. How Does Marching Cubes Work?
24. Marching “Squares”
25. Some Surface
26. Simplify: Binary
27. Marching Squares Basic Idea
28. Basic Idea Marching Squares
29. Basic Idea Marching Squares
30. Basic Idea Marching Squares
31. Basic Idea Marching Squares
32. Basic Idea Marching Squares
33. Basic Idea Marching Squares
34. Interpolated Cut Values
35. Marching “Squares” per-square cases ? ? ? ? 2x2x2x2 = 2^4 = 16 cases
36. 16 Cases
37. 16 Cases
38. 16 Cases
39. Ambiguous Cases
40. Only Edge Agreement Matters
41. Marching Cubes Cases 256 cases
42. Case Analysis Dr. Alan Cline
43. Case Analysis If you try to prove something by case analysis, you’ll probably get it wrong. Dr. Alan Cline
44. Marching Cubes Cases 256 cases
45. The entire case analysis
47. Marching Tetrahedra 16 cases one-possible fix Paul Bourke http:/ /paulbourke.net/geometry/polygonise/
48. oh, and patents…
49. Dual Contouring of Hermite Data Tao Ju, Frank Losasso, Scott Schaefer, & Joe Warren
50. Dual Contouring of Hermite Data Tao Ju, Frank Losasso, Scott Schaefer, & Joe Warren
51. “Hermite” Data aka. normals or gradient
52. “Hermite” Data aka. normals or gradient
53. The Dual Grid
54. Duality primal dual in 2d in 3d
55. Dual Topology
56. Finding Crossings
57. Finding Crossings
58. Finding Crossings
59. Finding Crossings
60. Finding Crossings
61. Finding Crossings
62. Finding Crossings
63. Final Surface
64. What’s so great about these algorithms? small working-set relatively simple fundamental problem
65. A Big Open Question
66. A Big Open Question Brian Curless professor @ UW in Seattle
69. How accurate is this… … compared to the actual world?
70. Fuhrmann & Goesele. Floating Scale Surface Reconstruction, SIGGRAPH 2014 4 scans noise reduction noise amplification
71. the End
72. Links / References • Lorensen & Cline. Marching Cubes, SIGGRAPH 1987 • Paul Bourke. Polygonizing a Scalar Field Using Tetrahedrons, Website • Ju et al. Dual Contouring of Hermite Data, SIGGRAPH 2002 • Schaefer & Warren. Dual Contouring: “The Secret Sauce”, White Paper • links to many papers: https:/ /swiftcoder.wordpress.com/planets/ isosurface-extraction/ super-valuable details here