1. Modeling Aaron Bloomfield CS 445: Introduction to Graphics Fall 2006 (Slide set originally by Greg Humphreys)

2. Outline  Acquisition Seashells Seashells Fractals Fractals Volumes Volumes Constructive Solid Geometry Constructive Solid Geometry Modeling Programs Modeling Programs

3. Model Construction Interactive modeling tools CAD programs Subdivision surface editors :) Scanning tools CAT, MRI, laser, magnetic, robotic arm, etc. Computer vision Stereo, motion, etc.

4. Interactive Modeling Tools User constructs objects with drawing program Menu commands, direct manipulation, etc. CSG, parametric surfaces, quadrics, etc. Cosmoworlds, SGI

5. Interactive Modeling Tools Example: Mechanical CAD H&B Figure 9.9

6. Model Construction Interactive modeling tools CAD programs Subdivision surface editors :) Scanning tools Laser, magnetic, robotic arm, etc. Computer vision Stereo, motion, etc.

7. Scanning tools Acquire geometry of objects with active sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm etc. Stanford Graphics Laboratory Lorensen

8. Scanning tools Acquire geometry of objects with active sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm etc. Depth Color Xp(Xc,Yc)

9. Laser Range Scanning Stanford Graphics Laboratory Example: 70 scans Volumetric reconstruction

10. Scanning tools Acquire geometry of objects with active sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm etc.

11. Scanning tools Acquire geometry of objects with active sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm etc.

12. Computer Vision Infer 3D geometry from images Stereo Motion Constraints etc.

13. Computer Vision Infer 3D geometry from images Stereo Motion Constraints etc.

14. Computer Vision Infer 3D geometry from images Stereo Motion Constraints etc. Debevec96

15. Procedural Modeling Goal: Describe 3D models algorithmically Best for models resulting from... Repeating processes Self-similar processes Random processes Advantages: Automatic generation Concise representation Parameterized classes of models

16. Outline Acquisition Acquisition  Seashells Fractals Fractals Volumes Volumes Constructive Solid Geometry Constructive Solid Geometry Modeling Programs Modeling Programs

17. Example: Seashells Create 3D polygonal surface models of seashells Fowler et al. Figure 7 “Modeling Seashells,” Deborah Fowler, Hans Meinhardt, and Przemyslaw Prusinkiewicz, Computer Graphics (SIGGRAPH 92), Chicago, Illinois, July, 1992, p 379-387. “Modeling Seashells,” Deborah Fowler, Hans Meinhardt, and Przemyslaw Prusinkiewicz, Computer Graphics (SIGGRAPH 92), Chicago, Illinois, July, 1992, p 379-387.

18. Example: Seashells Sweep generating curve around helico-spiral axis Fowler et al. Figure 1 Helico-spiral definition:

19. Example: Seashells Connect adjacent points to form polygonal mesh Fowler et al. Figure 6

20. Example: Seashells Model is parameterized: Helico-spiral: z 0,  z  r 0,  r    Generating curve: shape, N c,  c Fowler et al. Figure 1

21. Example: Seashells Generate different shells by varying parameters Fowler et al. Figure 2 Different helico-spirals

22. Example: Seashells Generate different shells by varying parameters Fowler et al. Figure 3 Different generating curves

23. Example: Seashells Fowler et al. Figures 4,5,7 Generate many interesting shells with a simple procedural model! Generate many interesting shells with a simple procedural model!

24. Outline Acquisition Acquisition Seashells Seashells  Fractals Volumes Volumes Constructive Solid Geometry Constructive Solid Geometry Modeling Programs Modeling Programs

25. Fractals Defining property: Self-similar with infinite resolution H&B Figure 10.100 Mandelbrot Set

26. Fractals Useful for describing natural 3D phenomenon Terrain Plants Clouds Water Feathers Fur etc. H&B Figure 10.80

27. Fractal Generation Deterministically self-similar fractals Parts are scaled copies of original Statistically self-similar fractals Parts have same statistical properties as original

28. Deterministic Fractal Generation General procedure: Initiator: start with a shape Generator: replace subparts with scaled copy of original H&B Figure 10.68

29. Deterministic Fractal Generation Apply generator repeatedly H&B Figure 10.69 Koch Curve

30. Deterministic Fractal Generation Mandelbrot Figure X Useful for creating interesting shapes!

31. Deterministic Fractal Generation Mandelbrot Figure 46 Useful for creating interesting shapes!

32. Deterministic Fractal Generation H&B Figures 75 & 109 Useful for creating interesting shapes!

33. Fractal Generation Deterministically self-similar fractals Parts are scaled copies of original Statistically self-similar fractals Parts have same statistical properties as original

34. Statistical Fractal Generation General procedure: Initiator: start with a shape Generator: replace subparts with a self-similar random pattern Random Midpoint Displacement

35. Statistical Fractal Generation Example: terrain H&B Figure 10.83b

36. Statistical Fractal Generation H&B Figure 10.83a Useful for creating mountains

37. Statistical Fractal Generation H&B Figure 10.82 Useful for creating 3D plants

38. Statistical Fractal Generation H&B Figure 10.79 Useful for creating 3D plants

39. Outline Acquisition Acquisition Seashells Seashells Fractals Fractals  Volumes Constructive Solid Geometry Constructive Solid Geometry Modeling Programs Modeling Programs

40. Solid Modeling Represent solid interiors of objects Surface may not be described explicitly Visible Human (National Library of Medicine) SUNY Stony Brook

41. Motivation 1 Some acquisition methods generate solids Example: CAT scan Stanford University

42. Motivation 2 Some applications require solids Example: CAD/CAM Intergraph Corporation

43. Solid Modeling Representations What makes a good solid representation? Accurate Concise Affine invariant Easy acquisition Guaranteed validity Efficient boolean operations Efficient display Lorensen

44. Voxels Partition space into uniform grid Grid cells are called a voxels (like pixels) Store properties of solid object with each voxel Occupancy Color Density Temperature etc. FvDFH Figure 12.20

45. Voxel Acquisition Scanning devices MRI CAT Simulation FEM SUNY Stony Brook Stanford University

46. Voxel Storage O(n 3 ) storage for nxnxn grid 1 billion voxels for 1000x1000x1000

47. Voxel Boolean Operations Compare objects voxel by voxel Trivial  =  =

48. Voxel Display Isosurface rendering Render surfaces bounding volumetric regions of constant value (e.g., density) Isosurface Visualization Princeton University

49. Voxel Display Slicing Draw 2D image resulting from intersecting voxels with a plane Visible Human (National Library of Medicine)

50. Voxel Display Ray casting Integrate density along rays through pixels Engine Block Stanford University

51. Voxels Advantages Simple, intuitive, unambiguous Same complexity for all objects Natural acquisition for some applications Trivial boolean operations Disadvantages Approximate Not affine invariant Large storage requirements Expensive display

52. Quadtrees & Octrees Refine resolution of voxels hierarchically More concise and efficient for non-uniform objects Uniform VoxelsQuadtree FvDFH Figure 12.21

53. Quadtree Boolean Operations AB A  B A  B FvDFH Figure 12.24

54. Quadtree Display Extend voxel methods Slicing Isosurface extraction Ray casting Finding neighbor cell requires traversal of hierarchy (O(1)) FvDFH Figure 12.25

55. Outline Acquisition Acquisition Seashells Seashells Fractals Fractals Volumes Volumes  Constructive Solid Geometry Modeling Programs Modeling Programs

56. Constructive Solid Geometry (CSG) Represent solid object as hierarchy of boolean operations Union Intersection Difference FvDFH Figure 12.27

57. CSG Acquisition Interactive modeling programs CAD/CAM H&B Figure 9.9

58. CSG Boolean Operations Create a new CSG node joining subtrees Union Intersection Difference FvDFH Figure 12.27

59. CSG Display & Analysis Ray casting Circle Box Union

60. Outline Acquisition Acquisition Seashells Seashells Fractals Fractals Volumes Volumes Constructive Solid Geometry Constructive Solid Geometry  Modeling Programs

61. Popular rendering programs 3D Studio Max ($3.5k) Made by Autodesk (makers of CAD programs) Runs only on Windows (Win32 and Win64) Movies made w/Max: Incredibles, X-Men, Star Wars III, etc. Maya ($2k or $6k) Made by Alias Originally by SGI Bought by Autodesk in Oct 2006 Runs on Windows, Linux Blender (free!) Others are less well known and less used

62. http://en.wikipedia.org/wiki/Image:3dsmax8Screen shot.jpg http://en.wikipedia.org/wiki/Image:3dsmax8Screen shot.jpg 3D Studio Max

63. Maya http://en.wikipedia.org/wiki/Image:Autodesk_Maya _8.0_win32.png http://en.wikipedia.org/wiki/Image:Autodesk_Maya _8.0_win32.png

64. http://en.wikipedia.org/wiki/Image:Blender_node_s creen_242a.jpg http://en.wikipedia.org/wiki/Image:Blender_node_s creen_242a.jpg Blender

65. Comparison of renderers http://wiki.cgsociety.org/index.php/Comparison_of_ 3d_tools http://wiki.cgsociety.org/index.php/Comparison_of_ 3d_tools And a better formatted version…

66. Elephant’s Dream Downloadable at http://orange.blender.org/http://orange.blender.org/ An open movie Meaning you can download the Blender files that were used to make it Made using only open-source software Blender, GIMP, CinePaint, Inkscape, etc. Length is 11 minutes (including 90 sec of credits) That’s 19,800 frames Took a 2.1 TFLOPS supercomputer cluster 125 days to render Used Bowie State’s XSeed supercomputer Took 9 minutes and 2.8 Gb per frame An “average” high-end PC has only a “few” GFLOPS (not TFLOPS!) So if you had a 3 Ghz computer w/4 Gb of RAM, it would take over 200 years to render! Or 3 days per frame Assuming a 3 Gz computer can do 3 TFLOPS (a generous assumption)