Modeling

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

2. Outline • Acquisition • Seashells • Fractals • Volumes • Constructive Solid Geometry • 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. Lorensen Stanford Graphics Laboratory

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

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

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 • Seashells • Fractals • Volumes • Constructive Solid Geometry • Modeling Programs

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

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

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

20. Example: Seashells • Model is parameterized: • Helico-spiral: z0, lz, r0, lr, Nq, Dq • Generating curve: shape, Nc, lc Fowler et al. Figure 1

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

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

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

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

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

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 Koch Curve H&B Figure 10.69

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

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

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

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 • Useful for creating mountains H&B Figure 10.83a

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

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

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

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

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 Stanford University SUNY Stony Brook

46. Voxel Storage • O(n3) 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