1. GATE-540 1 3D Object Representations (GATE-540) Dr.Çağatay ÜNDEĞER Instructor Middle East Technical University, GameTechnologies & General Manager SimBT Inc. e-mail : cagatay@undeger.com Game Technologies Program – Middle East Technical University – Spring 2010 Reference: Thomas Funkhouser, Princeton University

2. GATE-540 2 Outline 3D Objects Raw Data Types 3D Object Representations –Surface models –Solid models –High-Level Structures

3. GATE-540 3 Goals Develop 3D Analysis Algorithms: –Reconstruction –Segmentation –Feature Detection –Labeling –Matching –Classification –Retrielval –Recognition –Clustering Different methods are applicable to different representations.

4. GATE-540 4 3D Objects How can this simple object be represented in a computer?

5. GATE-540 5 3D Objects Is representing this object similar to the previous one an effective way? Highly smooth curves...

6. GATE-540 6 3D Objects How about this one? A volumetric body... Outer surface...

7. GATE-540 7 3D Objects How about these ones? Has soft and hard tissue... Has different densities... Has Interrior...

8. GATE-540 8 3D Objects What about this one? Composed of different geometric parts / shapes...

9. GATE-540 9 3D Objects This one?

10. GATE-540 10 3D Objects How about these? A deformable body... Animation integration...

11. GATE-540 11 3D Object Representations Raw Data –Point cloud –Range image –Polygon soup –... Surfaces –Mesh –Subdivision –Parametric –Implicit Solids –Voxels –BSP Tree –Cell Complex High-Level Structures –CSG –Constraint blocks –Generative model –Skeleton –Sweep model –Scene graph

12. GATE-540 12 Point Cloud Unstructured set of point samples Range finders, 3D scanners, computer vision

13. GATE-540 13 Range Image Set of 3D points that maps to pixels of a depth image From range scanners Range (depth) image

14. GATE-540 14 Range Image A kind of more structured point cloud Generating surfaces from 3d points

15. GATE-540 15 Polygon Soup Unstructures set of polygons or unconnected lines of polygons Mostly creates with interactive modeling sys.

16. GATE-540 16 Surface Objects Mesh Subdivision Parametric Implicit

17. GATE-540 17 Mesh Connected set of polygons (usually triangles)

18. GATE-540 18 Subdivision Surface Consists of a coarse mesh and subdivision rule Generates smooth surfaces with refinements

19. GATE-540 19 Parametric Surface Bezier / spline surface patches Defined with a parametric equation

20. GATE-540 20 Many smooth and deformable objects are difficult or inefficient to represent with basic primitives, even with bezier/spline surfaces. Field functions with control points, line segments and/or polygonally bounded planes are used to define shapes in space. Implicit Surface

21. GATE-540 21 Solid Objects Voxels BSP Tree Cell Complex

22. GATE-540 22 Voxels Uniform 3D grid of volumetric samples Mostly acquired from CAT, MRI, etc.

23. GATE-540 23 BSP Tree Binary space partition with labeled solid cells Constructed from polygonal representations

24. GATE-540 24 Cell Complex A topological space, an arrangement of polyhedral cells with adjacent cells linked and solid cells labeled e.g. Adjacency graph of BSP leaf cells

25. GATE-540 25 Topology of 3D Representations

26. GATE-540 26 High-Level Structures CSG (Constructive Solid Geometry) Constraint blocks Generative model Skeleton Sweep model Scene graph

27. GATE-540 27 CSG (Constructive Solid Geometry) Hierarchy of boolean set operators (union, difference, subtraction, intersection) applied to simple shapes

28. GATE-540 28 Constraint Blocks Set of simple shapes with geometric constraints

29. GATE-540 29 Generative Model Hierarchy of modification operators on a shape

30. GATE-540 30 Skeleton A set of connected bone structures deforming shape of a 3D model

31. GATE-540 31 Sweep Model A 3d model generated by sweeping a surface along a trajectory

32. GATE-540 32 Scene Graph Union of objects at leaf nodes of a tree

33. GATE-540 33 Summary Object representation is the key for our goal