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3D Object Representations (GATE-540)

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

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3D Object Representations (GATE-540)

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

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

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

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

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

  6. 3D Objects • How about this one? • A volumetric body... • Outer surface...

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

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

  9. 3D Objects • This one?

  10. 3D Objects • How about these? • A deformable body... • Animation integration...

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

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

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

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

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

  16. Surface Objects • Mesh • Subdivision • Parametric • Implicit

  17. Mesh • Connected set of polygons (usually triangles)

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

  19. Parametric Surface • Bezier / spline surface patches • Defined with a parametric equation

  20. Implicit Surface • 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.

  21. Solid Objects • Voxels • BSP Tree • Cell Complex

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

  23. BSP Tree • Binary space partition with labeled solid cells • Constructed from polygonal representations

  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. Topology of 3D Representations

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

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

  28. Constraint Blocks • Set of simple shapes with geometric constraints

  29. Generative Model • Hierarchy of modification operators on a shape

  30. Skeleton • A set of connected bone structures deforming shape of a 3D model

  31. Sweep Model • A 3d model generated by sweeping a surface along a trajectory

  32. Scene Graph • Union of objects at leaf nodes of a tree

  33. Summary • Object representation is the key for our goal

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