3D Object Representation


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1 3D Object Representation Jason Lawrence CS445: Graphics Acknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin
2 3D Object Representation How do we... o Represent 3D objects in a computer? o Construct such representations quickly and/or automatically with a computer? o Manipulate 3D objects with a computer? Different methods for different object representations
3 3D Objects How can this object be represented in a computer?
4 3D Objects This one? H&B Figure 10.46
5 3D Objects How about this one? Stanford Graphics Laboratory
6 3D Objects This one? H&B Figure 9.9
7 3D Objects This one?
8 Representations of Geometry 3D Representations provide the foundations for o Computer Graphics o ComputerAided Geometric Design o Visualization o Robotics They are languages for describing geometry data structures algorithms Data structures determine algorithms!
9 3D Object Representations Raw data o Point cloud o Range image o Polygon soup Surfaces o Mesh o Subdivision o Parametric o Implicit Solids o Voxels o BSP tree o CSG o Sweep Highlevel structures o Scene graph o Skeleton o Application specific
10 Point Cloud Unstructured set of 3D point samples o Acquired from range finder, random sampling, particle system implementations, etc Hoppe Hoppe
11 Point Cloud Unstructured set of 3D point samples o Acquired from range finder, random sampling, particle system implementations, etc Can associate colors/normals/ Hoppe etc. to the points Hoppe
12 Range Image An image storing depth instead of color o Acquired from structured range scanners Range Image Tesselation Range Surface Brian Curless SIGGRAPH 99 Course #4 Notes
13 Polygon Soup Unstructured set of polygons o Created with interactive modeling systems, combining range images, etc. Larson
14 3D Object Representations Raw data o Point cloud o Range image o Polygon soup Surfaces o Mesh o Subdivision o Parametric o Implicit Solids o Voxels o BSP tree o CSG o Sweep Highlevel structures o Scene graph o Skeleton o Application specific
15 Mesh Connected set of polygons (usually triangles) o May not be closed Stanford Graphics Laboratory
16 Subdivision Surface Coarse mesh & subdivision rule o Define smooth surface as limit of sequence of refinements Zorin & Schroeder SIGGRAPH 99 Course Notes
17 Parametric Surface Tensor product spline patches o Careful use of constraints to maintain continuity FvDFH Figure 11.44
18 Implicit Surface Points satisfying: F(x,y,z) = 0 Polygonal Model Implicit Model Bill Lorensen SIGGRAPH 99 Course #4 Notes
19 3D Object Representations Raw data o Point cloud o Range image o Polygon soup Surfaces o Mesh o Subdivision o Parametric o Implicit Solids o Voxels o BSP tree o CSG o Sweep Highlevel structures o Scene graph o Skeleton o Application specific
20 Voxels Uniform grid of volumetric samples o Acquired from CT, MRI, etc. FvDFH Figure Stanford Graphics Laboratory
21 BSP Tree Binary space partition with solid cells labeled o Constructed from polygonal representations a b c d e f a b c d e f g Object a b c d e f Binary Spatial Partition Binary Tree Naylor
22 CSG Hierarchy of boolean set operations (union, difference, intersect) applied to simple shapes FvDFH Figure H&B Figure 9.9
23 Sweep Solid swept by curve along trajectory Stephen Chenney U Wisconsin
24 Sweep Solid swept by curve along trajectory Stephen Chenney U Wisconsin o Curve may be arbitrary o Sweep polygon may deform (scale, rotate) with respect to the path orientation
25 3D Object Representations Raw data o Point cloud o Range image o Polygon soup Surfaces o Mesh o Subdivision o Parametric o Implicit Solids o Voxels o BSP tree o CSG o Sweep Highlevel structures o Scene graph o Skeleton o Application specific
26 Scene Graph Union of objects at leaf nodes Bell Laboratories avalon.viewpoint.com
27 Skeleton Graph of curves with radii Stanford Graphics Laboratory SGI
28 Application Specific Apo A1 (Theoretical Biophysics Group, University of Illinois at UrbanaChampaign) Architectural Floorplan
29 Equivalence of Representations Thesis: o Each fundamental representation has enough expressive power to model the shape of any geometric object o It is possible to perform all geometric operations with any fundamental representation! Analogous to TuringEquivalence: o All computers today are Turingequivalent, but we still have many different processors
30 Computational Differences Efficiency o Combinatorial complexity o Space/time tradeoffs o Numerical accuracy/stability Simplicity o Ease of acquisition o Hardware acceleration Usability
31 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections H&B Figure 10.46
32 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections Not Local Support
33 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections
34 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections Topological Genus Equivalences
35 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections
36 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections A Parameterization (not necessarily natural)
37 Surfaces What makes a good surface representation? o Concise o Local support o Affine invariant o Arbitrary topology o Guaranteed continuity o Natural parameterization o Efficient display o Efficient intersections
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