3D Object Representation
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1 3D Object Representation Connelly Barnes CS 4810: Graphics Acknowledgment: slides by Jason Lawrence, Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David Dobkin
2 3D Object Representation How do we... orepresent 3D objects in a computer? oconstruct such representations quickly and/or automatically with a computer? omanipulate 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? Imaging Economics
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 ocomputer Graphics ocomputer-aided Geometric Design ovisualization orobotics They are languages for describing geometry data structures algorithms Data structures determine algorithms!
9 3D Object Representations Raw data opoint cloud orange image opolygon soup Surfaces omesh osubdivision oparametric oimplicit Solids ovoxels obsp tree ocsg osweep High-level structures oscene graph oskeleton oapplication specific
10 Point Cloud Unstructured set of 3D point samples oacquired from range finder, random sampling, particle system implementations, etc Hoppe Czech Academy of Sciences
11 Point Cloud Unstructured set of 3D point samples oacquired from range finder, random sampling, particle system implementations, etc Can associate colors/normals/etc. Hoppe to the points Czech Academy of Sciences
12 Range Image An image storing depth instead of color oacquired from range scanners e.g. Microsoft Kinect Range Image Tesselation Range Surface Brian Curless SIGGRAPH 99 Course #4 Notes
13 Polygon Soup Unstructured set of polygons ocreated with interactive modeling systems, combining range images, etc. Larson
14 3D Object Representations Raw data opoint cloud orange image opolygon soup Surfaces omesh osubdivision oparametric oimplicit Solids ovoxels obsp tree ocsg osweep High-level structures oscene graph oskeleton oapplication specific
15 Mesh Connected set of polygons (usually triangles) omay not be closed Stanford Graphics Laboratory
16 Subdivision Surface Coarse mesh & subdivision rule odefine smooth surface as limit of sequence of refinements Zorin & Schroeder SIGGRAPH 99 Course Notes
17 Parametric Surface Tensor product spline patches ocareful 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 opoint cloud orange image opolygon soup Surfaces omesh osubdivision oparametric oimplicit Solids ovoxels obsp tree ocsg osweep High-level structures oscene graph oskeleton oapplication specific
20 Voxels Uniform grid of volumetric samples oacquired from CT, MRI, etc. FvDFH Figure Stanford Graphics Laboratory
21 BSP Tree Binary space partition with solid cells labeled oconstructed 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 Constructive Solid Geometry (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 ocurve may be arbitrary osweep polygon may deform (scale, rotate) with respect to the path orientation
25 Example of Several Representations Scalable KinectFusion Which representations are being used? 25
26 3D Object Representations Raw data opoint cloud orange image opolygon soup Surfaces omesh osubdivision oparametric oimplicit Solids ovoxels obsp tree ocsg osweep High-level structures oscene graph oskeleton oapplication specific
27 Scene Graph Union of objects at leaf nodes Bell Laboratories avalon.viewpoint.com
28 Skeleton Graph of curves with radii Stanford Graphics Laboratory SGI
29 Application Specific Apo A-1 (Theoretical Biophysics Group, University of Illinois at Urbana-Champaign) Architectural Floorplan
30 Equivalence of Representations Thesis: oeach fundamental representation has enough expressive power to model the shape of any geometric object oit is possible to perform all geometric operations with any fundamental representation! Analogous to Turing-Equivalence: oall computers today are Turing-equivalent, but we still have many different processors
31 Computational Differences Efficiency ocombinatorial complexity ospace/time trade-offs onumerical accuracy/stability Simplicity oease of acquisition ohardware acceleration Usability
32 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections H&B Figure 10.46
33 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections Not Local Support
34 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections
35 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections Topological Genus Equivalences
36 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections
37 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections A Parameterization (not necessarily natural)
38 Surfaces What makes a good surface representation? oconcise olocal support oaffine invariant oarbitrary topology oguaranteed continuity onatural parameterization oefficient display oefficient intersections
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