3D Modeling I. CG08b Lior Shapira Lecture 8. Based on: Thomas Funkhouser,Princeton University. Thomas Funkhouser 2000
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1 3D Modeling I CG08b Lior Shapira Lecture 8 Based on: Thomas Funkhouser,Princeton University
2 Course Syllabus I. Image processing II. Rendering III. Modeling IV. Animation Image Processing (Rusty Coleman, CS426, Fall99) Rendering (Michael Bostock, CS426, Fall99) Modeling (Dennis Zorin, CalTech) Animation (Angel, Plate 1)
3 Modeling How do we... Represent 3D objects in a computer? Acquire computer representations of 3D objects? Manipulate computer representations of 3D objects?
4 3D Objects How can this object be represented in a computer?
5 3D Objects This one? H&B Figure 10.46
6 3D Objects How about this one? Stanford Graphics Laboratory
7 3D Objects This one? H&B Figure 9.9
8 3D Objects This one?
9 3D Object Representations Points Point cloud Range image Surfaces Polygonal Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Application specific
10 Equivalence of Representations Thesis: Each representation has enough expressive power to model the shape of any geometric object It is possible to perform all geometric operations with any fundamental representation Analogous to Turing-equivalence Computers / programming languages Turingequivalent. But each does different things better!
11 Why different Representations? Efficiency for different tasks Acquisition Rendering Manipulation Animation Analysis Data Structures determine algorithms!
12 Modeling Operations What can we do with a 3D object representation? Edit Transform Smooth Render Animate Morph Compress Transmit Analyze Digital Michealangelo Pirates of the carribean Smoothing
13 3D Object Representations Desirable properties depend on intended use Easy to acquire Accurate Concise Intuitive editing Efficient editing Efficient display Efficient intersections Guaranteed validity Guaranteed smoothness
14 Outline Points Point cloud Range image Surfaces Polygonal Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Application specific
15 Range Image Set of 3D points mapping to pixels of depth image Acquired from range scanner Range Image Tesselation Range Surface Brian Curless SIGGRAPH 99 Course #4 Notes
16 Point Cloud Unstructured set of 3D point samples Acquired from range finder, computer vision, etc Hugues Hoppe Hugues Hoppe
17 Outline Points Point cloud Range image Surfaces Polygonal Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Application specific
18 Polygonal Mesh Connected set of polygons (usually triangles) Stanford Graphics Laboratory
19 Subdivision Surface Coarse mesh & subdivision rule Define smooth surface as limit of sequence of refinements Zorin & Schroeder SIGGRAPH 99 Course Notes
20 Parametric Surface Tensor product spline patchs Each patch is a parametric function Careful constraints to maintain continuity FvDFH Figure 11.44
21 Implicit Surface Points satisfying: F(x,y,z) = 0 Polygonal Model Implicit Model Bill Lorensen SIGGRAPH 99 Course #4 Notes
22 Outline Points Point cloud Range image Surfaces Polygonal Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Application specific
23 Voxels Uniform grid of volumetric samples Acquired from CAT, MRI, etc. FvDFH Figure Stanford Graphics Laboratory
24 BSP Tree Binary space partition with solid cells labeled 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
25 CSG (constructive solid geometry) Hierarchy of boolean set operations (union, difference, intersect) applied to simple shapes Boolean union Boolean difference Boolean intersection
26 CSG (constructive solid geometry) Hierarchy of boolean set operations (union, difference, intersect) applied to simple shapes
27 Sweep Solid swept by curve along trajectory Removal Path Sweep Model Bill Lorensen SIGGRAPH 99 Course #4 Notes
28 Outline Points Point cloud Range image Surfaces Polygonal Mesh Subdivision Parametric Implicit Solids Voxels BSP tree CSG Sweep High-level structures Scene graph Application specific
29 Scene Graph Union of objects at leaf nodes Bell Laboratories avalon.viewpoint.com
30 Application Specific Apo A-1 (Theoretical Biophysics Group, University of Illinois at Urbana-Champaign) Architectural Floorplan (CS Building, Princeton University)
31 Taxonomy of 3D Representations Discrete Continuous Voxels, Point Sets Combinatorial Functional Topological Set Membership Parametric Implicit Mesh Subdivision BSP Tree Cell Complex Bezier B-Spline Algebraic Naylor
32 Equivalence of Representations Thesis: Each representation has enough expressive power to model the shape of any geometric object It is possible to perform all geometric operations with any fundamental representation Analogous to Turing-equivalence Computers / programming languages Turingequivalent. But each does different things better!
33 Computational Differences Efficiency Combinatorial complexity (e.g. O( n log n ) ) Space/time trade-offs (e.g. z-buffer) Numerical accuracy/stability (degree of polynomial) Simplicity Ease of acquisition Hardware acceleration Software creation and maintenance Usability Designer interface vs. computational engine
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