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Graphics Graphics Korea University cgvr.korea.ac.kr Creating Virtual World I 김 창 헌 Department of Computer Science Korea University

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Presentation on theme: "Graphics Graphics Korea University cgvr.korea.ac.kr Creating Virtual World I 김 창 헌 Department of Computer Science Korea University"— Presentation transcript:

1 Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Creating Virtual World I 김 창 헌 Department of Computer Science Korea University http://cgvr.korea.ac.kr/courses/2002/cse425/

2 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Overview Model Construction 3D Object Representation Subdivision Surfaces Solid Modeling

3 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Model Construction Interactive Modeling Tools CAD programs Subdivision surface editors Scanning Tools CAT, MRI, laser, magnetic, robotic arm, etc. Computer Vision Stereo, motion, etc. Procedural Generation Sweeps, fractals, grammars

4 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Interactive Modeling Tools User Constructs Objects with Drawing Program

5 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Model Construction Interactive Modeling Tools CAD programs, subdivision surface editors Scanning Tools CAT, MRI Laser Range Scanning Magnetic, robotic arm Computer Vision Stereo, motion, etc. Procedural Generation Sweeps, fractals, grammars

6 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Scanning Tools Acquire Geometry of Objects with Active Sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm Etc.

7 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Scanning Tools Acquire Geometry of Objects with Active Sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm Etc. Color Depth

8 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Scanning Tools Acquire Geometry of Objects with Active Sensors CAT/MRI Laser range scanner Magnetic sensor Robotic arm Etc.

9 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Model Construction Interactive Modeling Tools CAD programs Subdivision surface editors Scanning Tools CAT, MRI, laser, magnetic, robotic arm, etc. Computer Vision Stereo Motion Procedural Generation Sweeps, fractals, grammars

10 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Computer Vision Infer 3D Geometry from Images Stereo Motion Constraints Etc.

11 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Computer Vision Infer 3D Geometry from Images Stereo Motion Constraints Etc.

12 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Computer Vision Infer 3D Geometry from Images Stereo Motion Constraints Etc.

13 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Model Construction Interactive Modeling Tools CAD programs, subdivision surface editors Scanning Tools CAT, MRI, laser, magnetic, robotic arm, etc. Computer Vision Stereo, motion, etc. Procedural Generation Sweeps Fractals Grammars

14 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Procedural Generation Goal: Describe 3D models algorithmically Best for Models Resulting from... Repeating processes Self-similar processes Random processes Advantages: Automatic generation Concise representation Parameterized classes of models

15 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Sweep Generate Different Shells by Varying Parameters Different helico-spiralsDifferent generating curves

16 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Fractal Defining Property: Self-similar with infinite resolution Mandelbrot Set

17 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Fractal Useful for Describing Natural 3D Phenomenon Terrain Plants Clouds Water Feathers Fur Etc.

18 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Deterministically Self-Similar Fractal Useful for Creating Interesting Shapes

19 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Statistically Self-Similar Fractal Useful for Creating Mountains and Trees

20 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Grammar Generate Description of Geometric Model by Applying Production Rules Useful for creating plants  Example: Tree  Branch Tree | Leaf Branch  Cylinder | [ Tree ] C[CL]C[C[CL][CL]]C[[CL][CL]]C[*]C[*][*]

21 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Grammar Useful for Creating Plants

22 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Creating Virtual World Model Construction 3D Object Representation Subdivision Surfaces Solid Modeling

23 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 3D Object Representations Raw Data Point cloud Range image Polygon soup Surfaces Mesh, Subdivision, Parametric, Implicit Solids Voxel, BSP tree, CSG, Sweep

24 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Point Cloud Unstructured Set of 3D Point Samples Acquired from range finder, computer vision, etc

25 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Range Image Set of 3D Points Mapping to Pixels of Depth Image Acquired from range scanner Range ImageTessellationRange Surface

26 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Polygon Soup Unstructured Set of Polygons Created with interactive modeling systems

27 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 3D Object Representations Raw Data Point cloud, Range image, Polygon soup Surfaces Mesh Subdivision Parametric Implicit Solids Voxel, BSP tree, CSG, Sweep

28 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Mesh Connected Set of Polygons (Usually Triangles) May not be closed

29 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision Surfaces Coarse Mesh & Subdivision Rule Define smooth surface as limit of sequence of refinements

30 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Parametric Surfaces Tensor Product Spline Patches Careful constraints to maintain continuity

31 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Implicit Surface Points satisfying: F(x,y,z) = 0 Polygonal ModelImplicit Model

32 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 3D Object Representations Raw Data Point cloud, Range image, Polygon soup Surfaces Mesh, Subdivision, Parametric, Implicit Solids Voxel BSP tree CSG Sweep

33 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxels Uniform Grid of Volumetric Samples Acquired from CAT, MRI, etc.

34 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr BSP Tree Binary Space Partition with Solid Cells Labeled Constructed from polygonal representations a b cd e f g Object a b cd e f g Binary Spatial Partition 1 2 3 4 5 6 7 1 2 a 3 b c 4 d 5 6 e 7 f BSP Tree

35 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr CSG Hierarchy of Boolean Set Operations (Union, Difference, Intersect) Applied to Simple Shapes

36 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Sweep Solid Swept by Curve Along Trajectory Constructing a Torus using Rotational Sweep

37 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Summary 3D Object Representations Taxonomy of 3D Object Representations Voxel Discrete Continuous Combinational Functional Mesh Subdivision Mesh Subdivision BSP Tree Bezier B-Spline Bezier B-Spline Algebraic TopologicalSet Membership ParametricImplicit

38 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Creating Virtual World Model Construction 3D Object Representation Subdivision Surfaces Solid Modeling

39 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision How do You Make a Smooth Curve?

40 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision Surfaces Coarse Mesh & Subdivision Rule Define smooth surface as limit of sequence of refinements

41 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Loop Subdivision Scheme How Refine Mesh? Refine each triangle into 4 triangles by splitting each edge and connecting new vertices

42 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Loop Subdivision Scheme Limit Surface Has Provable Smoothness Properties

43 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision Schemes There are different subdivision schemes Different methods for refining topology Different rules for positioning vertices  Interpolating versus approximating Face SplitVertex Split Doo-Sabin, Midege (C 1 ) Biquartic (C 2 ) Catmull-Clark (C 2 ) Kobbelt (C 1 ) Quad. Meshes Loop (C 2 ) Mod. Butterfly (C 1 ) Triangular Meshes Approximating Interpolating

44 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision Schemes LoopButterfly Catmull-ClarkDoo-Sabin

45 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Subdivision Schemes LoopButterflyCatmull-ClarkDoo-Sabin

46 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Polygon Meshes Mesh Representations Independent faces Vertex and face tables Adjacency lists Winged-Edge

47 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Summary Subdivision Surface Advantages: Simple method for describing complex surfaces Relatively easy to implement Arbitrary topology Smoothness guarantees Multiresolution Difficulties: Intuitive specification Parameterization Intersections

48 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Creating Virtual World Model Construction 3D Object Representation Subdivision Surfaces Solid Modeling

49 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Solid Modeling Represent Solid Interiors of Objects Surface may not be described explicitly

50 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Solid Modeling Representation Voxels Quadtrees & Octrees Binary Space Partitions Constructive Solid Geometry

51 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxels Partition Space into Uniform Grid Grid cells are called a voxels (like pixels) Store Properties of Solid Object with Each Voxel Occupancy Color Density Temperature Etc.

52 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxel Acquisition Scanning Devices MRI CAT Simulation FEM

53 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxel Display Isosurface Rendering Render surfaces bounding volumetric regions of constant value (e.g., density)

54 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxel Display Ray Casting Integrate density along rays through pixels

55 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Voxels Advantages Simple, intuitive, unambiguous Same complexity for all objects Natural acquisition for some applications Trivial boolean operations Disadvantages Approximate Large storage requirements Expensive display

56 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Solid Modeling Representation Voxels Quadtrees & Octrees Binary Space Partitions Constructive Solid Geometry

57 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Quadtrees & Octrees Refine Resolution of Voxels Hierarchically More concise and efficient for non-uniform objects Uniform Voxel Quadtree

58 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Solid Modeling Representation Voxels Quadtrees & Octrees Binary Space Partitions Constructive Solid Geometry

59 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Binary Space Partitions (BSPs) Recursive Partition of Space by Planes Mark leaf cells as inside or outside object a b cd e f g Object a b cd e f g Binary Spatial Partition 1 2 3 4 5 6 7 1 2 a 3 b c 4 d 5 6 e 7 f BSP Tree

60 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Solid Modeling Representation Voxels Quadtrees & Octrees Binary Space Partitions Constructive Solid Geometry

61 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr + ㅡ Block 1Block 2 Cylinder Constructive Solid Geometry (CSG) Represent Solid Object as Hierarchy of Boolean Operations Union Intersection Difference

62 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr CSG Acquisition Interactive Modeling Programs CAD/CAM

63 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr CSG Display & Analysis Ray Casting Union CircleBox

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