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07object3d 3

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									                                  Graphics



                     Solid Modeling


                   고려대학교 컴퓨터 그래픽스 연구실




cgvr.korea.ac.kr                      Graphics Lab @ Korea University
Solid Modeling
                                                                   CGVR

   Represent Solid Interiors of Objects
         Surface may not be described explicitly




cgvr.korea.ac.kr                                    Graphics Lab @ Korea University
Motivation
                                                    CGVR

   Some Acquisition Methods Generate Solids
         Example: CAT scan




cgvr.korea.ac.kr                     Graphics Lab @ Korea University
Motivation
                                                      CGVR

   Some Applications Require Solids
         Example: CAD/CAM




cgvr.korea.ac.kr                       Graphics Lab @ Korea University
Motivation
                                                                CGVR

   Some Algorithms Require Solids
         Example: ray tracing with refraction




cgvr.korea.ac.kr                                 Graphics Lab @ Korea University
Solid Modeling Representation
                                               CGVR

 Voxels
 Quadtrees & Octrees
 Binary Space Partitions
 Constructive Solid Geometry




cgvr.korea.ac.kr                Graphics Lab @ Korea University
Voxels
                                                                   CGVR

   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.




cgvr.korea.ac.kr                                    Graphics Lab @ Korea University
Voxel Acquisition
                                      CGVR

   Scanning Devices
         MRI
         CAT
   Simulation
         FEM




cgvr.korea.ac.kr       Graphics Lab @ Korea University
Voxel Storage
                                                                   CGVR

   O(n3) Storage for n x n x n Grid
         1 billion voxels for 1000 x 1000 x 1000




cgvr.korea.ac.kr                                    Graphics Lab @ Korea University
Voxel Boolean Operations
                                                    CGVR

   Compare Objects Voxel by Voxel




cgvr.korea.ac.kr                     Graphics Lab @ Korea University
Voxel Display
                                                              CGVR

   Isosurface Rendering
         Render surfaces bounding volumetric regions of
          constant value (e.g., density)




cgvr.korea.ac.kr                               Graphics Lab @ Korea University
Voxel Display
                                                               CGVR

   Slicing
         Draw 2D image resulting from intersecting voxels
          with a plane




cgvr.korea.ac.kr                                Graphics Lab @ Korea University
Voxel Display
                                                                 CGVR

   Ray Casting
         Integrate density along rays through pixels




cgvr.korea.ac.kr                                  Graphics Lab @ Korea University
Voxels
                                                                CGVR

   Advantages
         Simple, intuitive, unambiguous
         Same complexity for all objects
         Natural acquisition for some applications
         Trivial boolean operations
   Disadvantages
         Approximate
         Large storage requirements
         Expensive display



cgvr.korea.ac.kr                                 Graphics Lab @ Korea University
Solid Modeling Representation
                                               CGVR

 Voxels
 Quadtrees & Octrees
 Binary Space Partitions
 Constructive Solid Geometry




cgvr.korea.ac.kr                Graphics Lab @ Korea University
Quadtrees & Octrees
                                                                CGVR

   Refine Resolution of Voxels Hierarchically
         More concise and efficient for non-uniform objects




                   Uniform Voxel         Quadtree


cgvr.korea.ac.kr                                 Graphics Lab @ Korea University
Quadtree Boolean Operations
                                       CGVR




cgvr.korea.ac.kr        Graphics Lab @ Korea University
Solid Modeling Representation
                                               CGVR

 Voxels
 Quadtrees & Octrees
 Binary Space Partitions
 Constructive Solid Geometry




cgvr.korea.ac.kr                Graphics Lab @ Korea University
Binary Space Partitions (BSPs)
                                                                                   CGVR

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

   Single Geometric Operation
         Partition a convex region by a hyperplane
   Single Combinatorial Operation
         Two child nodes added as leaf nodes




cgvr.korea.ac.kr                                 Graphics Lab @ Korea University
BSP Display
                                                                            CGVR

   Visibility Ordering
         Determine on which side of plane the viewer lies
               Near-subtree -> polygons on split -> far-subtree

                              A                    Partitioning Tree
                    o2
                                                             A
                B                 o4
                                                   B                   C
       o1                          C
                                              o1       o2        o3          o4
                         o3                  3rd       4th       1st         2nd
                Viewer
                                                             Viewer

cgvr.korea.ac.kr                                             Graphics Lab @ Korea University
Solid Modeling Representation
                                               CGVR

 Voxels
 Quadtrees & Octrees
 Binary Space Partitions
 Constructive Solid Geometry




cgvr.korea.ac.kr                Graphics Lab @ Korea University
Constructive Solid Geometry
(CSG)                                                CGVR

   Represent Solid Object as Hierarchy of Boolean
    Operations
         Union
         Intersection
         Difference




cgvr.korea.ac.kr                      Graphics Lab @ Korea University
CSG Acquisition
                                                   CGVR

   Interactive Modeling Programs
         CAD/CAM




cgvr.korea.ac.kr                    Graphics Lab @ Korea University
CSG Display & Analysis
                                           CGVR

   Ray Casting

                              Union


                         Circle          Box




cgvr.korea.ac.kr            Graphics Lab @ Korea University
 Summary
                                                         CGVR



                      Voxels   Octree   BSP           CSG
Accurate               No       No      Some         Some
Concise                No       No       No           Yes
Affine Invariant       No       No       Yes          Yes
Easy Acquisition      Some     Some     No           Some
Guaranteed Validity    Yes      Yes     Yes           No
Efficient Boolean
                       Yes      Yes     Yes            Yes
Operations
Efficient Display      No       No      Yes             No

 cgvr.korea.ac.kr                         Graphics Lab @ Korea University

								
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