Solid Modeling 고려대학교 컴퓨터 그래픽스 연구실
Solid Modeling <ul><li>Represent Solid Interiors of Objects </li></ul><ul><ul><li>Surface may not be described explicitly ...
Motivation <ul><li>Some Acquisition Methods Generate Solids </li></ul><ul><ul><li>Example: CAT scan </li></ul></ul>
Motivation <ul><li>Some Applications Require Solids </li></ul><ul><ul><li>Example: CAD/CAM </li></ul></ul>
Motivation <ul><li>Some Algorithms Require Solids </li></ul><ul><ul><li>Example: ray tracing with refraction </li></ul></ul>
Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitio...
Voxels <ul><li>Partition Space into Uniform Grid </li></ul><ul><ul><li>Grid cells are called a  voxels  (like pixels) </li...
Voxel Acquisition <ul><li>Scanning Devices </li></ul><ul><ul><li>MRI </li></ul></ul><ul><ul><li>CAT </li></ul></ul><ul><li...
Voxel Storage <ul><li>O( n 3 ) Storage for  n  x  n  x  n  Grid </li></ul><ul><ul><li>1 billion voxels for 1000 x 1000 x 1...
Voxel Boolean Operations <ul><li>Compare Objects Voxel by Voxel </li></ul>
Voxel Display <ul><li>Isosurface Rendering </li></ul><ul><ul><li>Render surfaces bounding volumetric regions of constant v...
Voxel Display <ul><li>Slicing </li></ul><ul><ul><li>Draw 2D image resulting from intersecting voxels with a plane </li></u...
Voxel Display <ul><li>Ray Casting </li></ul><ul><ul><li>Integrate density along rays through pixels </li></ul></ul>
Voxels <ul><li>Advantages </li></ul><ul><ul><li>Simple, intuitive, unambiguous </li></ul></ul><ul><ul><li>Same complexity ...
Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitio...
Quadtrees & Octrees <ul><li>Refine Resolution of Voxels Hierarchically </li></ul><ul><ul><li>More concise and efficient fo...
Quadtree Boolean Operations
Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitio...
Binary Space Partitions (BSPs) <ul><li>Recursive Partition of Space by Planes </li></ul><ul><ul><li>Mark leaf cells as ins...
BSP Fundamentals <ul><li>Single Geometric Operation </li></ul><ul><ul><li>Partition a convex region by a hyperplane </li><...
BSP Display <ul><li>Visibility Ordering </li></ul><ul><ul><li>Determine on which side of plane the viewer lies </li></ul><...
Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitio...
Constructive Solid Geometry (CSG) <ul><li>Represent Solid Object as Hierarchy of Boolean Operations </li></ul><ul><ul><li>...
CSG Acquisition <ul><li>Interactive Modeling Programs </li></ul><ul><ul><li>CAD/CAM </li></ul></ul>
CSG Display & Analysis <ul><li>Ray Casting </li></ul>Union Circle Box
Summary Voxels Octree BSP CSG No No Some Some No No No Yes No No Yes Yes Some Some No Some Yes Yes Yes No Yes Yes Yes Yes ...
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object 3d(1)

  1. 1. Solid Modeling 고려대학교 컴퓨터 그래픽스 연구실
  2. 2. Solid Modeling <ul><li>Represent Solid Interiors of Objects </li></ul><ul><ul><li>Surface may not be described explicitly </li></ul></ul>
  3. 3. Motivation <ul><li>Some Acquisition Methods Generate Solids </li></ul><ul><ul><li>Example: CAT scan </li></ul></ul>
  4. 4. Motivation <ul><li>Some Applications Require Solids </li></ul><ul><ul><li>Example: CAD/CAM </li></ul></ul>
  5. 5. Motivation <ul><li>Some Algorithms Require Solids </li></ul><ul><ul><li>Example: ray tracing with refraction </li></ul></ul>
  6. 6. Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitions </li></ul><ul><li>Constructive Solid Geometry </li></ul>
  7. 7. Voxels <ul><li>Partition Space into Uniform Grid </li></ul><ul><ul><li>Grid cells are called a voxels (like pixels) </li></ul></ul><ul><li>Store Properties of Solid Object with Each Voxel </li></ul><ul><ul><li>Occupancy </li></ul></ul><ul><ul><li>Color </li></ul></ul><ul><ul><li>Density </li></ul></ul><ul><ul><li>Temperature </li></ul></ul><ul><ul><li>Etc. </li></ul></ul>
  8. 8. Voxel Acquisition <ul><li>Scanning Devices </li></ul><ul><ul><li>MRI </li></ul></ul><ul><ul><li>CAT </li></ul></ul><ul><li>Simulation </li></ul><ul><ul><li>FEM </li></ul></ul>
  9. 9. Voxel Storage <ul><li>O( n 3 ) Storage for n x n x n Grid </li></ul><ul><ul><li>1 billion voxels for 1000 x 1000 x 1000 </li></ul></ul>
  10. 10. Voxel Boolean Operations <ul><li>Compare Objects Voxel by Voxel </li></ul>
  11. 11. Voxel Display <ul><li>Isosurface Rendering </li></ul><ul><ul><li>Render surfaces bounding volumetric regions of constant value (e.g., density) </li></ul></ul>
  12. 12. Voxel Display <ul><li>Slicing </li></ul><ul><ul><li>Draw 2D image resulting from intersecting voxels with a plane </li></ul></ul>
  13. 13. Voxel Display <ul><li>Ray Casting </li></ul><ul><ul><li>Integrate density along rays through pixels </li></ul></ul>
  14. 14. Voxels <ul><li>Advantages </li></ul><ul><ul><li>Simple, intuitive, unambiguous </li></ul></ul><ul><ul><li>Same complexity for all objects </li></ul></ul><ul><ul><li>Natural acquisition for some applications </li></ul></ul><ul><ul><li>Trivial boolean operations </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Approximate </li></ul></ul><ul><ul><li>Large storage requirements </li></ul></ul><ul><ul><li>Expensive display </li></ul></ul>
  15. 15. Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitions </li></ul><ul><li>Constructive Solid Geometry </li></ul>
  16. 16. Quadtrees & Octrees <ul><li>Refine Resolution of Voxels Hierarchically </li></ul><ul><ul><li>More concise and efficient for non-uniform objects </li></ul></ul>Uniform Voxel Quadtree
  17. 17. Quadtree Boolean Operations
  18. 18. Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitions </li></ul><ul><li>Constructive Solid Geometry </li></ul>
  19. 19. Binary Space Partitions (BSPs) <ul><li>Recursive Partition of Space by Planes </li></ul><ul><ul><li>Mark leaf cells as inside or outside object </li></ul></ul>a b c d e f g Object a b c d 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
  20. 20. BSP Fundamentals <ul><li>Single Geometric Operation </li></ul><ul><ul><li>Partition a convex region by a hyperplane </li></ul></ul><ul><li>Single Combinatorial Operation </li></ul><ul><ul><li>Two child nodes added as leaf nodes </li></ul></ul>
  21. 21. BSP Display <ul><li>Visibility Ordering </li></ul><ul><ul><li>Determine on which side of plane the viewer lies </li></ul></ul><ul><ul><ul><li>Near-subtree -> polygons on split -> far-subtree </li></ul></ul></ul>A B C o2 o1 o3 o4 Viewer Partitioning Tree A B C o1 o2 o3 o4 3rd 4th 1st 2nd Viewer
  22. 22. Solid Modeling Representation <ul><li>Voxels </li></ul><ul><li>Quadtrees & Octrees </li></ul><ul><li>Binary Space Partitions </li></ul><ul><li>Constructive Solid Geometry </li></ul>
  23. 23. Constructive Solid Geometry (CSG) <ul><li>Represent Solid Object as Hierarchy of Boolean Operations </li></ul><ul><ul><li>Union </li></ul></ul><ul><ul><li>Intersection </li></ul></ul><ul><ul><li>Difference </li></ul></ul>
  24. 24. CSG Acquisition <ul><li>Interactive Modeling Programs </li></ul><ul><ul><li>CAD/CAM </li></ul></ul>
  25. 25. CSG Display & Analysis <ul><li>Ray Casting </li></ul>Union Circle Box
  26. 26. Summary Voxels Octree BSP CSG No No Some Some No No No Yes No No Yes Yes Some Some No Some Yes Yes Yes No Yes Yes Yes Yes No No Yes No Accurate Concise Affine Invariant Easy Acquisition Guaranteed Validity Efficient Boolean Operations Efficient Display
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