Graphics Solid Modeling cgvr korea ac kr 1

Graphics Solid Modeling 고려대학교 그래픽스 연구실 cgvr. korea. ac. kr 1 Graphics Lab @ Korea University

Solid Modeling n CGVR Represent Solid Interiors of Objects n Surface may not be described explicitly cgvr. korea. ac. kr 2 Graphics Lab @ Korea University

Motivation n CGVR Some Acquisition Methods Generate Solids n Example: CAT scan cgvr. korea. ac. kr 3 Graphics Lab @ Korea University

Motivation n CGVR Some Applications Require Solids n Example: CAD/CAM cgvr. korea. ac. kr 4 Graphics Lab @ Korea University

Motivation n CGVR Some Algorithms Require Solids n Example: ray tracing with refraction cgvr. korea. ac. kr 5 Graphics Lab @ Korea University

Solid Modeling Representation CGVR Voxels n Quadtrees & Octrees n Binary Space Partitions n Constructive Solid Geometry n cgvr. korea. ac. kr 6 Graphics Lab @ Korea University

Voxels n Partition Space into Uniform Grid n n CGVR Grid cells are called a voxels (like pixels) Store Properties of Solid Object with Each Voxel n n n Occupancy Color Density Temperature Etc. cgvr. korea. ac. kr 7 Graphics Lab @ Korea University

Voxel Acquisition n CGVR Scanning Devices MRI n CAT n n Simulation n FEM cgvr. korea. ac. kr 8 Graphics Lab @ Korea University

Voxel Storage n CGVR O(n 3) Storage for n x n Grid n 1 billion voxels for 1000 x 1000 cgvr. korea. ac. kr 9 Graphics Lab @ Korea University

Voxel Boolean Operations n CGVR Compare Objects Voxel by Voxel cgvr. korea. ac. kr 10 Graphics Lab @ Korea University

Voxel Display n CGVR Isosurface Rendering n Render surfaces bounding volumetric regions of constant value (e. g. , density) cgvr. korea. ac. kr 11 Graphics Lab @ Korea University

Voxel Display n CGVR Slicing n Draw 2 D image resulting from intersecting voxels with a plane cgvr. korea. ac. kr 12 Graphics Lab @ Korea University

Voxel Display n CGVR Ray Casting n Integrate density along rays through pixels cgvr. korea. ac. kr 13 Graphics Lab @ Korea University

Voxels n CGVR Advantages Simple, intuitive, unambiguous n Same complexity for all objects n Natural acquisition for some applications n Trivial boolean operations n n Disadvantages Approximate n Large storage requirements n Expensive display n cgvr. korea. ac. kr 14 Graphics Lab @ Korea University

Solid Modeling Representation CGVR Voxels n Quadtrees & Octrees n Binary Space Partitions n Constructive Solid Geometry n cgvr. korea. ac. kr 15 Graphics Lab @ Korea University

Quadtrees & Octrees n CGVR Refine Resolution of Voxels Hierarchically n More concise and efficient for non-uniform objects Uniform Voxel cgvr. korea. ac. kr 16 Quadtree Graphics Lab @ Korea University

Quadtree Boolean Operations cgvr. korea. ac. kr 17 CGVR Graphics Lab @ Korea University

Solid Modeling Representation CGVR Voxels n Quadtrees & Octrees n Binary Space Partitions n Constructive Solid Geometry n cgvr. korea. ac. kr 18 Graphics Lab @ Korea University

Binary Space Partitions (BSPs) n CGVR Recursive Partition of Space by Planes n Mark leaf cells as inside or outside object a 1 g a a 6 f f 5 e e b d c b 7 4 d g cgvr. korea. ac. kr 3 c Binary Spatial Partition 19 2 c 2 Object 1 b 3 d e 4 f 5 6 7 BSP Tree Graphics Lab @ Korea University

BSP Fundamentals n Single Geometric Operation n n CGVR Partition a convex region by a hyperplane Single Combinatorial Operation n Two child nodes added as leaf nodes cgvr. korea. ac. kr 20 Graphics Lab @ Korea University

BSP Display n CGVR Visibility Ordering n Determine on which side of plane the viewer lies o Near-subtree -> polygons on split -> far-subtree Partitioning Tree A o 2 A B o 4 B o 1 C o 3 Viewer cgvr. korea. ac. kr o 1 3 rd C o 2 4 th o 3 1 st o 4 2 nd Viewer 21 Graphics Lab @ Korea University

Solid Modeling Representation CGVR Voxels n Quadtrees & Octrees n Binary Space Partitions n Constructive Solid Geometry n cgvr. korea. ac. kr 22 Graphics Lab @ Korea University

Constructive Solid Geometry (CSG) n CGVR Represent Solid Object as Hierarchy of Boolean Operations Union n Intersection n Difference n cgvr. korea. ac. kr 23 Graphics Lab @ Korea University

CSG Acquisition n CGVR Interactive Modeling Programs n CAD/CAM cgvr. korea. ac. kr 24 Graphics Lab @ Korea University

CSG Display & Analysis n CGVR Ray Casting Union Circle cgvr. korea. ac. kr 25 Box Graphics Lab @ Korea University

Summary CGVR Voxels Octree BSP CSG No No Some Yes No Some Yes No Yes Some No Efficient Boolean Operations Yes Yes Efficient Display No No Yes No Accurate Concise Affine Invariant Easy Acquisition Guaranteed Validity cgvr. korea. ac. kr 26 Graphics Lab @ Korea University