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Three-Dimensional Object Representation

Three-Dimensional Object Representation. Jehee Lee Seoul National University. Object Representation. Graphics scenes can contain many different kinds of objects and material surfaces

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Three-Dimensional Object Representation

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  1. Three-DimensionalObject Representation Jehee Lee Seoul National University

  2. Object Representation • Graphics scenes can contain many different kinds of objects and material surfaces • Trees, flowers, clouds, rocks, water, bricks, wood paneling, rubber, paper, marble, steel, glass, plastic and cloth • So it may not be surprising that there is no single method that we can use to describe all the characteristics of these different shapes/materials

  3. Object Representation • Scene = an assembly of one or more models • A model contains • Structural description: Geometry of the shape • Surface description: Appearance and light

  4. 3D Object Representations • Boundary representation • A set of surfaces that separate the object interior from the environment • Eg) Polyhedra, curved boundary surfaces • Space-partitioning • Partitioning the spatial region into a set of small, nonoverlapping, contiguous solids (usually cubes) • Eg) Volumetric data, octrees, BSP trees • Procedural methods • Fractals, shape grammars • Constructive solid geometry • Physically-based modeling

  5. Issues in Model Selection • Computational cost • Storage space • Model construction time • Display time • Effectiveness in modeling the desired phenomena • Geometry • Looks good for image synthesis • Accuracy for simulation • Appearance • Looks / Accuracy

  6. Issues in Model Selection • Implementation complexity • The number of primitives • The complexity of each primitives • Ease of acquiring (or creating) data • Ease of manipulation • Operations on models • Ease of animation • Match to simulator • Cost of conversion • Physics of motion

  7. Polyhedra • A polyhedron is a 3D solid which consists of a collection of polygons, usually joined at their edges • The inside of the solid is divided by the polygons from the outside of the solid • Regular 2-manifold boundary surfaces

  8. Polyhedra • A polyhedron with zero-genus can be considered as a planar graph • Euler formula • Determines the validity of planar graphs • V: The number of vertices • E: The number of edges • F: The number of faces

  9. Polyhedra • Euler-Poincare formula • Generalizes the Euler formula for arbitrary dimension and genus • Polyhedra in three-dimension space follows • L: The number of Inner loops • S: The number of shells • G: The number of holds

  10. Functional Representation • Explicit surfaces • Implicit surfaces • Parametric surfaces • Issues • Representation power • Easy to render • Easy to manipulate (translate, rotate, and deform)

  11. Implicit Surfaces • Quadric surfaces • Implicit second-order polynomial equations • Superquadric surfaces • A generalization of quadric surfaces • Blobby objects (metaballs) • A collection of spherical density functions

  12. Quadric surfaces • Double cones • Ellipsoids • Hyperboloids of one sheet • Hyperboloids of two sheets

  13. Quadric surfaces • Elliptic paraboloids • Hyperbolic paraboloids

  14. Superquadrics • A generalization of quadric surfaces, formed by incorporating additional parameters into quadric equations • Increased flexibility for adjusting object shapes • Superellipses

  15. Superquadrics • Superellipsoid

  16. Blobby Objects • A collection of density functions • Equi-density surfaces

  17. Spatial Partitioning • Volume data • Use identical cells (voxels) • Space-filling tesselation with cubes or parallelopipeds • Expensive storage but simple data structure • Useful for medical imaging: volume visualization

  18. Spatial Partitioning • Octrees • Partition space into 8 cubes, recursively • Increase space efficiency of solid tesselations

  19. Spatial Partitioning • Binary Space Partitioning (BSP) trees • Subdivide a scene into two sections at each step with a plane that can be at any position and orientation

  20. Constructive Solid Geometry • Recursively combine simple primitives by boolean operations • Simple primitives • Transform or deform • Tree structure

  21. Constructive Solid Geometry Transformed Combined Primitives Tree structure

  22. Constructive Solid Geometry • Ray-casting methods for rendering CSG objects • Cast a ray through each pixel • Perform boolean operations along each ray

  23. Procedural Modeling • Self-similar fractals • Substitution ruls • Example: Koch curve

  24. Procedural Modeling • Substitution rules

  25. Procedural Modeling • Terrain by random perturbation

  26. Procedural Modeling • Natural scenes with trees, flowers, and grass

  27. Physically Based Modeling • Particle systems • Shape description is combined with physical simulation

  28. Physically Based Modeling • Procedural modeling + physically based simulation

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