Computer Graphics ppt, Assignments of Computer Graphics

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COMPUTER GRAPHICS

3D REPRESENTATION AN

SOLID MODELING

ANOOP RANA

BCA-

TH

SEM

1

3D MODELING

• 3D Representations
  • Wireframe models
  • Surface Models
  • Solid Models
  • Meshes and Polygon soups
  • Voxel/Volume models
  • Decomposition-based
    • Octrees, voxels
• Modeling in 3D
  • Constructive Solid Geometry (CSG), Breps and feature-based 2

REPRESENTING 3D OBJECTS

• Exact
  • Precise model of object topology
  • Mathematically represent all geometry - Approximate - A discretization of the 3D object - Use simple primitives to model topology and geometry 4

WIREFRAMES

• Basic idea:
  • Represent the model as the set of all of its edges
• Example:

A simple cube

• 12 lines
• 8 vertices
• How about the

faces?^5

Foley/VanDam, 1990/

SURFACE MODELS: EXAMPLES

• Utah Teapot
• Original IGES

standard

• Bezier patches 7

SOLIDS AND SOLID MODELING

• Solid modeling introduces a mathematical theory of solid shape - Domain of objects - Set of operations on the domain of objects - Representation that is - Unambiguous - Accurate - Unique - Compact - Efficient 8

SOLID OBJECT DEFINITIONS

• Boundary points
  • Points where distance to the object and the object’s complement is zero
• Interior points
  • All the other points in the object
• Closure
  • Union of interior points and boundary points 10

REGULARIZED BOOLEAN

OPERATIONS

• 3D Example
  • Two solids A and B
  • Intersection leaves a “dangling wall” - A 2D portion hanging off a 3D object
  • Closure of interior gives a uniform 3D result (^) 11 Pics/Math courtesy of Dave Mount @ UMD-CP

THE INDUCED CSG TREE

• Can also be

represented as a

directed acyclic

graph (DAG)

13 Pics/Math courtesy of Dave Mount @ UMD-CP

SWEEP REPRESENTATIONS

• An alternative way to

represent 3D obj.

• Idea
  • Given a primitive (e.g. polygon,sphere )
  • And a sweep (e.g. vector, curve…)
  • Define solid as space swept out by primitive 14 Foley/VanDam, 1990/

PROPERTIES OF 2-MANIFOLDS

• For any point on the boundary, its

neighborhood is a topological 2D disk

• If not a 2-manifold, neighborhood not a

disk

16 Foley/VanDam, 1990/

EULER’S FORMULA

• For simple polyhedra (no holes):

#Vertices - #Edges + #Faces = 2

17 Foley/VanDam, 1990/