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Geometric Modeling. How to design a graphical model? How to create a digital description of a real-world object?. Design Digitize. By other names. Data Generation CAD: Computer-Aided Design CAAD: Computer-Aided Architectural Design Geometric Modeling Computational Geometry.

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geometric modeling
Geometric Modeling
  • How to design a graphical model?
  • How to create a digital description of a real-world object?
  • Design
  • Digitize
by other names
By other names
  • Data Generation
  • CAD: Computer-Aided Design
  • CAAD: Computer-Aided Architectural Design
  • Geometric Modeling
  • Computational Geometry
approaches
Approaches
  • interactive design
  • procedural composition & construction
  • CSG: constructive solid geometry & boolean operators
  • subdivision surfaces
  • fractals
  • isosurfaces of implicit functions
geometric modeling basics
Geometric Modeling Basics
  • types of polygons & polyhedra
  • computing normals
  • geometric computations
  • OpenGL concerns
  • procedural approaches
types of polygons polyhedra
types of polygons & polyhedra
  • triangle – fixed length polygons
  • convex polygon / polyhedron
  • concave polygon / polyhedron
  • non-planar polygon
  • sliver triangles – error-prone normals
polygonal processing
Polygonal processing
  • triangulation
  • converting to convex polyhedra
  • intersection testing
  • closure testing
  • well-formed polyhedron:
    • closed,
    • non-self intersecting
    • 2D manifold
data structures
Data structures
  • face-based
  • winged edge
computing normals
computing normals
  • cross-product of edges
    • ordered edges at convex corner
  • summation method
computing vertex normals
computing vertex normals
  • for each vertex, i, n[i]=(0,0,0)
  • for each face, j
        • Compute the normal, nrml, for the face
        • For each vertex, i, of the face n[i] += nrml
  • for each vertex, I, normalize n[i]
opengl concerns
OpenGL concerns
  • vertex normals
  • convex polygons
  • triangle strip
  • quad strips
  • triangle fans
geometric computations
geometric computations
  • topology: genus, holes, & handles
  • Euler’s formula: E+2 = F+V+2G
  • Convex hull
  • distance to, contained in, intersected by
  • meshing & simplification
  • LoD: level of detail representations
procedural approaches
Procedural Approaches
  • composition from primitive shapes
  • extrusion
  • solid of revolution
  • lofting
  • sweep operator
scene graph
Scene Graph
  • Describe a scene
    • transformations
    • primitive objects
    • attributes
    • camera
    • lights

Hierarchical representation

File format to record scene description

scene graph14
Scene Graph

Scene {

transform {

attribute

primitive

}

transform {

attribute

primitive

transform {

attribute

primitive

}

}

}

scene

transformation

lights

camera

attributes

primitive