CS 285: SOLID MODELING

Lecture #7 -- Wednesday, Sept. 21, 2011

Warmup

RE: Design-Level (CAD-Model) Representations (see Lecture #6)

Data Structures for CAD/Graphics Systems (Overview)

• Non-hierarchical Boundary Representations
  - Winged-edge data structure for orientable 2-manifolds (Baumgart)
  - -- every edge connects to exactly two polygons, one on each side.
  - Radial-edge data structure for non-manifolds (Weiler, UniGrafix)
  - -- edges can connect to arbitrarily many polygons.
  - Half-edge data structure (e.g. http://www.flipcode.com/articles/article_halfedge.shtml)
  - -- a lean and regular variant for 2-manifolds..
  - Quad-edge data structure (Guibas and Stolfi)
  - -- a dual/symmetric treatment of vertices and faces.
  - Polygon soup ( .STL)
  - -- not really a "data structure" -- but useful for "display lists"
  - -- or for sending a part description to an RP machine.
  
  
• Subdivision Surfaces  (Subdivision Curves and Surfaces, PPT)
  -- recursively refined and rounded/smoothed.
  -- Catmull-CLark: Meshes of quadrilaterals (approximating).
  -- Loop: Triangle meshes (approximating).
  
  
• Cellular/Simplex Decompositions
  -- the 3D equivalent of a triangulated 2D polygon.
  -- finite-element meshes for structural analysis.
  -- (possible project: generate these directly in SLIDE for sound analysis, e.g., bells).

• Voxel-based Representations
  -- for 3D raster data from ultra-sound or Magnetic Resonance Imaging (MRI).
  "Tabulates" spatial occupancy. For efficient encoding use:
  - Run-length encoding
  - Octrees
  -- also important as a general spatial reference frame when data is unevenly distributed.
  - Wavelet-based (kD-tree-based) generalizations
  
  Implicit Surfaces
  - Defined as a threshold (or level-set) surface in a 3D scalar field.
  
  Adaptively Sampled Distance Fields
  - An indirect representation of a B-rep by a judiciously placed set of sample points,
     each recording the distance to the closest surface point.
  
  
• Hierarchical Combinations of the above with Instancing and with Boolean Operations

Which is the right one -- for what purpose ?

Solutions to Assignment #3

New Homework Assignment#5:

Modeling with SLIDE -- and (later) building it on the FDM!

Due: First draft: Monday, 9/26/2011:  4pm
Final Design: Wednesday, 9/28.2011: 10am