CS 285: SOLID MODELING

Lecture #3 -- We, Jan. 30, 2002.

Preparation

Design Plan, Choice of Parameters (Assignment 1)

Some shortcomings observed in the write-ups of A1:

• Vague plans -- asking for things to be delivered "by magic": (rounding the edges).
• Vague plans how elements should fit together: (the 12 flowers on the dodecahedron).
• Too many low-level paramaters: (all vertex coordinates)
• Redundant, dependent parameters: (diameter of dodecahedron, edge-length of pentagon).
• Lack of generic high-level parameters: (number of teeth on gear wheels).

More on SLIDE and Tcl

Review of Various Shape Representations for Different Purposes

What are the main concerns for these representations ?

• Design front ends and design languages
  -- Key constructs that are easy to use by the designers.
• Datastructures for manipulation, modification, analysis
  -- Full connectivity to nearest neighbors for efficient modification.
• Shape capture for fabrication, interchange formats
  -- Primitives that can readily be interpreted by the fabrication machines.

Design-Level Representations

• (Parameterized) Primitives
  Cubes, spheres, cylinders, cones, ...
  Look at the SLIDE Language.
• CSG -- Constructive Solid Geometry
  Combine solids with regularized boolean operations
• B-rep, Boundary Representation
  The surface of the solid described as a collection of planar polygons
  and/or curved (spline) patches.
  Subdivision surfaces !
• Voxels
  Partially occupied array of solid volume elements.
• Instancing
  --> This is the primary way to enforce symmetry in a design.
  Atoms for
  Nanotech Machines ( Differential Gear, Motion Controller, Atom Pump )
  Parametrized primitives, previously defined objects, ...
• Parameterized objects, "auto-shapes"
  2D: drafting symbols: n-gons, stars, "banners", ...
  (available in most drawing programs).
  3D: gear wheels, ...
  (often custom-built, not yet readily available).
• Features for manufacturing
  Through-holes, sink-holes, pockets, slots, shoulder pockets, ...
  (No consistent nomenclature or definitions; should also be parameterized).
• Procedural generation
  Spline patches -- defined by their type, control points, ...
  Sweeps -- defined by cross section and sweep path.
  L-systems -- parameterized instantiation based on expression trees.
  Wavy surface of the sea, fractal mountains, ...
• Procedural shape modification
  Edge bevelling or rounding.
  Subdivision -- procedural smoothing, related to splines.
• Structure of a design
  Scene hierarchy (logical/functional).
  Dynamic grouping during editing.
  Constraints -- (e.g., Pro-E.)
• The SLIDE Language
  combines many of the above representations.
  Many of the statements that have to do with rendering can be ignored for CS285.

How to convert between these different representations ?

If you could have only ONE of the above paradigms -- which one would you choose ?

Data Structures for Solid Modeling

• 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.
  - 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."

• 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).
  -- also important as a general spatial reference frame when data is unevenly distributed.
  "Tabulates" spatial occupancy. For efficient encoding use:
  - Run-length encoding
  - Octrees
  - Wavelet-based (kD-tree-based) generalizations

Which is the right one for what purpose ?

Current Homework Assignments:

A#2: Introduction to SLIDE -- DUE: Tuesday, Feb. 5, 6am. (by e-mail)