CS 285: SOLID MODELING

Lecture #2 -- Mo, Jan 24, 2000.

In the last lecture we looked at "solid"-"modeling";
-- now we will review:

Various Shape Representations for Different Purposes:

• 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
  Atoms for
  Nanotech Machines ( Differential Gear, Motion Controller, Atom Pump )
  parametrized primitives, previously defined objects, ...
  --> This is the primary way to enforce symmetry in a design.
• Parameterized objects, "auto-shapes"
  2D drafting symbols: n-gons, stars, "banners", ...
  3D: gear wheels, ...
• Features for manufacturing
  Through-holes, sink-holes, pockets, slots, shoulder pockets, ...
  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

• Octrees
  -- 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.
• 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.

Which is the right one for what purpose ?

Interchange Formats for Fabrication

• IGES -- Graphic Exchange Standard
  originally for technical drawings;
  true 3D added later.
• .STL
  low-level driver for SLA (Stereolithography) machines;
  --> defacto standard for SFF (Solid Free-form Fabrication);
  - -- wordy, redundant, potentially inconsistent, unclear semantics of polygon orientations.
  Example: a cube in .STL
• ACIS (Spatial Technologies)
  a general solid modeling kernel,
  allows dump of the complete data structure;
  - -- this is not really an interchange format.
• SIF -- Solid Interchange Format
  primarily for SFF (Solid Free-form Fabrication).
  Example: A cube in SIF (strawman) version 0.5, when complex faces were still OK.
  Example: A cube in SIF 2.0, the simplified clean replacement for .STL.
• Other SIF Dialects
  - For machining: SIF_DSG (Destructive Solid Geometry)
  - For layered manufacturing (SLA, SLS, FDM, 3D-Printing, ...): L_SIF

Will SIF make it in the real world ?

Current Homework Assignment:

READ: First two sections of the "Surface Design Interface ..." paper.

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