CS 285: SOLID MODELING

Lecture #8 -- Mo, Feb. 13, 2006.

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Discussion of issues that may have come up in Assignment#5.

What is the mathematical operation to describe the monogram block that I asked you to design ?
What are practical ways to design an appropriate object ?

What B-Rep data structure would you choose:

if you had to design an interactive CAD system that allows one to make large, but smooth, global deformations of a given object,
of the kind described in: Sederberg and Parry: "Free-Form Deformation of Solid Geometry Models" (FD86).

How to turn a given arbitrary B-Rep mesh into a mesh with only triangles ?

How to make a mesh with all quadrilaterals ? (perhaps for smoother subdivision).

What subdivision scheme(s) should you use, if you wanted to have a smooth output surface ?
(1), (2 ), (3), ...

How should you modify the mesh if the deformations are so large that there might be very long skinny triangles ?
What mesh-modification operators do you need to provide ?
see Hoppe.

B-Rep Data Structures (cont.)

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)
(or page 2 of : McMains et al: "Out-of-Core Build of a Topological Data Structure from Polygon Soup")
- -- 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.

Other Data Structures

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.

Paper Presentations

How to efficiently and effectively read a paper to prepare for these discussions:

Read: "Introduction," "Conclusions;" look at Figures and read captions.
This should typically tell you WHAT the authors have done, and WHY.
Now try to find out HOW they did it:
Look for the appropriate sections that describe the key techniques.
Also try to get an understanding what the limitations and caveats are of the described approach.
Might there be things that the authors do NOT tell you ?
You can probably skip the section on "Previous Work" or just skim it.
Write down a few of the key points you learned,
as well as some questions that are good for discussion in class.

Current Homework Assignment#5:

Due Wednesday 2/15/2006.

NEXT TIME: Bring your laptop computer to class to install Quickslice.

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