CS 285: SOLID MODELING
Lecture #4 -- Mo, Jan. 30, 2006.
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Discussion of Assignment #2 -- Generating Symmetrical Venn Digrams
I hope that I could convince you last time that Interactive Parametric Procedural Design is a useful and powerful way to design.
However, nobody want to start from scratch every time and write all the routines they need for a particular project.
So it would be nice to have some predefined, well-implemented machinery that is useful in may situations.
What are some examples of such machinery ?
To robustly implement a versatile geometric module is not a trivial undertaking. Let's study one example:
Case Study: Generalized Sweeps
What might we want to use it for ? (A) (B) (C) (D) (E)
What are the semantics of a useful sweep construct ?
What are some of its desirable properties ?
How can it be implemented robustly ?
Some Basic Concepts Needed:
The Frenet frame:
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Finding the Tangent
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Normal Plane
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Osculating Plane
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Normal vector
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Binormal
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Difference between Normal and second derivative
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The three coordinate planes and their relations to the 3 vectors.
Foundation: Sweeps along piecewise linear paths.
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How to properly join cylidrical tubes at an angle.
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How to join prismatic tubes, so edges line up.
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"Azimuth" and "axturn".
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How to calculate the torsion minimizing azimuths.
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The "twist" parameters.
Closed prismatic loop.
Sweeps along smooth curves.
- Any smooth curve in computer graphics becomes piecewise linear at some point.
The sweep parameters in SLIDE.
Use the sweep construct in SLIDE.
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