What is Curvature ? -- rate of rotation around B (1/R of the osculating circle)
What is Torsion ? -- rate of rotation of osculating plane (around tangent T)
Inflection points -- where curvature = 0 (==> N, B, undetermined)
Sweeps along Polylines (and piecewise linearly approximated curves)
Examples of mitered joints: 1234
Default: Cross-section remains perpendicular to tangent vector.
The "natural" orientation of the cross section based on the Frenet frame.
Azimuth determines alternate orientations around the tangent vector. Construction
of "ribs" in angle-divider plane at all segment junctions, -- stretched
by 1/cos(half-angle) in direction of normal vector
Minimizing torsion by projectin forward from one rib plane to the next.
Adding arbitrary additional azimuht values at any control point.
Adding additional (continuous) twist by adding a linear progression of azimuth at all rib positions.
Finding minimal amount of twist that closes a sweep loop.
[More on that in CS284 -- Next offering: Fall 2009. -- Undergraduate students who do well in CS 184 are welcome]
Shirley, 2nd Ed: Ch 15
Study: ( i.e., try to understand fully, so that you can answer
on an exam):
Shirley, 2nd Ed: Ch 15.6-15.7
Programming Assignment 6:due (electronically submitted) before Tuesday 3/17, 11pm <== ASSIGNMENT CAN BE DONE IN PAIRS !
Programming Assignment 7:due (electronically submitted) before Wednesday 4/1, 11pm <== ASSIGNMENT CAN BE DONE IN PAIRS !
Start the next assignment as soon as possible, so that you can ask
relevant questions and obtain good feedback and help BEFORE Spring