Just a quick minimal test:
By minor modification to Michael's orderCurves script, adding a section for crv.evaluateCurvature, and crv.evaluateDerivatives,
arrows were created for the Curvature Vector, and the second derivative vector at segment points.
The curvature vector is orthogonal to the tangent vector. (?)
The Curvature Vector "k" points towards the center of (invisible) osculating circle, from the parameter point "t". (The magnitude is probably "K". (?))
(As a mathematics side note, Note that (capital K) curvature "K" is a scalar. I've been reading up on vector functions. )
For the test clothoid, the k curvature vectors pointed in the same direction as the second derivative.
For test circle, test open circle-oid, and test ellipse, the k curvature vectors were directed several degrees differently than the second derivative arrows.
The second derivative arrows were much longer than the curvature vectors.
I'd like to do an update to curveExplorer with these vectors, with different colored arrows, but have no time now.
The user could select desired points. Several styles would be available. There would be a persist option checkbox...
There could be checkbox options for the desired vectors.
In the test script, the curvature and 2nd derivative arrow style color will be the same, and the same style as your current style selection.
Tangents are lime green.
- Brian
The attached file is a bare bones modification, alpha test version.
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