After a lot of revision, here is the script _ObliqueConeUnwrap,
which creates a planar "Net" of the unwrap of a cone-like surface.
Reference:
https://plus.google.com/+NilesJohnson/posts/jCmg66wyo83
The MoI .pdf file "ObliqueConeWedgeCut" shows Niles' ascii drawing, in a more comprehensible fashion,
from which comes the equation he uses in the SAGE program, based upon the pythagorean equation.
dTheta = Math.sqrt( Math.pow( dS, 2 ) - Math.pow( dR, 2 )) / R;
The script should use 500, 1000, 2000, or more points, for a "brute force numerical integration."
The unwrap curve is not "perfect," but the "tolerance" changes for more points.
Rebuild can be used. It was not necessary after all, to use Trim in the script.
An ObliqueCone is easily made in MoI by extruding either a circle, or an ellipse, closed or open, with command Extrude, using "To point" and "Unlock direction" buttons. The iso-curves should be uniform. The cone can be a right circular cone.
A cone-like surface may also be made with Extrude / To point / Unlock direction, using some other curve.
These surfaces are also candidates for _ObliqueConeUnwrap.
Possible overlap is ignored by the script. The script just needs an apex point, and a base curve.
The base curve may be a standalone curve, or an edge, and be closed or open.
The base curve could be nonPlanar, or sinusoidal. After the unwrap, if a center line from the Net center point is added,
Network can create the planar surface, with nice iso-curves that can match the iso-curves of the cone-like surface.
Placing a sphere at the apex, and doing intersect, makes a base curve which could be nonplanar,
The unwrap may be an arc of a circle. All of the "radial" line segments are the same length, and dR is zero. dTheta = dS/R.
- Brian