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From: bemfarmer
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
Attachments:
ObliqueConeWedgeCut.pdf
ObliqueEllipticalCone10.zip
_ObliqueConeUnwrap1_30_2018.zip
From: Finema
Hi Brian,
lot of work here !
it will be nice if you do a little video to show how to use this script
Also , i can't see your script in attachment
Thanks a lot.
From: bemfarmer
Hi Finema,
Script is now uploaded. (I did a last minute minor edit.)
I'll have to learn how to do a video...I did buy Camtasia a while back...
I've decided that the sphere intersect of an elliptical oblique cone has radials at equal curve intervals (untrimmed segments), but that
delta theta angles are NOT quite equal(?).
- Brian
From: bemfarmer
Unwrap of Extrusion of Circle or Ellipse
Define a simple extrusion as being along a line, without using curved "Path," "To Point," or "Tapered" selections in MoI Extrude command.
For such extrusions, the top curve will be of the same character as the base curve.
Reference for "Net of oblique circular cylinder" Niles Johnson:
https://plus.google.com/+NilesJohnson/posts/WsmXBbu3Vu9
A right circular cylinder is the result of a simple extrusion of a circle along a line perpendicular to the plane of the base circle.
Similarly, a right elliptical cylinder is the result of the simple extrusion of an ellipse, perpendicular to the base ellipse.
The draft angle in these cases is 0 degrees, (plus or minus multiples of 180 degrees). (So angles are modulus +/- 180 degrees.)
For other draft angles, excluding the flat case of 90 degrees, "oblique" objects result.
An oblique circular cylinder is the result of extrusion with non-zero, and non-90 degree, draft angle, and has an elliptical cross section.
Slice planes parallel to the base result in iso-line circles parallel to, and equal to, the base circle.
An oblique elliptical cylinder is the result of extrusion of an ellipse with non-zero, non-90, draft angle.
Slice planes parallel to the base result in iso-line ellipses parallel to, and equal to, the base ellipse.
Curiously, note that removing the base and top of a circular cylinder with a matched pair of non-parallel slice planes, results in an oblique elliptical cylinder, not an oblique circular cylinder. An oblique elliptical cylinder has only one particular slicing angle which results in a circle, rather than some other ellipse.
The belt ellipse of an oblique circular cylinder...
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