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Full Version: Cone and Conical Frustum Unwrap

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From: bemfarmer
30 Jan 2018   [#43] In reply to [#42]
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
2 Feb 2018   [#44]
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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