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CAD tip # 7800:
Question
A
The surface of a 3D hyperboloid is a ruled surface. So use the AutoCAD command RULESURF. The control edges may be two circles or ellipses (in a polyline form), with offset (twisted) origins. Use e.g. PLINE,Arc with two 180° segments, copy the circular pline in Z axis and rotate it (e.g. 2/5 of full circle - 144°).
There are two important variables for creation of a ruled surface (model) - SURFTAB1 (surface smoothness, e.g. 24) and MESHTYPE (surface/mesh type, e.g. 0).
An example of a hyperboloid created this way can be found in the Block catalog:
Similarly, in Inventor, you can use lofting with two parallel circular paths - see the parametric IPT model:
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