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Finding the limbs and cusps of generalized cylinders

✍ Scribed by Jean Ponce; David Chelberg

Publisher
Springer US
Year
1988
Tongue
English
Weight
794 KB
Volume
1
Category
Article
ISSN
0920-5691

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✦ Synopsis

This paper addresses the problem of finding analytically the limbs and cusps of generalized cylinders. Orthographic projections of generalized cylinders whose axis is straight and whose axis is an arbitrary 3D curve are considered in turn. In both cases, the general equations of the limbs and cusps are given. They are solved for three classes of generalized cylinders: solids of revolution, straight homogeneous generalized cylinders whose scaling sweeping rule is a polynomial of degree less than or equal to 5 and generalized cylinders whose axis is an arbitrary 3D curve but the cross section is circular and constant. Examples of limbs and cusps found for each class are given. Applications and extensions to perspective projection and completely general straight generalized cylinders are discussed.

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A generalized cylinder is an object bounded by a surface generated by moving a 2D contour curve along a 3D spine curve, possibly scaling the contour along the spine, and two end planes. Several important properties of such objects are presented. In particular, conditions to avoid local and global se