✦ LIBER ✦

A pythagorean hodograph quintic spiral

✍ Scribed by DJ Walton; DS Meek

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 795 KB
Volume: 28
Category: Article
ISSN: 0010-4485
DOI: 10.1016/0010-4485(96)00030-9

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✦ Synopsis

A polynomial curve with a Pythagorean hodograph has the properties that its arc-length is a polynomial of its parameter. and its offset is a rational algebraic expression. A quintic is the lowest degree Pythagorean hodograph curve that may have an inflection point and that inflection point allows a segment of it to be joined to a straight line segment while preserving continuity of curvature, continuity of position, and continuity of tangential direction.

The curvature of a spiral varies monotonically with arc-length. Spiral segments are useful in the design of fair curves. A Pythagorean hodograph quintic spiral is presented which allows the design of fair curves in a NURHS based CAD system. It is also suitable for applications such as highway design in which the clothoid has traditionally been used.

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