An analysis of symmetry for plane curves and plane curve algorithms. (English) Zbl 0757.65010
The work is complementary to that by the author [ibid. 6, 265-277 (1989; Zbl 0677.53016)]. General symmetry requirements for plane curve algorithms are defined. Planar paths and planar curves and connection with a functional equation are discussed. The definitions include symmetry and anti-symmetry properties of axis-invariant curve algorithms.
Two classes, \(A\) and \(B\), of axis-invariant curve forms are characterized. Necessary and sufficient conditions are found for which algorithms, that take specific general forms, possess the symmetry properties. An extension to space curves and surfaces is suggested. An application in computer aided design is mentioned.
Two classes, \(A\) and \(B\), of axis-invariant curve forms are characterized. Necessary and sufficient conditions are found for which algorithms, that take specific general forms, possess the symmetry properties. An extension to space curves and surfaces is suggested. An application in computer aided design is mentioned.
Reviewer: V.Burjan (Praha)
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
Keywords:
plane curve algorithms; symmetry; anti-symmetry; axis-invariant curve algorithms; computer aided designCitations:
Zbl 0677.53016References:
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