Exact offset procedures for simple solids
type: Item
instance of: scholarly article
title: Exact offset procedures for simple solids
zbMATH Open document ID: 0583.65095
DOI: 10.1016/S0167-8396(85)80002-9
published in: Computer Aided Geometric Design
publication date: 1985-01-01T00:00:00Z
review text: This paper outlines exact offset procedures for three basic classes of solid primitives: (1) solids of revolution with simple profile curves; (2) solids of linear extrusion with simple profile curves; and (3) convex planar polyhedra. Concepts from differential geometry are used to illustrate the complexity of offsets to general curves and surfaces, and to identify conditions under which offset geometries degenerate. Qualitative descriptions for offset surfaces to simple solids are then presented, in terms of their elementary constituent patches, and the geometrical and topological relationship of these patches to the progenitor primitives. Precise mathematical representations for the required surface elements, as parametric rational polynomial forms, are given. The uses and limitations of offset solids in a solid modeling environment are briefly assessed, and the difficulties of offsets for complex solids are enumerated.
Mathematics Subject Classification ID: 65S05
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 3934380
zbMATH Keywords: offset surfaces
zbMATH Keywords: solid primitives
zbMATH Keywords: automatic numerical-control machining
zbMATH Keywords: solids of revolution
zbMATH Keywords: solids of linear extrusion
zbMATH Keywords: convex planar polyhedra
zbMATH Keywords: solid modeling
author: Rida T. Farouki
MaRDI profile type: Publication
cites work: Q4091004
cites work: Q5790826
cites work: The approximation of non-degenerate offset surfaces
cites work: Q4178157
cites work: Q3781668
cites work: Q5811706
cites work: Q4756008
cites work: Q3258642
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description: scientific article; zbMATH DE number 3934380