An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry

Constructive Solid Geometry of the Trihedron

14th Design Automation Conference ◽

10.1115/detc1988-0002 ◽

1988 ◽

Author(s):

D. J. Wilde

Keyword(s):

Numerical Computation ◽

Set Theory ◽

Engineering Students ◽

Boundary Representation ◽

Computer Interface ◽

Constructive Solid Geometry ◽

Human Computer Interface ◽

Cad Systems ◽

Solid Geometry ◽

Cad Cam

Abstract As a first step toward a Constructive Solid Geometry for designing general polyhedra, this paper develops the set theory of the trihedron, loosely speaking any set combination of three planar half spaces (monohedra). The trihedron can be decomposed precisely into its primitive monohedra and its CSG-tree of union or intersection operations with no designer topological input other than the convexity or concavity of each edge, giving a human-computer interface simpler than those for existing right-hand rule boundary representation methods. The somewhat visual trigonometric concepts of classical solid geometry are formulated in terms of vectors and matrices appropriate for numerical computation. This reorganization may be useful not only for designers of CAD systems, but also for educators seeking to strengthen and modernize the geometric education of engineering students wonting to make full use of CAD/CAM technology.

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A topological enabled three-dimensional model based on constructive solid geometry and boundary representation

Cluster Computing ◽

10.1007/s10586-016-0634-1 ◽

2016 ◽

Vol 19 (4) ◽

pp. 2027-2037 ◽

Cited By ~ 4

Author(s):

Huang Ming ◽

Du Yanzhu ◽

Zhang Jianguang ◽

Zhang Yong

Keyword(s):

Three Dimensional ◽

Boundary Representation ◽

Constructive Solid Geometry ◽

Dimensional Model ◽

Three Dimensional Model ◽

Model Based ◽

Solid Geometry

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On the Integration of Parametric Polynominal Surface Representations Into CSG Based Solid Modelling

15th Design Automation Conference: Volume 1 — Computer-Aided and Computational Design ◽

10.1115/detc1989-0027 ◽

1989 ◽

Author(s):

A. Saia ◽

M. S. Bloor ◽

A. de Pennington

Keyword(s):

Shape Representation ◽

Sculptured Surface ◽

Constructive Solid Geometry ◽

Solid Modelling ◽

Surface Geometry ◽

B Spline ◽

Spline Surface ◽

Solid Geometry ◽

Modelling Techniques ◽

Surface Representations

Abstract The integration of sculptured surface and solid modelling techniques across a common geometric domain continues as an active source of research and development in computer aided geometric design. Although much progress has been made, fundamental difficulties remain due to the differing approaches to shape representation and subsequent evaluation found in the two modelling paradigms. The first part of the paper reviews some of the issues arising when addressing the integration of existing sculptured surface representations into a Constructive Solid Geometry (CSG) based solid modeller. The second part describes work at Leeds which proposes the use of a new evaluation technique known as ISOS (Inner Set Outer Set) for CSG defined objects which incorporate both quadric and B-spline surface geometry.

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