Incorporating Sharp Features in the General Solid Sweep Framework

This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a...

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Veröffentlicht in:Computer graphics forum Jg. 35; H. 5; S. 21 - 31
Hauptverfasser: Adsul, Bharat, Machchhar, Jinesh, Sohoni, Milind
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.08.2016
Schlagworte:
and object representations
Boundary representation
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Digital video
Hoisting
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations
Mathematical analysis
Orientation
Parameter robustness
Pilots
Singularities
solid
Studies
surface
Trimming
ISSN:0167-7055, 1467-8659
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Zusammenfassung:This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a significant and useful generalization of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by an analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explained by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body‐check such as orientation, singularities and self‐intersections are efficiently resolved. Examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.
Bibliographie:ArticleID:CGF12960
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12960