A Computational Framework for the Boundary Representation of Solid Sweeps

Adsul, Bharat; Machchhar, Jinesh; Sohoni, Milind

doi:10.14733/cadconfp.2014.34-36

Cited by 1 publication

(19 citation statements)

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“…The solid‐sweep framework of Adsul et al [AMS14, AMS15] offers a mathematical analysis which extends both the geometric as well as the topological understanding of the sweep of smooth solids, as described briefly in Section 1. The analysis of the smooth case given in [AMS14, AMS15] coupled with that of the sharp case proposed in this paper yields a complete framework for computation of the general solid sweep.…”

Section: Related Workmentioning

confidence: 99%

“…We recall the fundamental proposition from [AMS15, BLW97] and also elsewhere which provides a necessary condition for a point x ∈ ∂M to contribute the point γ x ( t ) on ε at time t , assuming that M is smooth . Let N x denote the unique unit outward normal to ∂M at x ∈ ∂M .…”

Section: Mathematical Structure Of the General Sweepmentioning

confidence: 99%

“…In this paper we extend the framework proposed in [AMS14, AMS15] to input solids of class G0. The contribution of [AMS14] was twofold.…”

Section: Introductionmentioning

confidence: 99%

“…While [AMS14] dealt with the geometric aspects of the construction of the envelope, the topological aspects related to the brep of the envelope were explored in [AMS15]. Solids with boundary composed of multiple smooth faces meeting smoothly were considered.…”

Section: Introductionmentioning

confidence: 99%

“…At each step of envelope construction, Adsul et al [AMS14, AMS15] make the critical assumption of existence of a unique unit outward normal at each point of ∂M . This assumption is relaxed in this work by allowing input solids to be of class G0.…”

Section: Introductionmentioning

confidence: 99%

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Incorporating Sharp Features in the General Solid Sweep Framework

Adsul

Machchhar

Sohoni

2016

Computer Graphics Forum

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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, i.e., to be of class G0 wherein, the unit outward normal to the solid may be discontinuous. In the earlier framework, the solid to be swept was restricted to be G1, and thus this is a significant and useful extension 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, self-intersection and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by a delicate analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explicated 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 are efficiently resolved. Many examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.

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