Geometric and computational aspects of manufacturing processes

Bose, Prosenjit

doi:10.1016/0097-8493(94)90061-2

Cited by 16 publications

(11 citation statements)

References 47 publications

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“…The following overview of related problems is not extensive. For a detailed discussion of problems related to manufacturing processes considered in computational geometry, the reader is referred to Bose [6], Bose and Toussaint [8], and the Handbook of Discrete and Computational Geometry by Goodman and O'Rourke [17].…”

Section: Introductionmentioning

confidence: 99%

Clamshell Casting

et al. 2007

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A popular manufacturing technique is clamshell casting, where liquid is poured into a cast and the cast is removed by a rotation once the liquid has hardened. We consider the case where the object to be manufactured is modeled by a polyhedron with combinatorial complexity n of arbitrary genus. The cast consists of exactly two parts and is removed by a rotation around a line in space. The following two problems are addressed: (1) Given a line of rotation l in space, we determine in O(n log n) time whether there exists a partitioning of the cast into exactly two parts, such that one part can be rotated clockwise around l and the other part can be rotated counterclockwise around l without colliding with the interior of P or the cast. If the problem is restricted further, such a partitioning is only valid when no reflex edge or face of P is perpendicular to l, the algorithm runs in O(n) time.(2) An algorithm running in O(n 4 log n) time is presented to find all the lines in space that allow a cast partitioning as described above. If we restrict the problem further and find all the lines in space that allow a cast partitioning as described above, such that no reflex edge or face of P is perpendicular to l, the algorithm's running time becomes O(n 4 α(n)). All of the running times are shown to be almost optimal.

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Section: Introductionmentioning

confidence: 99%

Clamshell Casting

et al. 2007

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“…These systems have to be augmented with a component verifying, purely on the basis of a CAD model of the object, that an object being designed can actually be manufactured using the intended techniques. The surveys by Bose and Toussaint [4], [6] and by Janardan and Woo [16] give an overview of geometric problems and algorithms arising in these manufacturing processes.…”

Section: Introductionmentioning

confidence: 99%

Casting with Skewed Ejection Direction

2005

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Casting is a manufacturing process in which liquid is poured into a cast (mold) that has a cavity with the shape of the object to be manufactured. The liquid then hardens, after which the cast is removed. We address geometric problems concerning the removal of the cast. A cast consists of two parts, one of which retracts in a given direction carrying the object with it. Afterwards, the object will be ejected from the retracted cast part. In this paper we give necessary and sufficient conditions to test the feasibility of the cast part retraction and object ejection, where retraction and ejection directions need not be the same. For polyhedral objects, we show that the test can be performed in O(n 2 log 2 n) time and the cast parts can be constructed within the same time bound. The complexity of the cast parts constructed is worst-case optimal. We also give a polynomial-time algorithm for finding a feasible pair of retraction and ejection directions for a given polyhedral object.

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“…Our definition of k-drainable polygons is inspired by the k-fillable polygons of [BT94][BvKT98], those mold shapes that can be filled with liquid metal poured into k holes. Despite the apparent inverse relationship between filling and draining, the two concepts are rather different.…”

Section: -Drainable Shapesmentioning

confidence: 99%

Draining a polygon—or—rolling a ball out of a polygon

Aloupis

Cardinal

Collette

et al. 2014

Computational Geometry

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We introduce the problem of draining water (or balls representing water drops) out of a punctured polygon (or a polyhedron) by rotating the shape. For 2D polygons, we obtain combinatorial bounds on the number of holes needed, both for arbitrary polygons and for special classes of polygons. We detail an O(n 2 log n) algorithm that finds the minimum number of holes needed for a given polygon, and argue that the complexity remains polynomial for polyhedra in 3D. We make a start at characterizing the 1-drainable shapes, those that only need one hole.

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Geometric and computational aspects of manufacturing processes

Cited by 16 publications

References 47 publications

Clamshell Casting

Clamshell Casting

Casting with Skewed Ejection Direction

Draining a polygon—or—rolling a ball out of a polygon

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