Controlled linear perturbation

Sacks, Elisha; Milenkovic, Victor; Kyung, Min-Ho

doi:10.1016/j.cad.2011.06.015

Cited by 6 publications

(10 citation statements)

References 24 publications

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“…Hachenberger [9] provides an exact implementation of this algorithm. The program is very slow [4,2,18]. Varadhan and Manocha [20] reduce the constant factor by computing the union approximately yet with the correct topology, using a volumetric grid.…”

Section: Prior Workmentioning

confidence: 99%

“…We [18] developed a robust implementation of a convex convolution algorithm. The data structures are incompatible with distributed computation.…”

Section: Prior Workmentioning

confidence: 99%

“…Although our algorithm has the same structure as our prior algorithm [18], we employ novel techniques that reduce memory usage and that enable distributed computation. We describe the algorithm briefly and discuss the innovations in detail.…”

Section: Prior Workmentioning

confidence: 99%

“…The problem with CP is that a large δ is required to resolve a singular predicate (zero value and zero gradient), e.g. 10 −5 in Minkowski sums [18].…”

Section: Robustnessmentioning

confidence: 99%

“…Our prior algorithm [18] using that approach is the first robust implementation of any convolution-based method for general polyhedra (Sec. 2).…”

Section: Introductionmentioning

confidence: 99%

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Robust polyhedral Minkowski sums with GPU implementation

Kyung

Sacks

Milenkovic

2015

Computer-Aided Design

Self Cite

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We present a Minkowski sum algorithm for polyhedra based on convolution. We develop robust CPU and GPU implementations, using our ACP robustness technique to enforce a user-specified backward error bound. We test the programs on 45 inputs with an error bound of 10 −8 . The CPU program outperforms prior work, including non-robust programs. The GPU program exhibits a median speedup factor of 36, which increases to 68 on the 6 hardest tests. For example, it computes a Minkowski sum with a million features in 20 seconds.Figure 1: Star and cube snapshots (a) and Minkowski sum (b).

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Section: Prior Workmentioning

confidence: 99%

“…We [18] developed a robust implementation of a convex convolution algorithm. The data structures are incompatible with distributed computation.…”

Section: Prior Workmentioning

confidence: 99%

Section: Prior Workmentioning

confidence: 99%

“…The problem with CP is that a large δ is required to resolve a singular predicate (zero value and zero gradient), e.g. 10 −5 in Minkowski sums [18].…”

Section: Robustnessmentioning

confidence: 99%

“…Our prior algorithm [18] using that approach is the first robust implementation of any convolution-based method for general polyhedra (Sec. 2).…”

Section: Introductionmentioning

confidence: 99%

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Robust polyhedral Minkowski sums with GPU implementation

Kyung

Sacks

Milenkovic

2015

Computer-Aided Design

Self Cite

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Robust Complete Path Planning in the Plane

Milenkovic

Sacks

Trac

2013

Springer Tracts in Advanced Robotics

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A Novel Approach to Line Clipping Against a Rectangular Window

Zhang

2023

Journal of Computing and Information Science in Engineering

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Line clipping against a rectangular window is a fundamental problem in computer graphics. A robust and fast algorithm is needed not only for the traditional graphics pipeline but also for new applications, including web maps, nanomaterials, and sensor measurements. In this paper, we present a novel approach, which is based on the idea of combining the geometric and algebraic approaches. In particular, the proposed approach first decomposes the 2D line clipping problem into a set of 1D clipping problems, and then solves the 1D clipping problem by the comparison operation only. Both theoretical analysis and experimental test were conducted to demonstrate the improved robustness (for degenerated cases) and computational efficiency of the proposed approach.

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Controlled linear perturbation

Cited by 6 publications

References 24 publications

Robust polyhedral Minkowski sums with GPU implementation

Robust polyhedral Minkowski sums with GPU implementation

Robust Complete Path Planning in the Plane

A Novel Approach to Line Clipping Against a Rectangular Window

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