3D Euler spirals for 3D curve completion

Harary, Gur; Tal, Ayellet

doi:10.1016/j.comgeo.2011.10.001

Cited by 41 publications

(58 citation statements)

References 24 publications

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“…Also, spatial paths based on 3D spirals, e.g. as suggested by Harary and Tal (2012), must be treated.…”

Section: Discussionmentioning

confidence: 99%

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Path Generation for High-Performance Motion of ROVs Based on a Reference Model

Fernandes¹,

Sørensen²,

Donha³

2015

MIC

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This paper deals with the generation of sufficiently smooth position, velocity, and acceleration references for guiding the motion of an ROV along purposefully defined curvature-continuous paths in automated missions. The references are meant to be employed in high-performance trajectory tracking and dynamic positioning applications. The path planning problem is not in the scope of this work. A reference model that synthesises references concerning a single Degree-of-Freedom (DoF) motion is initially described. Then, the use of the synthesised references as the parametrisation for other references concerning multiple DoF motion along curvature-continuous paths is exploited. Results from computer simulations and full-scale sea trials, both based on the NTNU's ROV Minerva, are presented and discussed.Keywords: Guidance system, Path generation, Reference model, ROV, Trajectory tracking. List of acronyms and abbreviations

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“…Also, spatial paths based on 3D spirals, e.g. as suggested by Harary and Tal (2012), must be treated.…”

Section: Discussionmentioning

confidence: 99%

“…Harary and Tal (2012) extended it to three dimensions, such that the torsion also changes linearly with the arc length. These characteristics can be explored for constructing curvature-and torsion-continuous paths, which are formed by straight lines connected through pairs of mirror-symmetric twin clothoids.…”

Section: Mirror-symmetric Twin Clothoidsmentioning

confidence: 99%

Path Generation for High-Performance Motion of ROVs Based on a Reference Model

Fernandes¹,

Sørensen²,

Donha³

2015

MIC

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“…Given boundary conditions, the most common way to construct a curve is to use splines [Far93]. Splines are fast and easy to compute, but they are not always the curves preferred by the human visual system [HT12]. We seek a curve that can be specified as easily, and yet is more appealing.…”

Section: Completion Of the Feature Curves And Their Surroundingsmentioning

confidence: 99%

Feature‐Preserving Surface Completion Using Four Points

Harary

Tal

Grinspun

2014

Computer Graphics Forum

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We present a user‐guided, semi‐automatic approach to completing large holes in a mesh. The reconstruction of the missing features in such holes is usually ambiguous. Thus, unsupervised methods may produce unsatisfactory results. To overcome this problem, we let the user indicate constraints by providing merely four points per important feature curve on the mesh. Our algorithm regards this input as an indication of an important broken feature curve. Our completion is formulated as a global energy minimization problem, with user‐defined spatial‐coherence constraints, allows for completion that adheres to the existing features. We demonstrate the method on example problems that are not handled satisfactorily by fully automatic methods.

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“…A variety of spirals have been investigated in computer graphics, including the 3D Helispirals [GS99]. Euler spirals [Lev08, HT10], and Logarithmic spirals. This paper focuses on the latter.…”

Section: Introductionmentioning

confidence: 99%

The Natural 3D Spiral

Harary

Tal

2011

Computer Graphics Forum

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a) A tail of a lizard (b) Oliva porphyria (c) A horn of a Big-Horn Sheep Figure 1: Modeling a variety of logarithmic-spiral structures in fauna. Real images of the objects are shown on the top left. AbstractLogarithmic spirals are ubiquitous in nature. This paper presents a novel mathematical definition of a 3D logarithmic spiral, which provides a proper description of objects found in nature. To motivate our work, we scanned spiral-shaped objects and studied their geometric properties. We consider the extent to which the existing 3D definitions capture these properties. We identify a property that is shared by the objects we investigated and is not satisfied by the existing 3D definitions. This leads us to present our definition in which both the radius of curvature and the radius of torsion change linearly along the curve. We prove that our spiral satisfies several desirable properties, including invariance to similarity transformations, smoothness, symmetry, extensibility, and roundness. Finally, we demonstrate the utility of our curves in the modeling of several animal structures.

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3D Euler spirals for 3D curve completion

Cited by 41 publications

References 24 publications

Path Generation for High-Performance Motion of ROVs Based on a Reference Model

Path Generation for High-Performance Motion of ROVs Based on a Reference Model

Feature‐Preserving Surface Completion Using Four Points

The Natural 3D Spiral

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