Optimizing CNC Programs Using Spline Techniques

Weiß, Volker; Seidel, Hans‐Peter; Greiner, Günther; Puchtler, Thomas; Eberlein, Werner

doi:10.1007/978-3-642-60607-6_6

Cited by 1 publication

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“…While there exists generalizations of models like the Fourier descriptors to space curves [15], splines can be used for space curves without any modification. Splines were introduced by Schoenberg [16] and de Boor [17] as interpolation methods, and have found use in signal & image processing [18], computer graphics [19], manufacturing processes [20], and others. Several types and variations of splines have been developed based on choice of basis and constraints; B-splines, Bézier curves, Rational B-splines, Trigonometric splines, to name a few.…”

Section: Related Workmentioning

confidence: 99%

Tangled Splines

Tatu¹

2016

Preprint

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Extracting shape information from object boundaries is a well studied problem in vision, and has found tremendous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying certain constraints is also intriguing. In this paper, we model and analyze the space of shapes represented by a 3D curve (space curve) formed by connecting n pieces of quarter of a unit circle. Such a space curve is what we call a Tangle, the name coming from a toy built on the same principle.We provide two models for the shape space of n-link open and closed tangles, and we show that tangles are a subset of trigonometric splines of a certain order. We give algorithms for curve approximation using open/closed tangles, computing geodesics on these shape spaces, and to find the deformation that takes one given tangle to another given tangle, i.e., the Log map. The algorithms provided yield tangles upto a small and acceptable tolerance, as shown by the results given in the paper.

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Section: Related Workmentioning

confidence: 99%

Tangled Splines

Tatu¹

2016

Preprint

View full text Add to dashboard Cite

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Optimizing CNC Programs Using Spline Techniques

Cited by 1 publication

References 3 publications

Tangled Splines

Tangled Splines

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