In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and∞. We show that for all w > 0 our estimations are strictly increasing with respect to w. Moreover, we find the pa...

Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively sh...

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

This paper presents an arc-length preserving axial deformation along a B-spline curve based on arc-length parameterization of the axial curve. Space spanned by arc length and rotation minimizing frame on the axis is taken as the embedded space. As in real life, the length of an object’s skeleton usually remains constant when it is axially deformed such as a swimming fish, a swaying tree etc, An...

A new method is proposed to detect circular arcs. The detection of a circular arc includes the determination of its center, radius, length, and midpoint. The Hough transform is applied to detect circular arcs by using center and radius as parameters. A peak value in the parameter space of the Hough transform indicates the existence of a circular arc. The center and radius of the circular arc ar...

BACKGROUND To assess repeatability of the Zhongshan Assessment Program (ZAP) software measurement of Anterior Segment Optical Coherence Tomography (ASOCT) images and correlate with graft trephine diameter following Descemet Stripping Automated Endothelial Keratoplasty (DSAEK) METHODS: Retrospectively evaluated interventional case series. 121 consecutive eyes undergoing DSAEK over a 26 month per...

The present bunch compressor design for the NLC allows control of the final bunch length by way of changes to the horizontal betatron phase advance of the 180ƒ-turnaround arc. This adjustability requirement significantly constrains the design and cost optimization of the system and excludes the possibility of using permanent-magnet quadrupoles in the arc. To relieve this constraint, and to avoi...

It is often desirable to evaluate parametric spline curves at points based on their arc-length instead of the curveÕs original parameter. Techniques are presented here for computing a reparameterization curve allowing approximate arc-length evaluation. This reparameterization curve is also expressed as a spline, allowing rapid evaluation as a function of arc-length. Using composition methods de...

We present the first treatment of the arc length of the Gaussian Process (gp) with more than a single output dimension. Gps are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing li...