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Designing NURBS Cam Profiles using Trigonometric Splines
 J. Mech. Design
, 1997
"... . We show how to design cam profiles using NURBS curves whose support functions are appropriately scaled trigonometric splines. In particular, we discuss the design of cams with various side conditions of practical interest, such as interpolation conditions, constant diameter, minimal acceleration o ..."
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. We show how to design cam profiles using NURBS curves whose support functions are appropriately scaled trigonometric splines. In particular, we discuss the design of cams with various side conditions of practical interest, such as interpolation conditions, constant diameter, minimal acceleration or jerk, and constant dwells. In contrast to general polynomial curves, these NURBS curves have the useful property that their offsets are of the same type, and hence also have an exact NURBS representation. 1. Introduction There are a number of schemes based on ordinary polynomial splines for the design of displacement functions describing cam profiles, see e.g. [20,21]. However, the existing schemes have the drawback that the parametric representation of the resulting cam profiles is not suitable for immediate practical application. In particular, these profile curves are not industry standard NURBS curves. Thus, to use polynomial splines in the manufacturing process, their representations...
Elasticurves: Exploiting Stroke Dynamics and Inertia for the Realtime Neatening of Sketched 2D Curves
"... Figure 1: Input strokes are drawn in red, with drawing speed indicated by the spacing of green input points (a). The input stroke in (a) is neatened using Laplacian smoothing with fixeddistance sampling (b), and using elasticurves (c). Note the sharp corners and smooth arcs on the waves and teeth i ..."
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Figure 1: Input strokes are drawn in red, with drawing speed indicated by the spacing of green input points (a). The input stroke in (a) is neatened using Laplacian smoothing with fixeddistance sampling (b), and using elasticurves (c). Note the sharp corners and smooth arcs on the waves and teeth in (c), compared to the featureless smoothing in (b). Elasticurves present a novel approach to neaten sketches in realtime, resulting in curves that combine smoothness with userintended detail. Inspired by natural variations in stroke speed when drawing quickly or with precision, we exploit stroke dynamics to distinguish intentional fine detail from stroke noise. Combining inertia and stroke dynamics, elasticurves can be imagined as the trace of a pen attached to the user by an oscillationfree elastic band. Sketched quickly, the elasticurve spatially lags behind the stroke, smoothing over stroke detail, but catches up and matches the input stroke at slower speeds. Connectors, such as lines or circulararcs link the evolving elasticurve to the next input point, growing the curve by a responsiveness fraction along the connector. Responsiveness is calibrated, to reflect drawing skill or device noise. Elasticurves are theoretically sound and robust to variations in stroke sampling. Practically, they neaten digital strokes in realtime while retaining the modeless and visceral feel of pen on paper.
Approximate Arc Length Parametrization
, 1996
"... Current approaches to compute the arc length of a parametric curve rely on table lookup schemes. We present an approximate closedform solution to the problem of computing an arc length parametrization for any given parametric curve. Our solution outputs a one or twospan Bezier curve which relates ..."
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Current approaches to compute the arc length of a parametric curve rely on table lookup schemes. We present an approximate closedform solution to the problem of computing an arc length parametrization for any given parametric curve. Our solution outputs a one or twospan Bezier curve which relates the length of the curve to the parametric variable. The main advantage of our approach is that we obtain a simple continuous function relating the length of the curve and the parametric variable. This allows the length to be easily computed given the parametric values. Tests with our algorithm on several thousand curves show that the maximum error in our approximation is 8.7% and that the average of maximum errors is 1.9%. Our algorithm is fast enough to compute the closedform solution in a fraction of a second. After that a user can interactively get an approximation of the arc length for an arbitrary parameter value. Keywords: arclength parametrization, approximation, curve design, Bezi...
Approximate Arc Length Parametrization
"... Current approaches to compute the arc length of a parametric curve rely on table lookup schemes. ..."
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Current approaches to compute the arc length of a parametric curve rely on table lookup schemes.