Results 71 to 80 of about 32,621 (175)
On the convergence of hybrid polynomial approximation to higher derivatives of rational curves
, 2008 In this paper, we derive the bounds on the magnitude of lth (l=2,3) order derivatives of rational Bézier curves, estimate the error, in the L∞ norm sense, for the hybrid polynomial approximation of the lth (l=1,2,3) order derivatives of rational Bézier ...
Tai, Chiew-Lan +3 more
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Two Ways to Construct a Smooth Piecewise Rational Curve
, 1993 Two approaches to constructing piecewise rational curves are compared and contrasted. One involves projecting a piecewise polynomial curve whose polynomial segments are joined according to given totally positive connection matrices.
Goodman, T.N.T.
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Reduced-knot nurbs representations of rational G1 composite Bézier curves
, 1994 It is well known that a rational G1 composite Bézier curve of degree n can be represented as a nurbs curve with knots of multiplicity n. An algorithm is presented that reduces the degree of multiplicity of some knots to n-1.
Wang, W, Cheng, F, Joe, B
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The arc-length and energy of rational Bézier curves
, 1997 Extending earlier work on polynomial Bézier curves, we define approximations to the length and energy of rational Bézier curves. The approximations are defined directly in terms of the control points and we investigates how the approximations behave ...
Gravesen, Jens
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Hybrid polynomial approximation to higher derivatives of rational curves
, 2011 In this paper, we extend the results published in JCAM volume 214 pp. 163–174 in 2008. Based on the bound estimates of higher derivatives of both Bernstein basis functions and rational Bézier curves, we prove that for any given rational Bézier curve, if ...
Guo-Jin Wang +3 more
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Approximating conic sections by constrained Bézier curves of arbitrary degree
, 2012 In this paper, an algorithm for approximating conic sections by constrained Bézier curves of arbitrary degree is proposed. First, using the eigenvalues of recurrence equations and the method of undetermined coefficients, some exact integral formulas for ...
Hu, Qian-Qian
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Necessary and sufficient conditions for rational quartic representation of conic sections
, 2007 Conic section is one of the geometric elements most commonly used for shape expression and mechanical accessory cartography. A rational quadratic Bézier curve is just a conic section. It cannot represent an elliptic segment whose center angle is not less
Hu, Qian-Qian +3 more
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Representation Of Rational Bézier Quadratics Using Genetic Algorithm, Differential Evolution And Particle Swarm Optimization [PDF]
, 2013 Data representation is a challenging problem in areas such as font reconstruction, medical image and scanned images. Direct mathematical techniques usually give smallest errors but sometime take a much longer time to compute.
Yahya, Zainor Ridzuan
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G2 composite cubic Bézier curves
, 1999 We present an algorithm for creating planar G2 spline curves using rational Bézier cubic segments. The splines interpolate a sequence of points, tangents and curvatures. In addition each segment has two more geometric shape handles.
Patterson, Richard R. +2 more
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