The algorithm is based on a parametric representation of the ellipse. It is particularly inexpensive in terms of the amount of computation required. Only a few integer shifts, additions, and subtractions are needed to generate each point鈥攚ithout compromising accuracy. Defining an ellipse in ...
Consider the ellipse {eq}x^2+\frac{y^2}{4}=1 {/eq}. One possible parameterized version of this equation would be: {eq}x(t)=cos(t) {/eq} and {eq}y(t)=2sin(t) {/eq}. In general, the parameterized ellipse has parameterized equations of {eq}x=acos(t), y=bsin(t) {/eq...
Find the parametric equations of the tangent line to the ellipse x = 3 cos theta, y = 4 sin theta at the point where theta = pi / 6. Find the equation of the tangent line to the polar curve of r = e^(-theta) at theta = pi. ...
A concise representation of the dynamics at each of the three stages in the cascade is provided by the scattering matrix S that relates the outgoing wave amplitudes to the incoming wave amplitudes as seen from the ports of a network. We begin by deriving the scattering matrix of the UDC ...
This paper presents a method of plane development for convex hull plate based on parametric surface representation, which can take into account deformation characteristics of the line heating forming process of convex hull plate and provide the shrinkage magnitude generated in the forming process. This...
Analysis of eye movement data Preprocessing Eye position was computed as the center (xycoordinates) of the ellipse that was fitted to the detected pupil points (see “Analysis of pupil and eyelid data”). We then applied the following signal processing to the eye position time series (xandy) ...
In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g., for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is ...
State-Space Representation of Unsteady Airfoil Behavior. AIAA J. 1990, 28, 836–844. [CrossRef] 111. Tobak, M. On the Use of the Indicial-Function Concept in the Analysis of Unsteady Motions of Wings and Wing-Tail Combinations; NACA 1188; NACA: Washington, DC, USA, 1954. 112. Silva,...
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H. Späth, Estimating the parameters of an ellipse when angular differences are known, Comput. Stat., 14 (1999), pp. 491-500. Google Scholar H. Späth, Least squares fitting of spheres and ellipsoids using not orthogonal distances, Math. Comm. 6 (2001), pp. 89-96. Google Scholar ...