Least eccentric ellipses for geometric Hermite interpolation |
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Authors: | John C. Femiani Chia-Yuan Chuang Anshuman Razdan |
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Affiliation: | Arizona State University Polytechnic, 7171 E. Sonoran Arroyo Mall, Mesa, AZ, United States |
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Abstract: | We present a rational Bézier solution to the geometric Hermite interpolation problem. Given two points and respective unit tangent vectors, we provide an interpolant that can reproduce a circle if possible. When the tangents permit an ellipse, we produce one that deviates least from a circle. We cast the problem as a theorem and provide its proof, and a method for determining the weights of the control points of a rational curve. Our approach targets ellipses, but we also present a cubic interpolant that can find curves with inflection points and space curves when an ellipse cannot satisfy the tangent constraints. |
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Keywords: | Hermite interpolation Bé zier curves Conics Ellipses |
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