The NURBS book
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Geometric Hermite interpolation with circular precision
Computer-Aided Design
The eccentricity of conic sections formulated as rational Bézier quadratics
Computer Aided Geometric Design
Geometric point interpolation method in R3 space with tangent directional constraint
Computer-Aided Design
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We present a rational Bezier 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.