Abstract
A cubic polynomial curve in the xy-plane, (x1 (t), x2(t)), whose cubic term has a coefficient of 0 reduces to a parabola in this special case; but a cubic polynomial cannot represent other conic section curves such as a circular arc, an elliptic arc, or a segment of an hyperbola. It is an interesting fact, however, that an elliptic or hyperbolic arc in R3 can be parametrically represented by three component functions c1(t), c2(t), and c3(t), where each component function is a ratio of two quadratic polynomials.
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