Single-valued curves in polar coordinates
Computer-Aided Design
The NURBS book (2nd ed.)
An introduction to NURBS: with historical perspective
An introduction to NURBS: with historical perspective
Determination of geometrical invariants of rationally parametrized conic sections
Mathematical Methods for Curves and Surfaces
Geometric recipes for constructing Bézier conics of given centre or focus
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
The eccentricity of conic sections formulated as rational Bézier quadratics
Computer Aided Geometric Design
Geometric characteristics of conics in Bézier form
Computer-Aided Design
Geometric characteristics of conics in Bézier form
Computer-Aided Design
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We show how to compute in a straightforward manner the geometric characteristics of a conic segment in rational Bezier form, by employing complex arithmetic. For a central conic, a simple quadratic equation defines the foci location, and its solution furnishes not only an explicit formula for the foci, but also for the center, axis direction and linear eccentricity.