Blending of Surfaces of Revolution and Planes by Dupin cyclides
نویسندگان
چکیده
This paper focuses on the blending of a plane with surfaces of revolution relying on Dupin cyclides, which are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century. A general algorithm is presented for the construction of two kinds of blends: pillar and recipient. This algorithm uses Rational Quadric Bézier Curves (RQBCs) to model the relevant arcs of the principal circles of the cyclides and allows the construction of a new blending primitive: the spindle Dupin cyclide. Our algorithm can also be used for the blending of the plane with particular surfaces of revolution such as the torus, the catenary and the pseudosphere.
منابع مشابه
From Dupin Cyclides to Scaled Cyclides
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives...
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