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A rational surfaceS(s,t)=(a(t)a⁎(s),a(t)b⁎(s),b(t)c⁎(s),c(t)c⁎(s)) can be generated from two orthogonal rational planar directrices: P(t)=(a(t),b(t),c(t)) in the xz-plane and P⁎(s)=(a⁎(s),b⁎(s),c⁎(s)) in the xy-plane. Moving a scaled copy of the curve P⁎(s) up and down along the z-axis with the size controlled by the curve P(t), we get the surface S(s,t). For example, when P⁎(s) is a circle with center...
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