A canal surface in R~3, generated by a parameterized curve C = m(t), is the Zariski closure of the envelope of the set of spheres with radius r (t) centered at m(t). This concept is a generalization of the classical notion of an offsets of a plane curve: first, the canal surface is a surface in 3-space rather than a curve in R~2 and second, the radius function r (t) is allowed to vary with the parameter t.
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