We provide a new technique for implicitizing rational surfaces of revolution using μ-bases. A degree n rational plane curve rotating around an axis ...

In many applications we need to compute the implicit representation of rational parametric surfaces. Previously, resultants and Gröbner bases have been applied ...

To implicitize the surface S(s,t), we construct a (2m-1)nx(2m-1)n sparse resultant matrix R"s","t for these three polynomials. We show that det(R"s","t)=0 is ...

We provide a new technique for implicitizing rational surfaces of revolution using @m-bases. A degree n rational plane curve rotating around an axis ...

The central idea in this approach is that if a surface has a base point of multiplicity k, the moving surface blending functions must have the same base point, ...

Moreover, μ-bases for a rational surface often have high degrees, so these resultants generally contain many extraneous factors. Here we develop fast algorithms ...

Here we shall show how to extend the notion of a µ-basis from rational surfaces of revolution to rational surfaces S(s, t ) with two orthogonal directrices.

Determine the implicit degree m of the rational surface P(s,t). 2. Determine the sum of the degree of the mu-basis,. 3. Determine the relationship between m and ...

MODULES WITH TWO QUASI-GENERATORS AND THE µ-BASIS. 37. µ-basis of a rational ruled surface as in Definition 1.6. They coincide. in the special case d = 4. M ...

We investigate conditions under which the resultant of a μ -basis for a rational tensor product surface is the implicit equation of the surface without any ...