Numerical Proper Reparametrization of Space Curves and Surfaces

The μ-basis is a newly developed algebraic tool in curve and surface representations and it is used to analyze some essential geometric properties of curves and surfaces. However, the theoretical frame of μ-bases is still developing, especially of surfaces. We study the μ-basis of a rational surface V defined parametrically by P(t¯),t¯=(t1,t2) not being necessarily proper (or invertible). For applications using the μ-basis, an inversion formula for a given proper parametrization P(t¯) is obtained. In addition, the degree of the rational map ϕP associated with any P(t¯) is computed. If P(t¯) is improper, we give some partial results in finding a proper reparametrization of V. Finally, the implicitization formula is derived from P (not being necessarily proper). The discussions only need to compute the greatest common divisors and univariate resultants of polynomials constructed from the μ-basis. Examples are given to illustrate the computational processes of the presented results.

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Numerical Proper Reparametrization of Space Curves and Surfaces

Cited by 3 publications

References 25 publications

New Proper Reparameterization of Plane Rational Bézier Curves

New Proper Reparameterization of Plane Rational Bézier Curves

Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using μ-basis

The μ-Basis of Improper Rational Parametric Surface and Its Application

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