The μ-Basis and Implicitization of Rational Space Curves

Rational space curves are widely used in geometric modeling,this paper studies the μ-basis of the space curves and computes the algebraic varieties based on the μ-basis.The μ-basis plays a bridging role between the parametric expression and implicit expression.After the definition μ-basis is given,the paper presents the symbolic formula to compute the μ-basis.In addition,based on the discussion of resultants,we obtain a class of space curves which can be implicitized by univariate resultant computations on the μ-basis.A typical counterexample is also proposed when the restriction is unsatisfied.