Classifying the Nonsingular Intersection Curve of Two Quadric Surfaces

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of the curve in ÈÊ ¿ (the 3D real projective space), and whether a particular component is a compact set in any affine realization of ÈÊ¿ . For example, we show that two quadrics intersect along a nonsingular space quartic curve in ÈÊ¿ with one connected component if and only if their characteristic equation has two distinct real roots and a pair of complex conjugate roots. Since the number of the real roots of the characteristic equation can be counted robustly with exact arithmetic, our results can be used to obtain structural information reliably before computing the parameterization of ...

• Type: Conference
• Year: 2002
• Where: GMP
• Authors: Changhe Tu, Wenping Wang, Jiaye Wang
• Keywords: Characteristic Equation, GMP 2002, Intersection Curves, Nonsingular Intersection Curve, Solid Modeling