کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
401849 | 676727 | 2010 | 18 صفحه PDF | دانلود رایگان |
The present paper investigates two-parameter families of spheres in R3 and their corresponding two-dimensional surfaces Φ in R4. Considering a rational surface Φ in R4, the envelope surface Ψ of the corresponding family of spheres in R3 is typically non-rational. Using a classical sphere-geometric approach, we prove that the envelope surface Ψ and its offset surfaces admit rational parameterizations if and only if Φ is a rational sub-variety of a rational isotropic hyper-surface in R4. The close relation between the envelope surfaces Ψ and rational offset surfaces in R3 is elaborated in detail. This connection leads to explicit rational parameterizations for all rational surfaces Φ in R4 whose corresponding two-parameter families of spheres possess envelope surfaces admitting rational parameterizations. Finally we discuss several classes of surfaces sharing this property.
Journal: Journal of Symbolic Computation - Volume 45, Issue 1, January 2010, Pages 1-18