کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
440820 | 691282 | 2016 | 10 صفحه PDF | دانلود رایگان |
• Geometric characterization of hexagonal cells without the interpolation property.
• New examples of unconfinable interior vertices.
• Interpolation properties of splines depend on the geometry of cells.
Let ΔnΔn be a cell with a single interior vertex and n boundary vertices v1,…,vnv1,…,vn. Say that ΔnΔn has the interpolation property if for every z1,…,zn∈Rz1,…,zn∈R there is a spline s∈S21(Δn) such that s(vi)=zis(vi)=zi for all i. We investigate under what conditions does a cell fail the interpolation property. The question is related to an open problem posed by Alfeld, Piper, and Schumaker in 1987 about characterization of unconfinable vertices.For hexagonal cells, we obtain a geometric criterion characterizing the failure of the interpolation property. As a corollary, we conclude that a hexagonal cell such that its six interior edges lie on three lines fails the interpolation property if and only if the cell is projectively equivalent to a regular hexagonal cell. Along the way, we obtain an explicit basis for the vector space S21(Δn) for n≥5n≥5.
Journal: Computer Aided Geometric Design - Volume 45, July 2016, Pages 73–82