کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
441633 691805 2009 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A cyclic basis for closed curve and surface modeling
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
A cyclic basis for closed curve and surface modeling
چکیده انگلیسی

We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from n to n+r, r⩾1 and prove that the control polygon of the degree elevated curve converges to the curve itself if r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with C∞ continuity at all of their points.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 26, Issue 5, June 2009, Pages 528-546