کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4638410 1632003 2015 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Detecting symmetries in polynomial Bézier curves
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Detecting symmetries in polynomial Bézier curves
چکیده انگلیسی

In a recent article, Alcázar (2014) presents algorithms for detecting central and mirror symmetries in planar polynomial curves, expressed with proper parameterization in the monomial (i.e., power) basis. However, for practical purposes in Computer Graphics and CAGD, the usual choice is the Bernstein–Bézier representation, because of its superior numerical and geometric characteristics. We point out that, in this form and for properly parameterized curves, detecting symmetry amounts to simply checking that the Bézier points exhibit pairwise symmetry. This result is a direct consequence of well-known properties of the Bézier representation, namely its symmetry, affine invariance, and uniqueness for proper parameterizations. Detecting the existence of a symmetric segment in a Bézier curve also amounts to a simple task, by analysing the last non-vanishing derivatives. Finally, these results carry over in a straightforward manner to symmetries in Euclidean space.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 288, November 2015, Pages 274–283
نویسندگان
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