کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639719 1341247 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
چکیده انگلیسی

Algorithms based on Pythagorean hodographs (PH) in the Euclidean plane and in Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. In this paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. On the basis of this approach we design a new, simple interpolation algorithm. The main advantage of the unifying method presented lies in the fact that it uses, after only some simple additional computations, an arbitrary algorithm for interpolation using planar PH curves also for interpolation using spatial MPH curves. We present the functionality of our method for G1G1 Hermite data; however, one could also obtain higher order algorithms.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 12, 15 April 2011, Pages 3413–3424
نویسندگان
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