کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
439994 690935 2016 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Average curve of nn smooth planar curves
ترجمه فارسی عنوان
منحنی میانگین منحنی های مسطح صاف NN
کلمات کلیدی
میانگین منحنی ها؛ محور میانی؛ تجزیه و تحلیل آماری از اشکال
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
چکیده انگلیسی


• We define the Average Curve (AC) of any compatible set of nn smooth Jordan curves.
• We define the inflation of the AC that conveys local variability.
• We present a linear-cost algorithm for computing a polygonal approximation of the AC.
• The AC and the inflation form a natural extension of the Medial Axis Transform.

We define the Average Curve (AC) of a compatible set of two or more smooth and planar, Jordan curves. It is independent of their order and representation. We compare two variants: the valley AC (vAC), defined in terms of the valley of the field that sums the squared distances to the input curves, and the zero AC (zAC), defined as the zero set of the field that sums the signed distances to the input curves. Our formulation provides an orthogonal projection homeomorphism from the AC to each input curve. We use it to define compatibility. We propose a fast tracing algorithm for computing a polygonal approximation (PAC) of the AC and for testing compatibility. We provide a linear-cost implementation for tracing the PAC of polygonal approximations of smooth input curves. We also define the inflation of the AC and use it to visualize the local variability in the set of input curves. We argue that the AC and its inflation form a natural extension of the Medial Axis Transform to an arbitrary number of curves. We propose extensions to open curves and to weighted averages of curves, which can be used to design animations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer-Aided Design - Volume 70, January 2016, Pages 46–55
نویسندگان
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