کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6876678 | 691162 | 2016 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Construction of G1 planar Hermite interpolants with prescribed arc lengths
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Construction of G1 planar Hermite interpolants with prescribed arc lengths Construction of G1 planar Hermite interpolants with prescribed arc lengths](/preview/png/6876678.png)
چکیده انگلیسی
The problem of constructing a plane polynomial curve with given end points and end tangents, and a specified arc length, is addressed. The solution employs planar quintic Pythagorean-hodograph (PH) curves with equal-magnitude end derivatives. By reduction to canonical form it is shown that, in this context, the problem can be expressed in terms of finding the real solutions to a system of three quadratic equations in three variables. This system admits further reduction to just a single univariate biquadratic equation, which always has positive roots. It is found that this construction of G1 Hermite interpolants of specified arc length admits two formal solutions - of which one has attractive shape properties, and the other must be discarded due to undesired looping behavior. The algorithm developed herein offers a simple and efficient closed-form solution to a fundamental constructive geometry problem that avoids the need for iterative numerical methods.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 46, August 2016, Pages 64-75
Journal: Computer Aided Geometric Design - Volume 46, August 2016, Pages 64-75
نویسندگان
Rida T. Farouki,