کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10132593 | 1645568 | 2018 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames
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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: C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames C1 and C2 interpolation of orientation data along spatial Pythagorean-hodograph curves using rational adapted spline frames](/preview/png/10132593.png)
چکیده انگلیسی
The problem of constructing a rational adapted frame (f1(ξ),f2(ξ),f3(ξ)) that interpolates a discrete set of orientations at specified nodes along a given spatial Pythagorean-hodograph (PH) curve r(ξ) is addressed. PH curves are the only polynomial space curves that admit rational adapted frames, and the Euler-Rodrigues frame (ERF) is a fundamental instance of such frames. The ERF can be transformed into other rational adapted frame by applying a rationally-parametrized rotation to the normal-plane vectors. When orientation and angular velocity data at curve end points are given, a Hermite frame interpolant can be constructed using a complex quadratic polynomial that parametrizes the normal-plane rotation, by an extension of the method recently introduced to construct a rational minimal twist frame (MTF). To construct a rational adapted spline frame, a representation that resolves potential ambiguities in the orientation data is introduced. Based on this representation, a C1 rational adapted spline frame is constructed through local Hermite interpolation on each segment, using angular velocities estimated from a cubic spline that interpolates the frame phase angle relative to the ERF. To construct a C2 rational adapted spline frame, which ensures continuity of the angular acceleration, a complex-valued cubic spline is used to directly interpolate the complex exponentials of the phase angles at the nodal points.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 66, November 2018, Pages 1-15
Journal: Computer Aided Geometric Design - Volume 66, November 2018, Pages 1-15
نویسندگان
Hwan Pyo Moon, Rida T. Farouki,