Rational framing motions and spatial rational Pythagorean hodograph curves
نویسندگان
چکیده
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining suitable framing motion. While the spherical component of motion is arbitrary, translation part determined be modestly sized and nicely structured system linear equations. Rather surprisingly, generic input data will only result in polynomial PH curves. provide complete characterization all cases that admit truly (non-polynomial) solutions. Examples illustrate our ideas relate them to existing literature.
منابع مشابه
On rational Minkowski Pythagorean hodograph curves
Minkowski Pythagorean hodograph curves are polynomial curves with polynomial speed, measured with respect to Minkowski norm. Curves of this special class are particularly well suited for representing medial axis transforms of planar domains. In the present paper we generalize this polynomial class to a rational class of curves in Minkowski 3-space. We show that any rational Minkowski Pythagorea...
متن کاملPythagorean-hodograph cycloidal curves
In the paper, Pythagorean-hodograph cycloidal curves as an extension of PH cubics are introduced. Their properties are examined and a constructive geometric characterization is established. Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined. The asymptotic approximation order analysis carried out indicates clearly which interpolatory curve s...
متن کاملRational approximation of rotation minimizing frames using Pythagorean–hodograph cubics
This article is devoted to the rotation minimizing frames that are associated with spatial curves. Firstly we summarize some results concerning the differential geometry of the sweeping surfaces which are generated by these frames (the so–called profile or moulding surfaces). In the second part of the article we describe a rational approximation scheme. This scheme is based on the use of spatia...
متن کاملPythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Follow up what we will offer in this article about pythagorean hodograph curves algebra and geometry inseparable. You know really that this book is coming as the best seller book today. So, when you are really a good reader or you're fans of the author, it does will be funny if you don't have this book. It means that you have to get this book. For you who are starting to learn about something n...
متن کاملInterpolation by G quintic Pythagorean-hodograph curves
In this paper, the G interpolation by Pythagorean-hodograph (PH) quintic curves in R, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is red...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2022
ISSN: ['0167-8396', '1879-2332']
DOI: https://doi.org/10.1016/j.cagd.2022.102160