Rotation Minimizing Frame and Rectifying Curves in E_1^n
نویسندگان
چکیده
منابع مشابه
Computation of Rotation Minimizing Frame
Due to its minimal twist, the rotation minimizing frame (RMF) is widely used in computer graphics, including sweep or blending surface modeling, motion design and control in computer animation and robotics, streamline visualization, and tool path planning in CAD/CAM. We present a novel simple and efficient method for accurate and stable computation of RMF of a curve in 3D. This method, called t...
متن کاملComputation of Rotation Minimizing Frame in Computer Graphics
We investigate the computation and properties of rotation minimizing frame (RMF), which is a moving orthonormal frame U(u) attached to a smooth curve x(u), called the spine curve, in 3D such that U(u) does not rotate about the instantaneous tangent of x(u). Due to its minimal-twist property, the RMF is widely used in computer graphics, including sweep or blending surface modeling, motion design...
متن کاملScalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves
The scalar–vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial. Apart from the familiar vector dot and cross products, this algorithm requires only the determination of the unique positive real root of a cubic equation, and special cases (e.g., double roots) are easily identified through the satisfaction of algebraic constraints on...
متن کاملQuintic space curves with rational rotation-minimizing frames
An adapted orthonormal frame (f1, f2, f3) on a space curve r(t), where f1 = r ′/|r′| is the curve tangent, is rotation–minimizing if its angular velocity satisfies ω · f1 ≡ 0, i.e., the normal–plane vectors f2, f3 exhibit no instantaneous rotation about f1. The simplest space curves with rational rotation–minimizing frames (RRMF curves) form a subset of the quintic spatial Pythagorean–hodograph...
متن کاملMinimizing Fusion Frame Potential
Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to ...
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: Journal of Applied Mathematics and Computation
سال: 2021
ISSN: 2576-0645,2576-0653
DOI: 10.26855/jamc.2021.03.007