3,657 research outputs found
Geometric properties and constrained modification of trigonometric spline curves of Han
New types of quadratic and cubic trigonometrial polynomial curves have
been introduced in [2] and [3]. These trigonometric curves have a global shape
parameter λ. In this paper the geometric effect of this shape parameter on the
curves is discussed. We prove that this effect is linear. Moreover we show that
the quadratic curve can interpolate the control points at λ = √2. Constrained
modification of these curves is also studied. A curve passing through a given
point is computed by an algorithm which includes numerical computations.
These issues are generalized for surfaces with two shape parameters. We show
that a point of the surface can move along a hyperbolic paraboloid
SUSY field theories, integrable systems and their stringy/brane origin -- II
Five and six dimensional SUSY gauge theories, with one or two compactified
directions, are discussed. The 5d theories with the matter hypermultiplets in
the fundamental representation are associated with the twisted spin
chain, while the group product case with the bi-fundamental matter corresponds
to the higher rank spin chains. The Riemann surfaces for theories with
fundamental matter and two compact directions are proposed to correspond to the
spin chain based on the Sklyanin algebra. We also discuss the obtained
results within the brane and geometrical engeneering frameworks and explain the
relation to the toric diagrams.Comment: LaTeX, 21 pages, no figure
Data Visualization Using Rational Trigonometric Spline
This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the
smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the
data. Positive, monotone, and constrained curve interpolating schemes, by using
Finding antipodal point grasps on irregularly shaped objects
Two-finger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a finger contact space to the object surface. Conditions are developed to identify the feasible grasping region, F, in the finger contact space. A “grasping energy function”, E , is introduced which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the “maximal” or “minimal” grasp. Further, modeling techniques are introduced for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces
Positive Data Visualization Using Trigonometric Function
A piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is
- …