Smooth-curve interpolation: A generalized spline-fit procedure

1966 ◽  
Vol 6 (4) ◽  
pp. 277-293 ◽  
Author(s):  
J. M. Glass
Keyword(s):  
Smooth Curve ◽  
Curve Interpolation

Smooth curve interpolation

1969 ◽  
Vol 9 (1) ◽  
pp. 69-77 ◽  
Author(s):  
C. H. Woodford
Keyword(s):  
Smooth Curve ◽  
Curve Interpolation

scholarly journals Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ayser Nasir Hassan Tahat ◽  
Abd Rahni Mt Piah ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Numerical Experiments ◽  
Smooth Curve ◽  
The Other ◽  
Data Interpolation ◽  
Shape Parameters ◽  
Interpolation Scheme ◽  
Shape Preserving ◽  
Curve Interpolation ◽  
Two Parameters

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness isC1. The outputs from a number of numerical experiments are presented.

Smooth curve drawing using a Bessel function

2015 ◽  
Author(s):  
Y. Q. Du ◽  
M. J. Pan ◽  
Q. Li ◽  
L. Li
Keyword(s):  
Bessel Function ◽  
Smooth Curve

scholarly journals Experimental Validation on Intersection Turning Trajectory Prediction Method for Advanced Driver Assistance System Based on Triclothoidal Curve

2021 ◽  
Vol 11 (13) ◽  
pp. 5900
Author(s):  
Yohei Fujinami ◽  
Pongsathorn Raksincharoensak ◽  
Shunsaku Arita ◽  
Rei Kato
Keyword(s):  
Traffic Accidents ◽  
Computational Cost ◽  
Prediction Method ◽  
Smooth Curve ◽  
Assistance System ◽  
Driver Assistance ◽  
Driver Assistance Systems ◽  
Trajectory Prediction ◽  
Left Turn ◽  
Left Hand

Advanced driver assistance systems (ADAS) for crash avoidance, when making a right-turn in left-hand traffic or left-turn in right-hand traffic, are expected to further reduce the number of traffic accidents caused by automobiles. Accurate future trajectory prediction of an ego vehicle for risk prediction is important to activate the assistance system correctly. Our objectives are to propose a trajectory prediction method for ADAS for safe intersection turnings and to evaluate the effectiveness of the proposed prediction method. Our proposed curve generation method is capable of generating a smooth curve without discontinuities in the curvature. By incorporating the curve generation method into the vehicle trajectory prediction, the proposed method could simulate the actual driving path of human drivers at a low computational cost. The curve would be required to define positions, angles, and curvatures at its initial and terminal points. Driving experiments conducted at real city traffic intersections proved that the proposed method could predict the trajectory with a high degree of accuracy for various shapes and sizes of the intersections. This paper also describes a method to determine the terminal conditions of the curve generation method from intersection features. We set a hypothesis where the conditions can be defined individually from intersection geometry. From the hypothesis, a formula to determine the parameter was derived empirically from the driving experiments. Public road driving experiments indicated that the parameters for the trajectory prediction could be appropriately estimated by the obtained empirical formula.

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

Cumulative yields of stable and long-lived isotopes of tin in neutron-induced fission

1983 ◽  
Vol 61 (11) ◽  
pp. 1490-1497 ◽  
Author(s):  
K. J. R. Rosman ◽  
J. R. De Laeter ◽  
J. W. Boldeman ◽  
H. G. Thode
Keyword(s):  
Stable Isotopes ◽  
Fine Structure ◽  
Fission Product ◽  
Mass Spectrometer ◽  
Smooth Curve ◽  
Mass Region ◽  
Neutron Fission ◽  
Source Mass ◽  
Induced Fission ◽  
Fission Yields

The relative cumulative fission yields of the six stable isotopes of tin (117Sn,118Sn, 119Sn, 120Sn, 122Sn, and 124Sn) and the long-lived isotope 126Sn have been measured in the thermal and epicadium neutron fission of 233U and 235U, and the epicadium neutron fission of 238U. Nanogram-sized fission product tin samples were extracted from irradiated uranium samples and analyzed in a solid source mass spectrometer. In each case a smooth curve can be drawn through the yield points of the seven isotopes of tin. There is, therefore, no evidence of "fine structure" in the 117 ≤ A ≤ 126 portion of the symmetric mass region.

ESTIMATING SURFACE NORMALS IN NOISY POINT CLOUD DATA

2004 ◽  
Vol 14 (04n05) ◽  
pp. 261-276 ◽  
Author(s):  
NILOY J. MITRA ◽  
AN NGUYEN ◽  
LEONIDAS GUIBAS
Keyword(s):  
Point Cloud ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Local Information ◽  
Least Square ◽  
Neighborhood Size ◽  
Point Cloud Data ◽  
Cloud Data ◽  
Normal Estimation ◽  
Least Square Fitting

In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.

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