scholarly journals Cubic and Hermite splines for VTK

2016 ◽  
Author(s):  
Nicole Kovacs ◽  
Terry Peters ◽  
Elvis Chen
Keyword(s):  
Spline Interpolation ◽  
Cubic Spline ◽  
Interpolation Function ◽  
Third Order ◽  
Order Polynomial ◽  
Hermite Splines ◽  
Hermite Spline ◽  
Parametric Functions ◽  
Interpolating Splines

A cubic spline is a spline where each curve is defined by a third-order polynomial, while a Hermite spline has each polynomial specified in Hermite form, being computed using tangent information as well as the position of the points. We propose two new classes for VTK, vtkCubicSpline and vtkHermiteSpline, which compute interpolating splines using a Cubic and a Hermite Spline Interpolation function, respectively. We also propose two new auxiliary classes, vtkParametricCubicSpline and vtkParametricHermiteSpline, that create parametric functions for the 1D interpolating aforementioned splines.

The Application of Cubic Spline Interpolation Function in Determining Rock Rheological Long-Term Strength

2014 ◽  
Vol 580-583 ◽  
pp. 205-208
Author(s):  
Mo Li Zhao ◽  
Qiang Yong Zhang
Keyword(s):  
Spline Interpolation ◽  
Least Square Method ◽  
Cubic Spline ◽  
Least Square ◽  
Maximum Deviation ◽  
Interpolation Function ◽  
Term Strength ◽  
Cubic Spline Interpolation ◽  
Dagangshan Hydropower Station

The rheological long-term strength is determined according to the triaxial rheological test data of diabase at the dam area of Dagangshan Hydropower Station. Firstly, based on the stress-strain isochronous curve method and connected the test points with cubic spline interpolation function, the maximum deviation point in the long-term interval is determined as the turning point and established the long-term strength by nonlinear least square method. The results show that this method is consistent with the other methods. Finally, the advantage and disadvantage of this method is analyzed. This method can overcome the randomness of artificial selecting the turning points. Therefore, maximum deviation point method is relatively a reasonable and effective method to determine the rheological long-term strength of rock.

scholarly journals Interpolation of equation-of-state data

2019 ◽  
Vol 626 ◽  
pp. A108
Author(s):  
V. A. Baturin ◽  
W. Däppen ◽  
A. V. Oreshina ◽  
S. V. Ayukov ◽  
A. B. Gorshkov
Keyword(s):  
Equation Of State ◽  
Hermite Interpolation ◽  
Spline Interpolation ◽  
Solar Model ◽  
B Splines ◽  
Second Derivatives ◽  
Hermite Splines ◽  
Order Of Magnitude ◽  
Hermite Spline ◽  
Mathematical Relations

Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation. Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines. Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum lgP difference lies in the range from 10−9 to 10−4, and Γ1 difference varies from 10−9 to 10−3. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at T ∼ 1.5 × 103−105 K. The best precision is achieved at higher temperatures, T >  105 K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.

Application of Spline Function in Solution for Pressure Angle of Oscillating-Roller-Followed Cam

2013 ◽  
Vol 753-755 ◽  
pp. 1582-1586
Author(s):  
Chun Xiang Dai ◽  
Jing Hua Yu ◽  
Hong Yu Meng
Keyword(s):  
Spline Function ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Cold Forging ◽  
Interpolation Function ◽  
Cubic Spline Interpolation ◽  
Pressure Angle ◽  
Basic Parameters ◽  
Cam Profile

Due to uncompleted cam basic parameters or unknown motion functions of follower, it is difficulty to calculate pressure angle for cam mechanisms while only given some discrete points on actual cam profile. After the research of solution for pressure angle of the oscillating-roller-followed disk cam used in cold forging machine, the article brings foreword detailed solutions under such condition above based on cubic spline interpolation function.

Construction of 3D Strata Model Based on the Multiple Source Data

2013 ◽  
Vol 671-674 ◽  
pp. 27-30
Author(s):  
Chun Yuan Liu ◽  
Shi Meng Gu ◽  
Yu Liu
Keyword(s):  
Spline Interpolation ◽  
Three Dimensional ◽  
Cubic Spline ◽  
Multiple Source ◽  
Triangular Prism ◽  
Interpolation Function ◽  
Cubic Spline Interpolation ◽  
Model Based ◽  
Source Data

According to the raw multi-source data, all strata should be standardized. With the aid of the cubic spline interpolation function, the virtual drilling could be created. With the help of Deluanay triangulation, every stratum is turned to triangular net, namely initial stratum surface. A top triangle of stratum is connected with a corresponding bottom triangle of stratum in the net. It makes a triangular prism unit. Finally, according to certain rules, numerous triangular prism units are assembled orderly to form a geologic body. The GTP model can realize 3D strata simulation and the purpose of true three-dimensional.

Application of Moments in Qualitative Analysis on Borehole Trajectory Curving

2015 ◽  
Vol 713-715 ◽  
pp. 1635-1639
Author(s):  
Rui Yuan ◽  
Yu Qiu Sun
Keyword(s):  
Spline Interpolation ◽  
Horizontal Wells ◽  
Moment Equation ◽  
Cubic Spline ◽  
Interpolation Function ◽  
Calculation Methods ◽  
Change Rate ◽  
Cubic Spline Interpolation ◽  
Variation Characteristics ◽  
Change Tendency

There are many calculation methods of horizontal borehole trajectory, such as cubic spline interpolation function which is based on three-moment equation. By calculating the moments of deviation and azimuth from cubic spline interpolation function respectively, it is easy obtain functions of deviation and azimuth change rate and average borehole curvature to analysis on curving of borehole trajectory. So it is one of the most common methods. However, the moments are always be neglected. Moments of deviation and azimuth, which could be used to qualitatively estimate borehole trajectory curving, are first proposed tentatively in this paper. Synthetically employing other useful parameters of estimation borehole trajectory curving, tens of high-angle directional and horizontal wells’ drilling data is computed and analyzed. Contrast to the variation characteristics of deviation and azimuth change rate, the deviation and azimuth moments have the similar change tendency respectively. The results of this study signify that the proposed parameters could provide some reference for assessment on borehole trajectory curving.

Describing NC Smooth Path Based on the Adjustable Form of the Cubic Spline Interpolation Function

2012 ◽  
Vol 215-216 ◽  
pp. 1158-1164
Author(s):  
Ai Ping Song ◽  
Jian Huang ◽  
Jian Ming Tao ◽  
Dan Ping Yi
Keyword(s):  
High Speed ◽  
Inflection Point ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Numerical Control ◽  
Smooth Transition ◽  
Interpolation Function ◽  
Cubic Spline Interpolation ◽  
Smooth Path ◽  
Cubic Polynomial

In order to describe the NC processing path better, and easy to realize path in a smooth transition of inflection point, this paper puts forward a kind of adjustable form of the cubic spline interpolation function; using the function can describe line, arc and freecurve, and realize smooth transition of inflection point through the control points which near the inflexion point. The spline function is of cubic polynomial, which calculation is simple, and it is easy to realize the operation of fast interpolation; it not only can describe various of NC paths, but also can be easy to realize the high speed of smooth processing between the NC orbit segments, which meets the needs of modern numerical control system for high speed, stability and flexible.

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