scholarly journals Optimal Intersection Curves for Surfaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jiwen Gao ◽  
Faiza Sarfraz ◽  
Misbah Irshad ◽  
Jia-Bao Liu
Keyword(s):  
Cubic Spline ◽  
Shape Parameters ◽  
Spline Curve ◽  
Surface Intersection ◽  
Different Types ◽  
Characteristic Points ◽  
Intersection Points ◽  
Implicit And Explicit ◽  
Intersection Curves ◽  
Cubic Spline Curve

In this article, an algorithm has been established to approximate parametric-parametric, explicit-implicit, and explicit-explicit surface intersection. Foremost, it extracts the characteristic points (boundary and turning points) from the sequence of intersection points and fits an optimal cubic spline curve to these points. Moreover, this paper utilizes genetic algorithm (GA) for optimization of shape parameters in the portrayal of cubic spline so that the error is minimal. The proposed algorithm is demonstrated with different types of surfaces to analyze its robustness and proficiency. In the end, all illustrations show the effectiveness of the algorithm which makes it more influential to resolve all complexities arises during intersection with a minimal error.

ACCURACY OF RIVER GEOMETRY INTERPOLATION USING CUBIC SPLINE CURVE AT ALB MISSING AREA AND INFULUENCE OF FLOW REGIME

2018 ◽  
Vol 74 (4) ◽  
pp. I_859-I_864
Author(s):  
Takayuki OKABE ◽  
Takanori YAMAZAKI ◽  
Atsumasa OZAWA ◽  
Shinichi MORITA ◽  
Shigeo HORIUCHI ◽  
...  
Keyword(s):  
Flow Regime ◽  
Cubic Spline ◽  
Spline Curve ◽  
Cubic Spline Curve

A finite element cable model and its applications based on the cubic spline curve

2013 ◽  
Vol 27 (5) ◽  
pp. 683-692 ◽  
Author(s):  
Zi-fan Fang ◽  
Qing-song He ◽  
Bing-fei Xiang ◽  
Hua-pan Xiao ◽  
Kong-de He ◽  
...  
Keyword(s):  
Finite Element ◽  
Cubic Spline ◽  
Cable Model ◽  
Spline Curve ◽  
Cubic Spline Curve

Geometric Model and Elastic Constant Prediction of 3D Four-Step Braided Composites Based on the Cubic Spline Curve

2016 ◽  
Vol 08 (02) ◽  
pp. 1650019 ◽  
Author(s):  
Chenbing Ni ◽  
Gaofeng Wei
Keyword(s):  
Geometric Model ◽  
Three Dimensional ◽  
Cubic Spline ◽  
Numerical Results ◽  
Unit Cell ◽  
Experimental Results ◽  
Numerical Calculations ◽  
Braided Composites ◽  
Spline Curve ◽  
Cubic Spline Curve

In this paper, the three-dimensional (3D) four-step ([Formula: see text]) rectangular braided composites are analyzed, the internal yarn spatial topology and mechanical model are determined, a new geometric model, which uses a cubic spline curve to fit yarn trajectory, is presented. The new geometric model can be divided into three types of unit cell models which are the interior, surface and corner unit cell. Based on the new proposed geometric model and the stiffness averaging theory, the corresponding elastic constants are predicted. The predicted numerical results are calculated, and compared with the experimental results. Numerical examples indicate that the numerical calculations well agree with the experimental results. Error values between numerical calculations and experimental results are less than 7.5%. The numerical results verify the validity and accuracy of the new geometrical model.

scholarly journals Rational Cubics and Conics Representation: A Practical Approach

1970 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Sarfraz ◽  
Z. Habib
Keyword(s):  
Computer Graphics ◽  
Cubic Spline ◽  
Practical Approach ◽  
Shape Parameters ◽  
Conic Sections ◽  
Interpolation Spline ◽  
Cubic Curves ◽  
Spline Curve ◽  
Special Cases

A rational cubic spline, with one family of shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally, at the knot intervals. The rational cubic spline attains parametric   smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline.Key Words: Computer Graphics, Interpolation, Spline, Conic, Rational Cubic

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