scholarly journals Monotone Smoothing Spline Curves Using Normalized Uniform Cubic B-splines

2013 ◽  
Vol 2013 (0) ◽  
pp. 152-157
Author(s):  
Hiroyuki Fujioka ◽  
Hiroyuki Kano
Keyword(s):  
Smoothing Spline ◽  
B Splines ◽  
Spline Curves

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Automated Optimisation of T-Root Rotor Grooves With B-Splines and Finite Element Analysis

2015 ◽  
Author(s):  
Jonathan Henson ◽  
Richard Dolan ◽  
Gareth Thomas ◽  
Christos Georgakis
Keyword(s):  
Finite Element ◽  
Steam Turbine ◽  
Peak Stress ◽  
Turbine Rotor ◽  
Element Analysis ◽  
B Splines ◽  
Steam Turbine Rotor ◽  
Spline Curves ◽  
Python Scripting ◽  
Gradient Based

An Alstom tool is described for the automated and simultaneous design optimisation of 2 and 4-hook T-root grooving of multiple steam turbine rotor stages in order to minimise the peak stress. The finite element axisymmetric thermal-stress calculation is performed with Abaqus in a few hours on modest hardware. The tool embeds Python scripting to facilitate the rotor groove model definition and meshing within Abaqus/CAE, with emphasis placed on minimising the effort for the initial setup. Rotor groove shapes are described with B-splines, maintained and modified within the in-house tool. Their shape is progressively refined as directed by a hybrid evolutionary-gradient based optimisation engine in order to achieve the minimum stress objective. In the region of highest stress, the groove boundary shape adjusts as the optimisation proceeds to conform to the local contours of stress. Application to a low pressure steam turbine rotor demonstrates comparable or lower stresses with this tool compared to those from manual expert optimisation. The method can be readily extended to other geometric entities on the rotor described with B-spline curves, e.g. cavities, seals.

scholarly journals Pemodelan Fertilitas Di Indonesia Tahun 2017 Menggunakan Pendekatan Regresi Nonparametrik Kernel dan Spline

2020 ◽  
Vol 4 (1) ◽  
pp. 48-60
Author(s):  
Istiqomatul Fajriyah Yuliati ◽  
Pardomuan Sihombing
Keyword(s):  
Total Fertility Rate ◽  
Prevalence Rate ◽  
Fertility Rate ◽  
Smoothing Spline ◽  
Contraceptive Prevalence Rate ◽  
B Splines ◽  
Contraceptive Prevalence

Tujuan dari penelitian ini adalah untuk menganalisis pola hubungan Total Fertility Rate (TFR) dengan Contraceptive Prevalence Rate (CPR). Analisis yang sering digunakan untuk pemodelan adalah analisis regresi. Analisis regresi menurut pendekatannya dapat dibedakan menjadi dua, parametrik dan nonparametrik. Metode regresi nonparametrik yang sering digunakan adalah regresi kernel dan spline. Pada penelitian ini untuk regresi kernel yang digunakan adalah regresi kernel dengan metode penaksir Nadaraya-Watson (NWE) dan penaksir polinomial lokal (LPE), sedangkan untuk regresi spline yang digunakan adalah smoothing spline dan b-splines. Hasil pengepasan kurva (fitting curve) menunjukkan bahwa model regresi nonparametrik terbaik adalah model regresi b-splines dengan degree 2 dan jumlah knot 5. Hal ini dikarenakan model regresi b-splines memiliki kurva yang halus dan terlihat lebih mengikuti sebaran data dibandingkan kurva model regresi lainnya. Model regresi b-splines terpilih memiliki nilai koefisien determinasi R2 sebesar 76.86%, artinya besarnya variasi variabel TFR yang dijelaskan oleh model regresi b-splines sebesar 76.86%, sedangkan sisanya 23.14% dijelaskan oleh variabel lainnya yang tidak dimasukkan ke dalam model.

scholarly journals Examining the Use of B-Splines in Parking Assist Systems

2014 ◽  
Vol 490-491 ◽  
pp. 1025-1029 ◽  
Author(s):  
Mohamed Elbanhawi ◽  
Milan Simic
Keyword(s):  
Intelligent Vehicles ◽  
Parallel Parking ◽  
B Splines ◽  
Spline Curves ◽  
Parking Spot ◽  
Feasible Range ◽  
Automatic Parking ◽  
Path Curvature ◽  
Continuous Curvature ◽  
The Relationship

The main objective of the presented study and simulations conducted was to investigate the prospect of using B-spline curves for the automatic parking, i.e. self-driving, or intelligent vehicles. We consider the problem of parallel parking for a non-holonomic vehicle with a known maximum path curvature. The relationship between the properties of the path and the geometry of corresponding parking spot is revealed. The unique properties of B-splines are exploited to synthesize a path that is smooth and of continuous curvature. The contributions of this project are in the generations of better, smooth continuous paths. This improves passenger comfort during the parallel parking maneuver and allow vehicles to park in tighter spots by increasing the feasible range of the parking manoeuver.

A Moving Morphable Voids Approach for Topology Optimization With Closed B-Splines

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Bingxiao Du ◽  
Wen Yao ◽  
Yong Zhao ◽  
Xiaoqian Chen
Keyword(s):  
Topology Optimization ◽  
B Spline ◽  
B Splines ◽  
Spline Curves ◽  
Beam Design ◽  
Merging Process ◽  
Order Degree ◽  
Structural Boundary ◽  
Ks Function ◽  
Selection Of

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.

B-Splines Geometric Modeling for Dynamic Analysis Behaviour in Offshore Systems

2006 ◽  
Author(s):  
Fa´bio G. T. de Menezes ◽  
Prota´sio Dutra Martins
Keyword(s):  
Geometric Modeling ◽  
Floating Body ◽  
Design Work ◽  
Oil Drilling ◽  
B Spline ◽  
B Splines ◽  
Hydrodynamic Behaviour ◽  
Spline Curves ◽  
Definition Of ◽  
Floating Systems

This work reports a study of B-Spline curves and surfaces applied to the geometric definition of hulls of ships and oil drilling and production platforms. The research aims at defining mathematically the floating body surface in suitable formats for the analysis of functional behaviour of the design object with sophisticated methods and tools. The WAMIT system was chosen as a reference in the research due to its reliability as a professional tool for hydrodynamic behaviour of floating systems in practice. The B-Spline model is input to the WAMIT system in the required format for the analysis of hull motion response to waves. The quality of the results obtained with B-Splines modeling was compared the ones obtained with flat panels. B-Splines have shown to be an effective approach, more efficient in computing terms when compared with the flat panels approach and suitable to optimization scripts. It revealed itself as a more adequate procedure to the design work as it simplifies the hull form mathematical definition of floating systems.

An Algorithm for Two-Dimensional Geometric Boundary Construction From Finite Element Node Displacement Data

1991 ◽  
Author(s):  
Andrei G. Jablokow ◽  
Brian J. Gilmore ◽  
Kent Clark
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Two Dimensional ◽  
Design Data ◽  
B Splines ◽  
Spline Curves ◽  
Dimensional Boundary ◽  
Finite Element Node ◽  
Geometric Boundary ◽  
Boundary Curves

Abstract This paper describes a system for constructing geometric models from elastically deflected finite element meshes. Two dimensional boundary curves are constructed by fitting B-Spline curves to the deflected Finite Element model. Cubic B-Splines are generated using least squares fitting techniques to the boundary curves of the Finite Element results. The fitted curves are connected end-to-end. The algorithm is useful after analysis for interfacing analysis results with design data in a shape optimization system based on Finite Element techniques.

Fairing Spatial B-Spline Curves

1996 ◽  
Vol 40 (04) ◽  
pp. 351-367 ◽  
Author(s):  
Kostis G. Pigounakis ◽  
Nickolas S. Sapidis ◽  
Panagiotis D. Kaklis
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Test Cases ◽  
Three Solutions ◽  
B Splines ◽  
Spline Curves ◽  
Visualization Tools ◽  
Aided Design ◽  
Knot Removal ◽  
Curve Fairing

Three-dimensional curves are playing an increasing role in ship-hull modeling and many other areas of computer-aided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies currently pursued by CAD researchers: local fairing by knot removal, and local/global fairing based on "energy" minimization. The performance of the algorithms is studied for both cubic and quintic B-splines using realistic test cases. Finally, a comparison with existing techniques is presented and some visualization tools for spatial-curve fairing are briefly discussed.

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