B-Spline Curve Approximation with Nearly Arc-Length Parameterization

2014 ◽  
Vol 513-517 ◽  
pp. 3372-3376 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin ◽  
Yun Ding
Keyword(s):  
Three Dimensional ◽  
Smooth Curve ◽  
Least Square ◽  
Arc Length ◽  
Key Factors ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Fitting Algorithm ◽  
Data Points

An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

scholarly journals Two view NURBS reconstruction based on GACO model

2021 ◽  
Author(s):  
Deepika Saini ◽  
Sanoj Kumar ◽  
Manoj K. Singh ◽  
Musrrat Ali
Keyword(s):  
Optimization Algorithms ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Least Square ◽  
Ant Colony ◽  
Free Form ◽  
Reconstruction Process ◽  
Nurbs Curve ◽  
Data Points ◽  
Ant Colony Optimization Algorithms

AbstractThe key job here in the presented work is to investigate the performance of Generalized Ant Colony Optimizer (GACO) model in order to evolve the shape of three dimensional free-form Non Uniform Rational B-Spline (NURBS) curve using stereo (two) views. GACO model is a blend of two well known meta-heuristic optimization algorithms known as Simple Ant Colony and Global Ant Colony Optimization algorithms. Basically, the work talks about the solution of NURBS-fitting based reconstruction process. Therefore, GACO model is used to optimize the NURBS parameters (control points and weights) by minimizing the weighted least-square errors between the data points and the fitted NURBS curve. The algorithm is applied by first assuming some pre-fixed values of NURBS parameters. The experiments clearly show that the optimization procedure is a better option in a case where good initial locations of parameters are selected. A detailed experimental analysis is given in support of our algorithm. The implemented error analysis shows that the proposed methodology perform better as compared to the conventional methods.

scholarly journals Modeling technology of curved surface development for puffer fish

2020 ◽  
Vol 12 (4) ◽  
pp. 168781402091602
Author(s):  
Honggen Zhou ◽  
Jie Cui ◽  
Guizhong Tian ◽  
Yesheng Zhu ◽  
Changfeng Jia
Keyword(s):  
Three Dimensional ◽  
Least Square ◽  
Curved Surface ◽  
B Spline ◽  
Implicit Equation ◽  
Moving Least Square ◽  
Average Value ◽  
Modeling Technology ◽  
Surface Development ◽  
Puffer Fish

The drag reduction mechanism of puffer epidermis was closely related to its real geometry. In order to solve the modeling problem of epidermal spines on the puffer surface, a modeling method for the expansion of puffer shape was proposed. The three-dimensional scanning and non-uniform rational B-spline surface modeling technology was used to reconstruct the puffer model. According to the curvature characteristics, the surface mathematical equations including exponential, logarithmic, and sinusoidal functions were established based on the multinomial function. The surface was generated by a mathematical equation, and the surface was divided into several non-uniform rational B-spline patches according to curvature. After discretization, the point cloud Gaussian curvature and average value were calculated based on the implicit equation of moving least square surface, and whether the surface is approximately extensible or not was judged. Finally, the puffer surface was divided into 46 curved patches. In this article, the surface expansion algorithm gave priority to ensure the area unchanged, and four feature surfaces were selected according to the epidermal spines arrangement of the puffer surface. The results showed that the technique can simply and efficiently unfold the curved surface of the puffer fish, thus the mapping relationship between the epidermal spines on the surface and the plane was determined, which established a foundation for the accurate arrangement and modeling of the epidermal spines on the surface.

A New Nonlinear Least Square Algorithm for Voigt Spectral Lines

1980 ◽  
Vol 34 (3) ◽  
pp. 351-360 ◽  
Author(s):  
R. J. Noll ◽  
A. Pires
Keyword(s):  
Least Square ◽  
Spectral Lines ◽  
Single Line ◽  
Second Derivatives ◽  
Fitting Algorithm ◽  
Starting Conditions ◽  
Data Points ◽  
Lorentz Line ◽  
Few Data ◽  
Raphson Method

In this paper a new fitting algorithm which works with Voigt functions is discussed. The fitting algorithm used is an extension of the rapidly convergent gradient method of Fletcher and Powell, who claim faster convergence than the Newton-Raphson method which has been used by Chang and Shaw for fitting Lorentz line widths. The Fletcher and Powell algorithm involves the effects of second derivatives although second derivatives are not explicitly calculated. In our algorithm, first and second derivatives are computed not numerically, but analytically via a modification to Drayson's Voigt function subroutine. This algorithm provides rapid convergence even when there are few data points. Profiles have been fitted with as few as five data points. Our typical line fits involve 40 points. The run time of the algorithm has been compared with the shrinking cube algorithm of Hillman and found to be at least 10 times faster under identical starting conditions. Sample single line and single line plus background are shown illustrating the speed and efficiency of the new algorithm, as well as the importance of good zero-order estimates to start the iterations.

Fast converging elitist genetic algorithm for knot adjustment in B-spline curve approximation

2019 ◽  
Vol 13 (4) ◽  
pp. 317-328
Author(s):  
Johannes Bureick ◽  
Hamza Alkhatib ◽  
Ingo Neumann
Keyword(s):  
Genetic Algorithm ◽  
Real Data ◽  
Adjustment Problem ◽  
Data Set ◽  
New Approach ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Data Gaps

Abstract B-spline curve approximation is a crucial task in many applications and disciplines. The most challenging part of B-spline curve approximation is the determination of a suitable knot vector. The finding of a solution for this multimodal and multivariate continuous nonlinear optimization problem, known as knot adjustment problem, gets even more complicated when data gaps occur. We present a new approach in this paper called an elitist genetic algorithm, which solves the knot adjustment problem in a faster and more precise manner than existing approaches. We demonstrate the performance of our elitist genetic algorithm by applying it to two challenging test functions and a real data set. We demonstrate that our algorithm is more efficient and robust against data gaps than existing approaches.

Research on Algorithm for Space Weld Reconstruction and Torch Pose Simulation

2014 ◽  
Vol 1049-1050 ◽  
pp. 833-837
Author(s):  
Peng Yang ◽  
Dong Xing Hui ◽  
Zheng Kai ◽  
Li Shu Tian
Keyword(s):  
Coordinate Transformation ◽  
Spline Interpolation ◽  
Three Dimensional ◽  
Automatic Welding ◽  
Control Points ◽  
B Spline ◽  
Spline Curve ◽  
Planning Algorithm ◽  
Control Terminal ◽  
Path Planning Algorithm

A path planning algorithm based on B-spline interpolation techniques was constructed for automatic welding system.The system used a B-spline curve to reconstruct the weld,it was achieved by reversing the control points of B-spline curve through the prescribed date points. The weld posture model was then obtained from the osculating plane and normal plane of B-spline curve. By taking a series coordinate transformation to the weld posture model, the torch posture model based on control terminal was provided.Experiments show that the new algorithm can readily be used for various three-dimensional welding tasks.

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