The Number of Regular Control Curves of NURBS Curve

Author(s):  
Han Wang ◽  
Chun-Gang Zhu
2021 ◽  
Vol 11 (11) ◽  
pp. 4959
Author(s):  
Peng Guo ◽  
Yijie Wu ◽  
Guang Yang ◽  
Zhebin Shen ◽  
Haorong Zhang ◽  
...  

The curvature of the NURBS curve varies along its trajectory, therefore, the commonly used feedrate-planning method, which based on the acceleration/deceleration (Acc/Dec) model, is difficult to be directly applied in CNC machining of a NURBS curve. To address this problem, a feedrate-planning method based on the critical constraint curve of the feedrate (CCC) is proposed. Firstly, the problems of existing feedrate-planning methods and their causes are analyzed. Secondly, by considering both the curvature constraint and the kinematic constraint during the Acc/Dec process, the concept of CCC which represents the relationship between the critical feedrate-constraint value and the arc length is proposed. Then the CCC of a NURBS curve is constructed, and it has a concise expression conforming to the Acc/Dec model. Finally, a feedrate-planning method of a NURBS curve based on CCC and the Acc/Dec model is established. In the simulation, a comparison between the proposed method and the conventional feedrate-planning method is performed, and the results show that, the proposed method can reduce the Acc/Dec time by over 40%, while little computational burden being added. The machining experimental results validate the real-time performance and stability of the proposed method, and also the machining quality is verified. The proposed method offers an effective feedrate-planning strategy for a NURBS curve in CNC machining.


Author(s):  
Deepika Saini ◽  
Sanoj Kumar ◽  
Manoj K. Singh ◽  
Musrrat Ali

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.


Author(s):  
Junzhao Han ◽  
Wenhua Chen

To limit velocity fluctuations and to achieve a controllable jerk value in a glass polishing process, a new velocity control algorithm is proposed based on nonuniform rational B-splines (NURBS). The key of this algorithm is replacing the traditional linear acceleration–deceleration with flexible NURBS acceleration–deceleration. Based on the linear acceleration–deceleration algorithm, the control points of the NURBS curve are confirmed, and the final velocity of the polishing wheel center is solved using the Preston equation. With jerk continuity and limitations of the servo system, nonlinear equations are constructed, and the weighting factors corresponding to the control points are obtained. Cubic velocity control equations can be derived from the obtained feature parameters, which include the final velocity, control points, weighting factors and knot vectors. Based on the proposed NURBS acceleration–deceleration algorithm, a fourth-order Runge–Kutta formula was used to obtain the initial points, and the Milne–Hamming equation was used to predict and correct the next point. The predictor-corrector interpolation algorithm for parametric trajectory was implemented during the polishing process. The experimental results indicate that the proposed approach guarantees limited fluctuations of the relative velocity at contact points and ensure smoother velocity changes at dangerous points.


2013 ◽  
Vol 756-759 ◽  
pp. 3826-3830
Author(s):  
Pei Sen Deng ◽  
Shao Ping Chen ◽  
Jun Cheng Shen

This paper converts a NURBS curve to piecewise rational Bézier curves by knot insertion algorithm, and then discusses the algorithm of continuous connection of NURBS curves. Meanwhile, explores the method to keep the same shape of the NURBS curves after connecting through the point translation and vector rotation theory. Finally, gives an instance to verify the validity of the algorithm.


2011 ◽  
Vol 64 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Sung Ho Hwang ◽  
Dong Uk Park ◽  
Kwon Chul Ha ◽  
Hyun Woo Cho ◽  
Chung Sik Yoon

AimsTo evaluate concentrations of airborne bacteria in university laboratories, hospital diagnostic laboratories, and a biowaste site in Seoul, Korea. To measure total airborne bacteria (TAB), the authors assessed sampling site, type of ventilation system, weather and detection of Gram-negative bacteria (GNB), indoors and outdoors.MethodAn Andersen one-stage sampler (Quick Take 30; SKC Inc) was used to sample air at a flow rate of 28.3 l/min for 5 min on nutrient medium in Petri dishes located on the impactor. A total of 236 samples (TAB, 109 indoor and nine outdoor; GNB, 109 indoor and nine outdoor) were collected three times in each spot from the 11 facilities to compare airborne bacteria concentrations.ResultsTAB concentrations ranged from undetectable to 3451 CFU/m3 (mean 384 CFU/m3), and GNB concentrations from undetectable to 394 CFU/m3 (mean 17 CFU/m3). TAB concentrations were high in window-ventilated facilities and facilities in which GNB were detected; concentrations were also high when it was rainy (all p values <0.05). TAB concentrations correlated significantly with GNB (r=0.548, p<0.01), number of bacteria species (r=0.351, p<0.01) and temperature (r=0.297, p<0.01). The presence of heating, ventilating, and air conditioning (HVAC), the number of TAB species and the detection of GNB affect TAB concentrations in laboratories.ConclusionsIt is recommended that special attention be given to regular control of indoor environments to improve the air quality of university and hospital laboratories.


Author(s):  
Stepanenko

The purpose of the study is to study the organization and procedure for conducting an audit of operating expenses of the enterprise. Materials and methods. The study used research methods such as monographs and synthesis (when analyzing existing publications), analysis, induction and deduction, comparisons and key components. Research results. The essence of the audit is to provide practical assistance to the management and economic services of the enterprise in the management and management of its finances, as well as the establishment of financial and management accounting, providing various consultations. Audit can be divided into the following stages: organizational, pilot, final. Operating expenses are a major component of an enterprise's costs. These are the costs associated with the main activity of the enterprise (production of products, services, performance of work). According to P (C) BO 16 “Expenses” to operating expenses include administrative expenses, sales expenses, other operating expenses. Expenditure audit entities may include: accounting policies, cost accounting transactions, records in primary documents, accounting records and reporting, information on accounting misconduct, and abuses that have been documented in audit acts, audits, auditors' reports. The audit of costs should begin with the verification of the statement of financial results to confirm the accuracy of its performance, the study of the organization of production (if the enterprise is engaged in production) and technological processes, the study of cost estimates, planned calculations and other conditions. When reviewing the accumulation and write-off of administrative expenses, sales costs and other operating expenses, the auditor should check the correctness of the classification of expenses to administrative, sales and other operating expenses. The following techniques are used to collect audit evidence: document verification, confirmation, counting, surveys, analytical procedures. Through the procedures of observation, questioning and confirmation, they obtain the supporting information contained in the accounting records. The calculation procedure consists in checking the arithmetic accuracy of the primary documents and accounting records or in performing the calculations independently (inventory). Analytical procedures involve the analysis of the most important indicators and ratios, including a summary study of deviations and relationships that conflict with other information relevant to the case or deviate from the expected indicators. During the cost audit, the auditor checks the appropriateness of the formulas used in the calculations, the correctness of the calculation procedures (the amount of tests depends on the materiality of the estimated values). Conclusions. Operating expense audit is an integral part of an enterprise's overall audit. Improving organizational aspects of cost audit is associated with deepening the practice of analytical procedures at all stages of the audit. For organization of internal audit of expenses at the enterprise it is necessary to carry out regular control of correctness of their formation.


Sign in / Sign up

Export Citation Format

Share Document