Approximating curve by a single segment of B-Spline or Bézier curve directly in CAD environment

The paper presents the method of approximating curves with a single segment of the B-Spline and Bézier curves. The method for determining a single curve segment using the optimization methods in the CATIA environment is shown. The algorithms of simulated annealing and design of experiment are used for optimization. For the same purpose, a new original procedure for determining the distance between the given curves using explicit parameters in the CATIA environment was also used. This approximation of the cyclic curves results in the curve oscillation as shown in the examples. The results show that the approximation method with Bézier curve using control points as “free” points can be applied to obtain the best results of approximation.

Area Properties of Strictly Convex Curves

We study functions defined in the plane E 2 in which level curves are strictly convex, and investigate area properties of regions cut off by chords on the level curves. In this paper we give a partial answer to the question: Which function has level curves whose tangent lines cut off from a level curve segment of constant area? In the results, we give some characterization theorems regarding conic sections.

A New GNB Model of Crash Frequency for Freeway Sharp Horizontal Curve Based on Interactive Influence of Explanatory Variables

Crash prediction of the sharp horizontal curve segment of freeway is a key method in analyzing safety situation of freeway horizontal alignment. The target of this paper is to improve predicting accuracy after considering the elastic influence of explanatory variables and interaction of explanatory variables on crash rate prediction. In the paper, flexibility and elasticity are defined to express the elastic influence of explanatory variables and interaction of explanatory variables on crash rate prediction. Thus, we proposed 6 types of models to predict crash frequency. These 6 types of models include 2 NB models (models 1 and 2), 2 GNB models (models 3 and 4), one NB model (model 5), and one GNB model (model 6) with flexibility and variable elasticity considered. The alignment and crash report data of 88 sharp horizontal curve segments from different institutions were surveyed to build the crash models. Traffic volume, highway horizontal radius, and curve length have been assigned as explanatory variables. Subsequently, statistical analysis is performed to determine the model parameters and conducted sensitivity analysis by AIC, BIC, and Pseudo R2. The results demonstrated the effective use of flexibility and elasticity in analyzing explanatory variables and in predicting freeway sharp horizontal curve segments. In six models, the result of model 6 is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 sharp horizontal curve segments with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than the others.

Pre-load on the guiding/stabilizing wheels and the critical lateral force of a straddle-type monorail vehicle

The anti-overturning ability of a straddle-type monorail vehicle is influenced by the contact status between the guiding and stabilizing wheels and the track beam; therefore, an initial pre-load is required for the stabilizing and guiding wheels to enhance the anti-overturning ability of the straddle-type monorail vehicle. Determining the reasonable pre-load for the stabilizing and guiding wheels is a significant problem in the operation of a straddle-type monorail vehicle. D’Alembert’s principle has been adopted to transform the dynamic problem that straddle-type monorail vehicle runs on curve segment to the statics problem. The formula describing the relationship between the critical lateral force of the vehicle and the pre-load of the stabilizing wheels is derived from the lateral roll equation of the straddle monorail vehicle and is verified using the multibody dynamics software UM. Subsequently, the reasonable pre-load for the stabilizing wheels is analyzed from the perspectives of comfort and safety based on the formula of critical lateral force. Finally, the maximum and minimum speed limits on a curve for a straddle-type monorail vehicle are discussed based on the aforementioned analysis.

Rigidity of Nonnegatively Curved Surfaces Relative to a Curve

We prove that any properly oriented $\mathcal{C}^{2,1}$ isometric immersion of a positively curved Riemannian surface $M$ into Euclidean 3-space is uniquely determined, up to a rigid motion, by its values on any curve segment in $M$. A generalization of this result to nonnegatively curved surfaces is presented as well under suitable conditions on their parabolic points. Thus, we obtain a local version of Cohn-Vossen’s rigidity theorem for convex surfaces subject to a Dirichlet condition. The proof employs in part Hormander’s unique continuation principle for elliptic partial differential equations. Our approach also yields a short proof of Cohn-Vossen’s theorem.

A Method to Estimate Voltage Sag Caused by Transformer Excitation Inrush Current

Due to excitation inrush current, no-load transformer accesses system can cause different degree of voltage sag. Therefore presents a method to estimate voltage sag caused by closing no-load transformer. Firstly, accord to the point of saturation magnetic flux and transformer core general single value curve equation to establish general nonlinear magnetization curve. Use the linear features of saturated magnetization curve segment to estimate the maximum inrush current and calculate the maximum depth of voltage sag. According to the magnetic flux decay time to estimate the duration of voltage sag. Simulate closing no-load transformer in a 10kV distribution network, and compare the simulated result with the calculated result. The results show that the proposed method is validity and accuracy.

A Method to Estimate Voltage Sag Caused by Transformer Excitation Inrush Current

Due to excitation inrush current, no-load transformer accesses system can cause different degree of voltage sag. Therefore presents a method to estimate voltage sag caused by closing no-load transformer. Firstly, accord to the point of saturation magnetic flux and transformer core general single value curve equation to establish general nonlinear magnetization curve. Use the linear features of saturated magnetization curve segment to estimate the maximum inrush current and calculate the maximum depth of voltage sag. According to the magnetic flux decay time to estimate the duration of voltage sag. Simulate closing no-load transformer in a 10kV distribution network, and compare the simulated result with the calculated result. The results show that the proposed method is validity and accuracy.

A Feature-Based Section Curve Reconstructing Strategy

ntegrating section feature recognition with forward design is an effective method to reconstruct section curve and change feature architecture patterns from 2D to 3D. This paper proposes solutions to filter the points on the slices of point cloud data, automatically sequence the points on slices, recognize section curve feature, fit each curve segment and reconstruct section curves. All the relevant algorithms are implemented in Matlab. The point cloud data of sighting scope is used to validate the strategy. Also, Error analysis is carried out in Geomagic Studio. This strategy proves its feasibility and accuracy of completing reverse modeling process.