Efficient and reliable road modeling for digital maps based on cardinal spline

In order to realize an optimal balance between the efficiency and reliability requirements ofroad models,a road modeling method for digital maps based on cardinal spline is studied.First,the cardinal spline is chosen to establish an initial road model,which is specified by a series of control points and tension parameters.Then,in view of the initial road model,a gradual optimization algorithm,which can determine the reasonable control points and optimal tension parameters according to the degree of the change of road curvature,is proposed to determine the final road model.Finally,the proposed road modeling method is verified a d evaluated through experiments,and it is compared with the conventional method for digital maps based on the B-spline.The results show that the proposed method can resize a neaoptimal balance between the efficiency and reliability requirements.Compared with the conventional method based on the B-spline,this method occupies less data storage and achieves higher accuracy.

Planar Cardinal Spline Curves with Minimum Strain Energy

In this paper, we focus on how to use strain energy minimization to obtain the optimal value of the fl＇ee parameter of the planar Cardinal spline curves. The unique solution can be easily obtained by minimizing an appropriate approximation of the strain energy. An example is presented to illustrate the effectiveness of our method.

A Partial Approximation Shepard Method Based on Cardinal Spline About Messy Data

With regards to Shepard method, in the paper, we present a better one based on partial approximation to fit messy data. In the method, partial cubic cardinal spline function is chosen as weight function (?)(x) in the Shepard formula which is (?)(x)∈C2 and has good attenuation characteristics. So the traditional Shepard method is improved and the better results can be achieved in practical applications.

Recovery of band limited functions via cardinal splines

The main result of this paper asserts that if a function f is in the class Bπ,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its derivatives f(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric ofL q(?)), 1 <p=q < ∞, or 11 <p=q < ? ∞.

On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators

This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.

Nikolskii type inequality for cardinal splines

The Nikolskii type inequality for cardinal splines $$||s||_{p(R)} \leqslant 2(1 + 4\pi )2^{1 - \tfrac{q}{p}} \left( {\frac{\pi }{h}} \right)^{\tfrac{1}{q} - \tfrac{1}{p}} ||s||_{ q(R)} ,0 < q < p \leqslant \infty $$ is proved, which is exact in the sense of order, where ∈ ? m,h , and ? m,k is the space of cardinal splines with nodes $$\left\{ {jh + \frac{1}{2}(m - 1)h} \right\}_{j \in z} $$

Modeling the special intersections for enhanced digital map

A new lane-level road modeling method based on cardinal spline is proposed for the special intersections which are covered by vegetation or artificial landscape in their central regions.First,cardinal spline curves are used to fit the virtual lanes inside special intersections,and an initial road model is established using a series of control points and tension parameters.Then,the progressive optimization algorithm is proposed to determine the final road model based on the initial model.The algorithm determines reasonable control points and optimal tension parameters according to the degree of road curvature changes,so as to achieve a balance between the efficiency and reliability of the road model.Finally,the proposed intersection model is verified and evaluated through experiments.The results show that this method can effectively describe the lane-level topological relationship and geometric details of this kind of special intersection where the central area is covered by vegetation or artificial landscape,and can achieve a good balance between the efficiency and reliability of the road model.