Interpolation of Point Values From Isoline Maps

A Bidirectional Hermitian Spline (BHS) method for the estimation of point values from isoline maps is presented and compared to three other methods. Hermitian splines are used and first derivatives are estimated by either Akima's method or by a clamped cubic spline, if Akima's method returns a zero first derivative. Every desired point value is interpolated twice, once by each of two orthogonally-directed splines. The two spline estimates are then averaged using the error formula for Hermitian splines. In addition, a periodic Hermitian spline is constructed around the study-area perimeter (representing a cross-sectional profile of the edge) to damp undesirable edge effects. Point values can be estimated from small-scale isoline maps drawn in spherical coordinates or from large-scale isoline maps drawn in Cartesian coordinates.     

随机删失下半参数模型的补偿估计方法

考虑半参数测量模型L=Bx+S+Δ,x∈Rd为未知回归参数,S为未知Borel函数。本文首先利用自然样条函数法,找到符合条件的非参数自然插值样条函数。其次利用补偿法并综合最小二乘法,导出了这种平差方法的解算公式。在本文的最后,将这种方法与最小二乘平差方法进行了比较分析,结果说明,半参数测量模型能更接近于真实情况。     

The Hammer projection of the ellipsoid of revolution (azimuthal, transverse, rescaled equiareal)

The classical Hammer projection of the sphere, which is azimuthal transverse rescaled equiareal, is generalized to the ellipsoid of revolution. Its first constituent, the azimuthal transverse equiareal projection of the biaxial ellipsoid, is derived giving equations for an equiareal transverse azimuthal projection. The second constituent, the equiareal mapping of the biaxial ellipsoid with respect to a transverse frame of reference and a change of scale, is then considered; results give collections of the general mapping equations generating the ellipsoidal Hammer projection, which lead to a world map. Received: 14 May 1996 / Accepted: 21 February 1997     

基于二元样条函数的DEM传递误差模型

根据两点数值微分公式建立了基于二元样条函数的规则格网数字高程模型(DEM)的表面表达模型,得出了基于二元样条函数的传递误差公式。公式表明,二元样条函数的DEM传递误差与双线性多项式的传递误差相同。但由于样条函数的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此,基于样条函数的DEM表面模型具有更高的精度。     

整体大地测量的确定性参数模型

本文将整体大地测量各类观测方程中作为随机信号的重力场参数（ΔN，ξ，η）均表达为重力异常Δg的泛函，又引入Δg的B样条函数并以样条系数C_(11)作待定参数，提出一种整体大地测量的确定性参数模型，给出了相应系数矩阵的表达式和算法，最后对该模型的求解问题作了说明。     

不同电离层映射函数对导航精度的影响分析

介绍广播星历映射函数、投影映射函数、几何映射函数和椭球映射函数4种不同的电离层映射函数,基于Klobuchar电离层模型分析不同电离层映射函数对导航精度的影响。结果表明,不同电离层映射函数对导航精度的影响在厘米级到分米级;在不同太阳活动期,椭球映射函数和几何映射函数对导航精度影响基本相同;在太阳活动活跃期,导航精度由高到低依次为几何映射函数、投影映射函数、广播星历映射函数;在太阳活动平稳期,导航精度由高到低依次为广播星历映射函数、投影映射函数、几何映射函数。建议在导航定位中,电离层映射函数在太阳活动活跃期时采用几何映射函数,在太阳活动低谷期时采用广播星历映射函数。     

无人机机载相机曝光时刻摄影中心三维坐标高精度插值算法研究

随着机载定位定向系统（POS）的不断完善,无人机技术已成为高精度摄影测量的重要途径．由于POS系统中全球卫星导航系统（GNSS）接收机的采样频率有限,需要对机载相机曝光点时刻摄影中心三维坐标进行插值计算．本文对常用的四种插值算法进行了研究,并通过实测数据对比不同插值算法的优劣,结果表明,当GNSS原始数据采样频率高于1 Hz时,三次样条插值算法误差均方根误差优于5 cm,更适用于无人机曝光时刻摄影中心三维坐标的高精度插值．      

高斯投影的复变函数表示

借助复变函数理论讨论高斯投影的复变函数表示,与传统的高斯投影实数域表达式相比,本文导出的高斯投影正反解表达式形式紧凑,公式简单,特别是基于复变函数建立的尺度比和子午线收敛角公式能表示为闭合形式;当e=0时,高斯投影正反解公式均为简单准确的闭合表达式。最后,通过算例对导出的新公式进行验算。     

Application of space oblique mercator projection in remote sensing

The concept of SOM was originated by Colvocoresses, which was mathematically developed and later modified by Snyder. It is most suitable for continuous mapping of satellite imagery, true to scale along ground track. Simplified mathematical formulation without complicated integral equations and constants of SOM projection for Landsat, SPOT and IRS satellites on Clarke and Everest spheroids are presented in this paper for ease of calculations.     

Equations of the Mayr Projection

In this study, the pseudo-cylindrical projection of Franz Mayr is examined in detail. The computation of one of Mayr's projection equations depends on the solution of an elliptical integral. It is this characteristic of the projection that most likely contributes to it being the neglected one among the group of the pseudo-cylindrical projections available today. Franz Mayr used the Legendre tables for the elliptical functions E and F and gave the plane coordinates within one-degree latitude intervals on the 90° meridian. The research reported here derives analytical expressions instead of using the elliptical integral and the interpolation between the table values. Four different solutions have been introduced for mapping applications. The distortion quantities are also presented and discussed.     

GIS中曲线误差带模型的一种算法

针对ＧＩＳ中对曲线位置不确定性分析的要求,提出了一种采用数值方法计算拟合曲线点位误差的算法,给出了确定ＧＩＳ中任意曲线误差带模型的具体计算步骤与计算公式,并结合实例,绘制了三次样条拟合曲线的误差带。     

Transverse Mercator with an accuracy of a few nanometers

Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of Krüger’s series for the mapping to higher order. The exact method provides an accuracy of 9 nm over the entire ellipsoid, while the errors in the series method are less than 5 nm within 3900 km of the central meridian. In each case, the meridian convergence and scale are also computed with similar accuracy. The speed of the series method is competitive with other less accurate algorithms and the exact method is about five times slower.     

极区不分带高斯投影的正反解表达式

针对传统高斯投影公式在极区难以应用的问题,通过引入等角余纬度及等量纬度的表达式,推导出严密的复数等角余纬度公式,进而得到严密的极区高斯投影正解表达式;借助符号迭代法及指数函数与三角函数间的关系式,推导出对应的极区高斯投影反解表达式;基于极区高斯投影正解表达式,推导出可用于极区的长度比、子午线收敛角公式;最后,以CGCS2000椭球为例,与实数型幂级数高斯投影公式计算的结果进行对比,验证了本文推导公式的正确性。由于本文推导公式不受带宽限制,且可用于整个极区的表示,对于编制极区地图及极区导航具有重要的参考价值。     

Gauss投影的复变函数表示

利用复变函数理论重新讨论了高斯投影。研究表明，高斯投影的复变函数表示具有形式紧凑、公式简单、计算效率高等优点，特别是基于复变函数建立的尺度比和子午线收敛角公式能表示为闭合形式。     

月球制图的投影选择与设计

月球地图投影是月球地图数学基础的主要内容,月球地图投影选择与设计是月球测绘的基础性和前瞻性工作.本文提出了月球地图投影系统设计的基本原则,选择与设计了适应月球全球、月球区域、月球大中比例尺的多层次、多尺度、多类型的月球地图投影系列,初步构建了月球地图投影的基本框架.     

地图矢量数据处理研究

本文以1:250万中华人民共和国大型挂图的制作研究中的数据格式转换为实例,重点讨论全数字制图环境下多源海量数据的提取和格式转换等问题,为数字地图新产品的开发提供了数据基础。根据制图基础数据的特点确定了把源数据Coverage层转化为CorelD raw能接收的DXF格式的数据转换方法,详细讨论了利用Arc/Info进行矢量数据的转换、投影变换的过程,包括数据合并、投影变换、数据提取、点状要素处理、拓扑关系的建立、比例尺控制、图层套和、数据输出等处理。     

Spherical panel clustering and its numerical aspects

In modern approximation methods, linear combinations in terms of (space localizing) radial basis functions play an essential role. Areas of application are numerical integration formulae on the unit sphere Ω corresponding to prescribed nodes, spherical spline interpolation and spherical wavelet approximation. The evaluation of such a linear combination is a time-consuming task, since a certain number of summations, multiplications and the calculation of scalar products are required. A generalization of the panel clustering method in a spherical setup is presented. The economy and efficiency of panel clustering are demonstrated for three fields of interest, namely upward continuation of the Earth's gravitational potential, geoid computation by spherical splines and wavelet reconstruction of the gravitational potential. Received: 1 October 1997 / Accepted: 1 April 1998     

多视纹理映射中无需设定偏差的快速可见性检测

在多视纹理映射中,Z缓冲区算法和光线追踪算法是两种主流的可见性检测算法。但其精度受限于人工设定的偏差。本文提出一种无需设定偏差的可见性检测方案。首先,根据倾斜摄影的投影参数设计了一种基于着色器编程的影像模拟算法,生成各影像视角下的初始可见性图(initial visibility map,IVM)。其中,完全不可见面元在模拟的过程中会被深度测试自动剔除。然后,基于矢量栅格化准则和像素深度对IVM中的可见面元执行投影区域优化(projection coverage refinement,PCR)。最后,提出惰性投影(lazy projection,LP)和迭代点边采样(iterative vertex-edge sampling,IVES)快速区分出IVM中的完全可见面元和非完全可见面元。利用两个数据集对本文算法进行了论证。结果表明本文算法的效率和精度均优于主流算法。     

The Miller Oblated Stereographic Projection for Africa,Europe, Asia and Australasia

The Miller Oblated Stereographic Projection, implemented by both the American Geographical Society and the Defense Mapping Agency in small-scale mapping of Africa, Europe, Asia and Australasia, is conformal for most land masses, reducing overall scale and area distortion by using a double projection. “Fill-in” sections are not conformal. Developed in 1953–1955 by O. M. Miller, the projection is implemented via tables for map construction. With the advent of computer-assisted intelligence and operations systems that use this projection to provide electronic images, the computation of rectangular projection coordinates from geographic locations via table look-up is no longer adequate. This paper presents an algorithm, based upon the original Miller work, which performs this transformation in a form applicable to scientific programming languages.     

基于小波的图像插值方法

本文在分析已有插值基函数和小波函数、小波变换的基础上提出一种应用小波作为插值基函数进行图像插值的方法,给出了该方法在一般图像插值方面在多幅图像的信息揉合和累积方面的应用,并分析了一般图像插值方法在图像之间存在辐照度差异时的可行性和在同名点之间存在相对空间信息差异时的操作方法。最后,采用４幅ＰＯＬＤＥＲ多角度遥感图像对本文所述方法进行了验证。实验表明,本文所述方法是可以较好地进行图像插值的。