共查询到18条相似文献，搜索用时 250 毫秒
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研究了极球面投影海图上准确便捷地量测距离的方法。推导了极球面投影下大圆航线和等角航线的方程,形状分析表明极区宜采用大圆航线量测距离;根据极球面投影下直线的几何意义推导了其距离计算公式,距离差值分析表明可用直线代替大圆航线准确量测距离;根据极球面投影上小圆线投影为圆的性质,提出了一种基于等距圆的准确便捷的距离量测方法,以满足极球面投影海图的极区导航应用需要。 相似文献
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等角航线又名恒向线,在椭球面上它是与经线方向保持定角α的航向线。如图1所示,设Sl为等角投影面上等角航线的表象,该等角航线的航向角为α,坐标方位角为Φ。P点的子午线收敛角为γ,根据微分几何学[1]关于曲率的定义,可以写出等角投影面上的经、纬线和斜航线的曲率公式,令P点图1等角投影面上的等角航线的子午圈曲率半径为M和卵西圈曲率半径为N,投影长度比为m,则有：或者下面分析常用等角投影面上的等角航线的曲率情况：（1）墨卡托投影面上（基准纬度中0）代人（1）、（2）、（3）式得到：凡一K,＝KI—0说明等角航线被表象为… 相似文献
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大椭圆航线设计的空间矢量方法 总被引：2，自引：2，他引：0
针对传统大圆航线设计采用的球体模型和现代导航设备采用的椭球体模型不统一引起航行误差的问题,研究了基于空间矢量的大椭圆航线设计方法。通过采用空间矢量代数方法直接求解大椭圆顶点,并提出依据长轴矢量和短轴矢量的大椭圆描述方法,应用两个基本矢量推导大椭圆航线方位和航程计算公式,进而研究了大椭圆航线设计算法,重点提出了基于Newton-Raphson(N-R)的等距离航线设计算法。对比算例表明,大圆航线与大椭圆航线设计结果差异明显,大椭圆航线设计算法与航行阶段采用的地球模型一致,可消除大圆航线设计引起的误差,提高航海计算精度。 相似文献
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基于THREE.JS和Google Map API编写了二维和三维地图并存的网页,并实现了二维和三维地图窗口的数据交互。同时以等角航线为例,实现了等角航线的二三维可视化,并进行了大圆航线的三维可视化,与等角航线进行对比,突出了两种航线的形态特征与航行的优缺点。 相似文献
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考虑地球扁率的RNAV航路规划 总被引：3，自引：0，他引：3
考虑地球扁率的影响,在地理坐标系下推算区域导航(RNAV)航路点的经纬度坐标以及各航段的初始真航线角(TC)与航线距离,为机载区域导航设备提供更为精确的航迹指引和更为快捷的直飞航线。以IAG-75椭球参数为计算依据,根据空间向量分析,导出了RNAV大椭圆圈航线的初始TC、航线距离以及基于中间插值的航路点纬度计算方法。经计算,从B215航路的阜康至大王庄,现行等角航线距离为2642km,简化大圆航线模型的航线距离为2423.8km,而考虑地球扁率影响的大椭圆航线模型的航线距离为2435.3km。 相似文献
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极区不分带高斯投影的正反解表达式 总被引：1，自引：1，他引：0
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。 相似文献
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关于等角航线、大圆航线的教学研究 总被引：2，自引：0，他引：2
关于等角航线、大圆航线的教学研究张国坤（四平师院地理系，１３６００）大地球体可以代替实际地球体，它又能被一个极近似大地水准面的地球椭球体来代替。地球椭球体可表述地球的形状、大小。大地球体可表达地球上某点的地理坐标位置。在绘制小比例尺地图时，大地球体被... 相似文献
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《测量评论》2013,45(72):90-92
AbstractWhen developing the argument leading to the stereographic solution of the spherical triangle and its application to field astronomy (Empire Survey Review, Vol. 2, No. 10, October, 1933, p. 226) A. J. Potter rendered a very useful service in demonstrating how proofs of the two practically useful properties of the stereographic projection can be provided along lines that demand no more than simple geometry in their development. The proof advanced for the unique property that any circle on the. sphere remains a circle in projection is at once simple and complete; but in the attempt to prove that the projection is orthomorphic in the sense that angles everywhere remain true there is the difficulty that the argument was developed for what must be regarded as a special case in that the point was located on the great circle through the origin of the projection normal to the plane of the projection. Treatment of the problem along similar lines for other points away from the central meridian does not seem to admit of such ready solution and the alternative approach suggested here, while still not demanding. anything beyond simple geometry for its understanding, affords a proof for a general case. 相似文献
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利用空间矢量方法推导出了椭球面上只与起止点地理坐标有关的大椭圆航线方程，代入4种常用海图投影的正解公式，得到不同投影平面上的大椭圆参数方程；利用上述参数方程进而推导出了不同投影面上大椭圆航线的曲率与曲率半径公式。选取伦敦到纽约的大椭圆航线为例，通过绘制不同投影面上的大椭圆航线并分析其曲率、曲率半径变化曲线可知，大椭圆航线在日晷投影上的表象为曲率处处为0的直线，而在其他投影面上的表象为曲率较小但不断变化的曲线。利用推导的曲率半径公式可以计算各类大椭圆航线上任意位置的“代曲直距”，方便在不同比例尺的海图上对大椭圆航线进行量测和绘制，提高作图效率。 相似文献
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针对球体横墨卡托投影与基于地球椭球体的导航设备结合使用存在误差以及传统椭球横墨卡托投影依据经差分带不适用于极区的问题，在分析双重投影可用于极区存在计算奇异和计算溢出问题的基础上，研究了一种基于双重投影的横墨卡托投影极区应用改进方法。首先利用函数等效变换和经线长度比计算公式推导出椭球投影到球体上的坐标变换、球体半径和长度比计算公式，然后利用分段函数的方法研究了球体横墨卡托投影计算公式，综合两个阶段给出了完整的坐标变换公式和长度比计算公式，最后推导了子午线收敛角计算公式。理论分析和算例仿真表明，该改进方法能够解决极区投影计算奇异和计算溢出问题，近极点地区长度变形较小，且与导航设备采用的地球模型一致，可消除由于地球模型不同引起的误差，提高航海绘算精度。 相似文献
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Sebastian Orihuela 《The Cartographic journal》2013,50(2):158-165
The Lagrange projection represents conformally the terrestrial globe within a circle. This is achieved by compressing the latitude and longitude and by applying the new coordinates into the equatorial stereographic projection. The same concept can be generalized to any conformal projection, although the application of this technique to other analytical functions is less known. In this work, the general Lambert–Lagrange projection formula is proposed and the application of the modified coordinates is discussed on projections: stereographic, conformal conic and Gauss–Schreiber. In general, the results are merely a curiosity, except for the case of Gauss–Schreiber, where the use of coordinates with altered scale can be applied in the optimization of conformal projections. 相似文献
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双等距离投影及其应用 总被引：1，自引：0，他引：1
双等距离投影是指自图上两定点出发至图上任意点间的距离都与实地等长的投影。本文先从球面极坐标出发，讨论了双等距离投影公式的建立，继而给出了在地理坐标下的正轴和斜轴投影计算方法。本文证明了该投影的性质属任意投影，其计算方法是可行的，有实用价值。双等距离投影在测量上可用于圆圆系统定位，在军事上可用于敌情监测等。 相似文献
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《制图学和地理信息科学》2013,40(2):143-150
The choice of a projection for world distributions depends on a number of considerations. Primarily this involves the properties of equivalence and conformality. But there are instances where requirements regarding the use of these mutually exclusive properties would allow a compromise projection. This article presents the mathematical basis, a construction procedure, and an analysis of area and angular deformation of one such projection, a modified van der Grinten. Mathematical expressions are derived which are used to locate parallels and meridians. Parallels of the modified grid are straight lines located at an increasing distance from the equator. Meridians are arcs of circles intersecting the construction equator truly. Distribution of S and 2ω are shown. 相似文献
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《The Cartographic journal》2013,50(2):109-116
AbstractIn this paper the cartographic grids engraved on two antique instruments from Iran for finding the sacred direction and distance to Mecca are discussed. It appears that these grids can be well explained in terms of the Mecca-centred retro-azimuthal orthographic projection described in 1968 by J. E. Jackson. In this projection the lines of constant latitude reduce to a set of ellipses with their major axes parallel to the equator and the lines of the constant longitudes reduce to a set of non-equidistant straight lines parallel to the north-south direction. It is shown that the curves actually engraved on the instrument conform to this projection and can be fairly easily constructed. This interpretation of the grid on the Iranian instruments stands in contrast with another explanation, recently proposed by King (1999), which is based on medieval Arabic concepts such as the so-called 'methods of the zijes'. Insufficiently accurate workmanship makes it impossible to distinguish between the two explanations through the study of the instruments themselves. The newly gained insight into the projection itself, however, shows that a direct relation between the Iranian maps and Islamic mappings insight knows from the ninth century, as suggested by King, does not exit. Thus, it is concluded that it is as yet completely unknown when and where the very idea behind the Iranian cartographic grid was first conceived, and that the quest for their historical background is still open. 相似文献