同一坐标系中,由任意两点计算地图旋转角度
----原创文章,转载请注明出处,谢谢
一、引言
在各种GIS/GPS应用中,地图旋转是不可或缺的一部分,尤其明显的是用在实时导航,对象跟踪等应用方面。用来计算地图旋转时偏转角的坐标点有动态和静态两种之分。动态在这里指的是在已知当前点的情况下,下一点的具体位置是不确定的;而静态指的是下一点的具体位置是确定的。动态的应用我们常见到的是GPS导航、游戏中的赛车(多赛道、可转弯等)以及调度等中的实时地图旋转,而静态更常见的是作为一种功能的演示,如模拟导航,模拟赛车等。地图旋转只有在同一坐标系中进行才有意义,地图旋转角度的计算才有依据,本文主要着重点在于如何由前后两点计算地图旋转角度,同时主要考虑动态的方式,静态方式的旋转地图原理是一样的,就不分开介绍了。
二、约定和术语
² 参考坐标系:本文所依据的坐标系为北京54下的依据高斯克吕格投影所建立的坐标系,即高斯平面坐标系,它的图像如图:
X代表为正北方向,Y代表正东方向,为了使y值都为正,将纵坐标轴西移500km。
² 正切函数是直角三角形中,对边与邻边的比值。放在直角坐标系中(如图)即 tanθ=y/x
其中tanθ的定义域为(-∏/2,+∏/2),值域为(-∞,+∞)
² 偏转角:约定偏转角为北偏东的角度,将地图按照偏转角进行旋转后将始终朝着运动方向行驶。在高斯平面坐标系中,正北即为X轴,正东即为Y轴,所以tanθ还是为y/x,只是角度的位置有了变化,如图所示。
² 反正切:函数y=tanx的反函数叫做反正切函数,记做:y=arctanx.
定义域:R;值域:(-π/2,π/2)
三、计算偏转角
假设存在一起始点pntBegin,并且存在一个原点为pntBegin的平面坐标系,同时约定要旋转的角度为rotateAngle,则下一点pntDest根据方位有几种情况,其示意图如下,我们可以分类进行讨论:
l 若pntDest.x1>=pntBegin.x0,则该点在第一和第四象限,具体对应点为pntDest(1)和pntDest(4),分别对应的北偏东角度为α(1)和α(4),根据Y值的不同,我们又可以分两种情况,
n 若pntDest.y>=pntBegin.y://在第一象限
rotateAngle=arctan2(fabs(p0.x-p1.x),fabs(p0.y-p1.y));
n 若pntDest.y<pntBegin.y://在第四象限
rotateAngle=arctan2(fabs(p0.x-p1.x),fabs(p0.y-p1.y));
rotateAngle=∏-rotateAngle;
l 若pntDest.x1<pntBegin.x0,则该点在第二和第三象限,具体对应点为pntDest(2)和pntDest(3),分别对应的北偏东角度为α(2)和α(3),根据Y值的不同,分两种情况进行讨论,
n 若pntDest.y>=pntBegin.y://在第二象限
rotateAngle=arctan2(fabs(p0.x-p1.x),fabs(p0.y-p1.y));
rotateAngle= 2*∏-rotateAngle;
n 若pntDest.y<pntBegin.y://在第三象限
rotateAngle=arctan2(fabs(p0.x-p1.x),fabs(p0.y-p1.y));
rotateAngle=∏+rotateAngle;
四、在超图平台中实现
注:开发语言为VC6,平台为eSuperMap;
代码如下:
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
2
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
3
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
4
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
5
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
6
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
7
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
8
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
9
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
10
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
11
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
12
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
13
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
14
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
15
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
16
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
17
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
18
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
19
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
20
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
21
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
22
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
23
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
24
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
25
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
26
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
27
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
28
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
29
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
30
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
31
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
32
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
33
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
34
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
35
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
36
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
37
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
38
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
39
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
40
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
41
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
42
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
43
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
44
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
45
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
46
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
47
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
48
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
49
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockEnd.gif)
50
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
51
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockEnd.gif)
五、结束语
整个计算过程并不复杂,甚至相当简单,重要的是要理解这个过程。各个开发平台也许有些出入,但是原理都应该相似,所以思路我相信是可以移植的。同时关于在下一点在坐标系上的情况我也已经考虑进去了,这里就不再说明了。同时,欢迎各位多提宝贵意见,集思广益,共同学习。