高斯投影坐标正反算
V B程序
文件编码(GHTU-UITID-GGBKT-POIU-WUUI-8968)
高斯投影坐标正反算
学院:
班级:
学号:
姓名:
课程名称:
指导老师:
实验目的:
1.了解高斯投影坐标正反算的基本思想;
2.学会编写高斯正反算程序,加深了解。
实验原理:
高斯投影正算公式中应满足的三个条件:
1. 中央子午线投影后为直线;
2. 中央子午线投影后长度不变;
3. 投影具有正形性质,即正形投影条件。
高斯投影反算公式中应满足的三个条件:
1. x坐标轴投影成中央子午线,是投影的对称轴;
2. x轴上的长度投影保持不变;
3. 正形投影条件,即高斯面上的角度投影到椭球面上后角度没有
变形,仍然相等。
操作工具:
计算机中的
代码:
Dim a As Double, b As Double, x As Double, y As Double, y_#
Dim l_ As Double, b_ As Double, a0#, a2#, a4#, a6#, a8#, m2#, m4#, m6#, m8#, m0#, l0#, e#, e1#
Dim deg1 As Double, min1 As Double, sec1 As Double, deg2 As Double, min2 As Double, sec2 As Double
Private Sub Command1_Click()
Dim x_ As Double, t#, eta#, N#, W#, k1#, k2#, ik1%, ik2%, dh% deg1 = Val
min1 = Val
sec1 = Val
deg2 = Val
min2 = Val
sec2 = Val
l_ = (deg1 * 3600 + min1 * 60 + sec1) / 206265
b_ = (deg2 * 3600 + min2 * 60 + sec2) / 206265
dh = Val
k1 = ((l_ * 180 / + 3) / 6)
k2 = (l_ * 180 / / 3)
ik1 = Round(k1, 0)
ik2 = Round(k2, 0)
If dh = 6 Then
l0 = 6 * ik1 - 3
Else
If dh = 3 Then
l0 = 3 * ik2
Else
MsgBox "error", 48, "error": Exit Sub
End If
End If
l = l_ - l0 * / 180
e = Sqr(a * a - b * b) / a
m0 = a * (1 - e * e)
m2 = e * e * m0 * 3 / 2
m4 = e * e * m2 * 5 / 4
m6 = m4 * e * e * 7 / 6
m8 = e * e * m6 * 9 / 8
a0 = m0 + m2 / 2 + m4 * 3 / 8 + m6 * 5 / 16 + m8 * 35 / 128
a2 = m2 / 2 + m4 / 2 + m6 * 15 / 32 + m8 * 7 / 16
a4 = m4 / 8 + m6 * 3 / 16 + m8 * 7 / 32
a6 = m6 / 32 + m8 / 16
a8 = m8 / 128
x_ = a0 * b_ - a2 * Sin(2 * b_) / 2 + a4 * Sin(4 * b_) / 4 - Sin(6 * b_) * a6 / 6 + Sin(8 * b_) * a8 / 8
t = Tan(b_)
e1 = Sqr((a * a - b * b) / (b * b))
eta = Sqr(e1 * e1 * Cos(b) * Cos(b))
W = Sqr(1 - e * e * Sin(b_) * Sin(b_))
N = a / W
x = x_ + N * Sin(b_) * Cos(b_) * l * l / 2 + N * Sin(b_) *
Cos(b_) ^ 3 * (5 - t * t + 9 * eta * eta + 4 * eta ^ 4) * l ^ 4 / 24 + N * Sin(b_) * Cos(b_) ^ 5 * (61 - 58 * t * t + t ^ 4) * l ^ 6 / 720
y = N * Cos(b_) * l + N * Cos(b_) ^ 3 * (1 - t * t + eta * eta) * l * l * l / 6 + N * Cos(b_) ^ 5 * (5 - 18 * t * t + t ^ 4 + 14 * eta * eta - 58 * eta * eta * t * t) * l ^ 5 / 120
Text7 = x
If dh = 6 Then
y_ = y + 500000 + 1000000 * ik1
Else
If dh = 3 Then
y_ = y + 500000 + 1000000 * ik2
Else
MsgBox "error", 48, "error": Exit Sub
End If
End If
Text8 = y_
End Sub
Private Sub Command2_Click()
Dim bf#, j%, Wf#, Vf#, Nf#, Mf#, c#, tf#, etaf#, dh%, ik%
x = Val
y_ = Val
e = Sqr((a * a - b * b) / (a * a))
m0 = a * (1 - e * e)
m2 = e * e * m0 * 3 / 2
m4 = e * e * m2 * 5 / 4
m6 = m4 * e * e * 7 / 6
m8 = e * e * m6 * 9 / 8
a0 = m0 + m2 / 2 + m4 * 3 / 8 + m6 * 5 / 16 + m8 * 35 / 128 a2 = m2 / 2 + m4 / 2 + m6 * 15 / 32 + m8 * 7 / 16
a4 = m4 / 8 + m6 * 3 / 16 + m8 * 7 / 32
a6 = m6 / 32 + m8 / 16
a8 = m8 / 128
bf = x / a0
For j = 1 To 10
bf = (x + a2 / 2 * Sin(2 * bf) - a4 * Sin(4 * bf) / 4 + a6 * Sin(6 * bf) / 6 - a8 * Sin(8 * bf) / 8) / a0
Next j
e1 = Sqr(a * a - b * b) / b
Vf = Sqr(1 + e1 * e1 * Cos(bf) * Cos(bf))
Wf = Sqr(1 - e * e * Sin(bf) * Sin(bf))
Nf = a / Wf
c = a * a / b
Mf = c / Vf ^ 3
tf = Tan(bf)
e1 = Sqr((a * a - b * b) / (b * b))
etaf = Sqr(e1 * e1 * Cos(bf) * Cos(bf))
ik = Int(y_ / 1000000)
y = y_ - ik * 1000000 - 500000
b_ = bf - tf * y * y / (2 * Mf * Nf) + tf * (5 + 3 * tf *
tf + etaf * etaf - 9 * etaf * etaf * tf * tf) * y * y * y * y / (24 * Mf * Nf * Nf * Nf) + tf * (61 + 90 * tf * tf + 45 * tf * tf * tf * tf) * y * y * y * y * y * y / (720 * Mf * Nf * Nf * Nf * Nf * Nf)
l = y / (Nf * Cos(bf)) - (1 + 2 * tf * tf + etaf * etaf) * y * y * y / (6 * Nf * Nf * Nf * Cos(bf)) + (5 + 28 * tf * tf + 24 * tf * tf * tf * tf + 6 * etaf * etaf + 8 * etaf * etaf * tf * tf) * y * y * y * y * y / (120 * Nf * Nf * Nf * Nf * Nf * Cos(bf))
dh = Val
If dh = 6 Then
l0 = 6 * ik - 3
Else
If dh = 3 Then
l0 = 3 * ik
Else
MsgBox "error", 48, "error": Exit Sub End If
End If
l_ = l0 * / 180 + l
sec1 = l_ * 206265
deg1 = Int(sec1 / 3600)
min1 = Int((sec1 - deg1 * 3600) / 60) sec1 = sec1 - deg1 * 3600 - min1 * 60 sec2 = b_ * 206265
deg2 = Int(sec2 / 3600)
min2 = Int((sec2 - deg2 * 3600) / 60) sec2 = sec2 - deg2 * 3600 - min2 * 60 Text1 = deg1
Text2 = min1
Text3 = Round(sec1, 5)
Text4 = deg2
Text5 = min2
Text6 = Round(sec2, 5) End Sub
Private Sub Command3_Click() End
End Sub
Private Sub Command4_Click() = ""
= ""
= ""
= ""
= ""
= ""
= ""
= ""
= ""
= ""
End Sub
Private Sub Option1_Click() a = 6378245
b =
End Sub
Private Sub Option2_Click()
a = 6378140
b = 6356755.
End Sub
Private Sub Option3_Click()
a = 6378137
b =
End Sub
Private Sub Option4_Click()
a = 6378137
b =
End Sub
Private Sub Option5_Click()
a = Val(InputBox("a", "plsase input"))
b = Val(InputBox("b", "please input")) End Sub
界面截图如下:
使用方法:
1.如下所示,高斯投影坐标正算时,在经度纬度相应的文本框里输入经
纬度,再在度号对应的文本框里输入是六度带还是三度带,最后按坐标正算按钮即可,答案会显示在X,Y相应的文本框里;
2.如果要进行坐标反算,则输入X,Y与度号,最后按坐标反算按钮即
可得到所需的大地经纬度;
3.注意选择需要的椭球。