hallo roland alter samariter, da sind doch noch die bienchen und die blümchen.
bis denn
Umrechnungsformeln oder ???
Moderator: Roland
-
Hartmut
- Beiträge: 815
- Registriert: 25.05.2004 - 18:56
- Wohnort: Prachuab Khiri Khan 11°44'37"N 99°47'17"E
- Kontaktdaten:
moin,
hallo roland alter samariter, da sind doch noch die bienchen und die blümchen.
bis denn
hallo roland alter samariter, da sind doch noch die bienchen und die blümchen.
bis denn
ich bin zwar verantwortlich, für das was ich sage, aber nicht dafür, wie du es verstehst.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
Hartmut, Hartmut,
wir sind hier keine durch und durch schlechten Menschen
Wir wissen (fast) nie, wer am anderen Ende sitzt.
MacToolz müht sich mit dem Problem, müsste aber selber sagen, ob er sich eine Lösung zutraut. Hm, gibt es da nicht so "GIS"-Programme, die auf einem Laptop laufen und alles gleich im richtigen Format speichern ..
Grüße Roland
wir sind hier keine durch und durch schlechten Menschen
Wir wissen (fast) nie, wer am anderen Ende sitzt.
MacToolz müht sich mit dem Problem, müsste aber selber sagen, ob er sich eine Lösung zutraut. Hm, gibt es da nicht so "GIS"-Programme, die auf einem Laptop laufen und alles gleich im richtigen Format speichern ..
Grüße Roland
-
Hartmut
- Beiträge: 815
- Registriert: 25.05.2004 - 18:56
- Wohnort: Prachuab Khiri Khan 11°44'37"N 99°47'17"E
- Kontaktdaten:
moin,
wenn du da die NMEA-daten meinst, die kannst du vom hyperterminal (bestandteil von windows) aufzeichnen lassen. fugawi schreibt auch ein protokoll wenn gewünscht. da gibts aber noch jede menge.
was macht der urlaub, ihr habt da je einen schönen tümpel, segelt da auch wer ???
bis denn
wenn du da die NMEA-daten meinst, die kannst du vom hyperterminal (bestandteil von windows) aufzeichnen lassen. fugawi schreibt auch ein protokoll wenn gewünscht. da gibts aber noch jede menge.
was macht der urlaub, ihr habt da je einen schönen tümpel, segelt da auch wer ???
bis denn
ich bin zwar verantwortlich, für das was ich sage, aber nicht dafür, wie du es verstehst.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
-
mactoolz
Hi,
GIS hin oder her. GIS Können wir auch nutzen. Nur das Problem ist, das wir die Daten in GIS nicht selber pflegen können. Als nächstes braucht GIS tierisch lange bis man alles eingerichtet und bla bla gemacht. Also voll umständlich.
Als nächstes, würde ich es auch gerne für eigene Private Zwecke nutzen und nicht auf andere Programme zurück greifen müssen.
Selber programmieren finde ich besser. Nur leider bliebt es an der Berechnung hängen .........
Das Protokoll oder die Daten aus der GPS Maus auslesen habe ich in VBA schon umgesetzt.
Also ich abe geschaut und versucht zu ergooglen wo auf welchen Meridian wir (NRW) liegen. Sprich es müste dann ja ungefähr 7,5 sein. Das gibt es ja garnicht, oder ???
Es werden doch nur 3 Schritte angenommen. ???
MacToolz
GIS hin oder her. GIS Können wir auch nutzen. Nur das Problem ist, das wir die Daten in GIS nicht selber pflegen können. Als nächstes braucht GIS tierisch lange bis man alles eingerichtet und bla bla gemacht. Also voll umständlich.
Als nächstes, würde ich es auch gerne für eigene Private Zwecke nutzen und nicht auf andere Programme zurück greifen müssen.
Selber programmieren finde ich besser. Nur leider bliebt es an der Berechnung hängen .........
Das Protokoll oder die Daten aus der GPS Maus auslesen habe ich in VBA schon umgesetzt.
Also ich abe geschaut und versucht zu ergooglen wo auf welchen Meridian wir (NRW) liegen. Sprich es müste dann ja ungefähr 7,5 sein. Das gibt es ja garnicht, oder ???
Es werden doch nur 3 Schritte angenommen. ???
MacToolz
Hi MacToolz,mactoolz hat geschrieben:Also ich abe geschaut und versucht zu ergooglen wo auf welchen Meridian wir (NRW) liegen. Sprich es müste dann ja ungefähr 7,5 sein. Das gibt es ja garnicht, oder ???
Kartografie ist Geschichte/Historie
und NRW spielt darin keine Rolle . . .
Die kartografische Vermessung des deutschen Reiches bezieht sich auf Potsdam, die italienische Kartografie auf die Sternwarte des Vatikanstaats (Monte Mario), die Kartografie der K&K-Monarchie bezieht sich auf die alte Westgrenze des Habsburgerreiches auf der Kanareninsel El Hierro, und das Britische Empire bezieht sich auf die Sternwarte von Greenwich.
In diesem Sinne - weitergoogeln
Grüsse - Anton
-
Hartmut
- Beiträge: 815
- Registriert: 25.05.2004 - 18:56
- Wohnort: Prachuab Khiri Khan 11°44'37"N 99°47'17"E
- Kontaktdaten:
moin,
soweit ich weiß ist der meridian immer ganzzahlig, kannst aber auch längengrad dazu sagen.
bis denn
soweit ich weiß ist der meridian immer ganzzahlig, kannst aber auch längengrad dazu sagen.
bis denn
ich bin zwar verantwortlich, für das was ich sage, aber nicht dafür, wie du es verstehst.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
rechtschreibfehler sind gewollt und deswegen mit voller Absicht erstellt. wer welche findet, darf sie behalten, verschenken oder auch versteigern.
Hallo MacToolz,
also Einer der Landesvermessung NRW geht noch, dann muss ich erstmal nach den Katzen schauen ...
Gute Nacht
Roland
also Einer der Landesvermessung NRW geht noch, dann muss ich erstmal nach den Katzen schauen ...
Gute Nacht
Roland
Zuletzt geändert von Roland am 12.08.2006 - 23:04, insgesamt 1-mal geändert.
Hallo Roland,Roland hat geschrieben:wenn Du Landesvermessung oder Geodäsie statt Kartographie gesagt hättest
da merkt man meinen Amateur-Status
Ich schreibe auch 'Ortofoto' und nicht 'Orthophoto' wie das http://www.lverma.nrw.de
Anton
-
mactoolz
Hi,
schaut euch mal das an was ich gefunden habe.
--------------------------------------------------------------------------
'********************************************************************************************* _
THE FUNCTIONS IN THIS MODULE ARE WRITTEN TO BE "STAND ALONE" WITH AS LITTLE DEPENDANCE _
ON OTHER FUNCTIONS AS POSSIBLE. THIS MAKES THEM EASIER TO COPY TO OTHER VB APPLICATIONS. _
WHERE A FUNCTION DOES CALL ANOTHER FUNCTION THIS IS STATED IN THE COMMENTS AT THE START OF _
THE FUNCTION. _
*********************************************************************************************
Private Const Pi = 3.14159265358979
Function Lat_Long_H_to_X(phi, lam, H, a, b)
'1.Schritt ???
'Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian X coordinate.
'Input: - _
Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute X
Lat_Long_H_to_X = (V + H) * (Cos(RadPHI)) * (Cos(RadLAM))
End Function
Function Helmert_X(x, y, z, dX, Y_Rot, Z_Rot, S)
'2.Schritt
'Computed Helmert transformed X coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), X translation (DX) all in meters ; _
Y and Z rotations in seconds of arc (Y_Rot, Z_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadY_Rot = (Y_Rot / 3600) * (Pi / 180)
RadZ_Rot = (Z_Rot / 3600) * (Pi / 180)
'Compute transformed X coord
Helmert_X = x + (x * sfactor) - (y * RadZ_Rot) + (z * RadY_Rot) + dX
End Function
Function Helmert_Y(x, y, z, dY, X_Rot, Z_Rot, S)
'2a Schritt
'Computed Helmert transformed Y coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), Y translation (DY) all in meters ; _
X and Z rotations in seconds of arc (X_Rot, Z_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadX_Rot = (X_Rot / 3600) * (Pi / 180)
RadZ_Rot = (Z_Rot / 3600) * (Pi / 180)
'Compute transformed Y coord
Helmert_Y = (x * RadZ_Rot) + y + (y * sfactor) - (z * RadX_Rot) + dY
End Function
Function Helmert_Z(x, y, z, dZ, X_Rot, Y_Rot, S)
'2b Schritt
'Computed Helmert transformed Z coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), Z translation (DZ) all in meters ; _
X and Y rotations in seconds of arc (X_Rot, Y_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadX_Rot = (X_Rot / 3600) * (Pi / 180)
RadY_Rot = (Y_Rot / 3600) * (Pi / 180)
'Compute transformed Z coord
Helmert_Z = (-1 * x * RadY_Rot) + (y * RadX_Rot) + z + (z * sfactor) + dZ
End Function
Function XYZ_to_Lat(x, y, z, a, b)
'Convert XYZ to Latitude (PHI) in Dec Degrees.
'Input: - _
XYZ cartesian coords (X,Y,Z) and ellipsoid axis dimensions (a & b), all in meters.
'THIS FUNCTION REQUIRES THE "Iterate_XYZ_to_Lat" FUNCTION
'THIS FUNCTION IS CALLED BY THE "XYZ_to_H" FUNCTION
RootXYSqr = Sqr((x ^ 2) + (y ^ 2))
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
PHI1 = Atn(z / (RootXYSqr * (1 - e2)))
phi = Iterate_XYZ_to_Lat(a, e2, PHI1, z, RootXYSqr)
XYZ_to_Lat = phi * (180 / Pi)
End Function
Function Iterate_XYZ_to_Lat(a, e2, PHI1, z, RootXYSqr)
'Iteratively computes Latitude (PHI).
'Input: - _
ellipsoid semi major axis (a) in meters; _
eta squared (e2); _
estimated value for latitude (PHI1) in radians; _
cartesian Z coordinate (Z) in meters; _
RootXYSqr computed from X & Y in meters.
'THIS FUNCTION IS CALLED BY THE "XYZ_to_PHI" FUNCTION
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE _
"Projection and Transformation Calculations.xls" SPREADSHEET
V = a / (Sqr(1 - (e2 * ((sIn(PHI1)) ^ 2))))
phi2 = Atn((z + (e2 * V * (sIn(PHI1)))) / RootXYSqr)
Do While Abs(PHI1 - phi2) > 0.000000001
PHI1 = phi2
V = a / (Sqr(1 - (e2 * ((sIn(PHI1)) ^ 2))))
phi2 = Atn((z + (e2 * V * (sIn(PHI1)))) / RootXYSqr)
Loop
Iterate_XYZ_to_Lat = phi2
End Function
Function XYZ_to_Long(x, y)
'Convert XYZ to Longitude (LAM) in Dec Degrees.
'Input: - _
X and Y cartesian coords in meters.
XYZ_to_Long = (Atn(y / x)) * (180 / Pi)
End Function
Function XYZ_to_H(x, y, z, a, b)
'Convert XYZ to Ellipsoidal Height.
'Input: - _
XYZ cartesian coords (X,Y,Z) and ellipsoid axis dimensions (a & b), all in meters.
'REQUIRES THE "XYZ_to_Lat" FUNCTION
'Compute PHI (Dec Degrees) first
phi = XYZ_to_Lat(x, y, z, a, b)
'Convert PHI radians
RadPHI = phi * (Pi / 180)
'Compute H
RootXYSqr = Sqr((x ^ 2) + (y ^ 2))
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
H = (RootXYSqr / Cos(RadPHI)) - V
XYZ_to_H = H
End Function
Function Lat_Long_H_to_Y(phi, lam, H, a, b)
'Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian Y coordinate.
'Input: - _
Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute Y
Lat_Long_H_to_Y = (V + H) * (Cos(RadPHI)) * (sIn(RadLAM))
End Function
Function Lat_H_to_Z(phi, H, a, b)
'Convert geodetic coord components latitude (PHI) and height (H) to cartesian Z coordinate.
'Input: - _
Latitude (PHI) decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute X
Lat_H_to_Z = ((V * (1 - e2)) + H) * (sIn(RadPHI))
End Function
Function Lat_Long_to_East(phi, lam, a, b, e0, f0, PHI0, LAM0)
'Project Latitude and longitude to Transverse Mercator eastings.
'Input: - _
Latitude (PHI) and Longitude (LAM) in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
eastings of false origin (e0) in meters; _
central meridian scale factor (f0); _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
IV = nu * (Cos(RadPHI))
V = (nu / 6) * ((Cos(RadPHI)) ^ 3) * ((nu / rho) - ((Tan(RadPHI) ^ 2)))
VI = (nu / 120) * ((Cos(RadPHI)) ^ 5) * (5 - (18 * ((Tan(RadPHI)) ^ 2)) + ((Tan(RadPHI)) ^ 4) + (14 * eta2) - (58 * ((Tan(RadPHI)) ^ 2) * eta2))
Lat_Long_to_East = e0 + (P * IV) + ((P ^ 3) * V) + ((P ^ 5) * VI)
End Function
Function Lat_Long_to_North(phi, lam, a, b, e0, n0, f0, PHI0, LAM0)
'Project Latitude and longitude to Transverse Mercator northings
'Input: - _
Latitude (PHI) and Longitude (LAM) in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0); _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" FUNCTION
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
M = Marc(bf0, N, RadPHI0, RadPHI)
i = M + n0
II = (nu / 2) * (sIn(RadPHI)) * (Cos(RadPHI))
III = ((nu / 24) * (sIn(RadPHI)) * ((Cos(RadPHI)) ^ 3)) * (5 - ((Tan(RadPHI)) ^ 2) + (9 * eta2))
IIIA = ((nu / 720) * (sIn(RadPHI)) * ((Cos(RadPHI)) ^ 5)) * (61 - (58 * ((Tan(RadPHI)) ^ 2)) + ((Tan(RadPHI)) ^ 4))
Lat_Long_to_North = i + ((P ^ 2) * II) + ((P ^ 4) * III) + ((P ^ 6) * IIIA)
End Function
Function E_N_to_Lat(East, North, a, b, e0, n0, f0, PHI0, LAM0)
'Un-project Transverse Mercator eastings and northings back to latitude.
'Input: - _
eastings (East) and northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0) and _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Latitude
VII = (Tan(PHId)) / (2 * rho * nu)
VIII = ((Tan(PHId)) / (24 * rho * (nu ^ 3))) * (5 + (3 * ((Tan(PHId)) ^ 2)) + eta2 - (9 * eta2 * ((Tan(PHId)) ^ 2)))
IX = ((Tan(PHId)) / (720 * rho * (nu ^ 5))) * (61 + (90 * ((Tan(PHId)) ^ 2)) + (45 * ((Tan(PHId)) ^ 4)))
E_N_to_Lat = (180 / Pi) * (PHId - ((Et ^ 2) * VII) + ((Et ^ 4) * VIII) - ((Et ^ 6) * IX))
End Function
Function E_N_to_Long(East, North, a, b, e0, n0, f0, PHI0, LAM0)
'Un-project Transverse Mercator eastings and northings back to longitude.
'Input: - _
eastings (East) and northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0) and _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Longitude
x = ((Cos(PHId)) ^ -1) / nu
XI = (((Cos(PHId)) ^ -1) / (6 * (nu ^ 3))) * ((nu / rho) + (2 * ((Tan(PHId)) ^ 2)))
XII = (((Cos(PHId)) ^ -1) / (120 * (nu ^ 5))) * (5 + (28 * ((Tan(PHId)) ^ 2)) + (24 * ((Tan(PHId)) ^ 4)))
XIIA = (((Cos(PHId)) ^ -1) / (5040 * (nu ^ 7))) * (61 + (662 * ((Tan(PHId)) ^ 2)) + (1320 * ((Tan(PHId)) ^ 4)) + (720 * ((Tan(PHId)) ^ 6)))
E_N_to_Long = (180 / Pi) * (RadLAM0 + (Et * x) - ((Et ^ 3) * XI) + ((Et ^ 5) * XII) - ((Et ^ 7) * XIIA))
End Function
Function InitialLat(North, n0, afo, PHI0, N, bfo)
'Compute initial value for Latitude (PHI) IN RADIANS.
'Input: - _
northing of point (North) and northing of false origin (n0) in meters; _
semi major axis multiplied by central meridian scale factor (af0) in meters; _
latitude of false origin (PHI0) IN RADIANS; _
n (computed from a, b and f0) and _
ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters.
'REQUIRES THE "Marc" FUNCTION
'THIS FUNCTION IS CALLED BY THE "E_N_to_Lat", "E_N_to_Long" and "E_N_to_C" FUNCTIONS
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE "Projection and Transformation Calculations.xls" SPREADSHEET
'First PHI value (PHI1)
PHI1 = ((North - n0) / afo) + PHI0
'Calculate M
M = Marc(bfo, N, PHI0, PHI1)
'Calculate new PHI value (PHI2)
phi2 = ((North - n0 - M) / afo) + PHI1
'Iterate to get final value for InitialLat
Do While Abs(North - n0 - M) > 0.00001
phi2 = ((North - n0 - M) / afo) + PHI1
M = Marc(bfo, N, PHI0, phi2)
PHI1 = phi2
Loop
InitialLat = phi2
End Function
Function Marc(bf0, N, PHI0, phi)
'Compute meridional arc.
'Input: - _
ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters; _
n (computed from a, b and f0); _
lat of false origin (PHI0) and initial or final latitude of point (PHI) IN RADIANS.
'THIS FUNCTION IS CALLED BY THE - _
"Lat_Long_to_North" and "InitialLat" FUNCTIONS
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE "Projection and Transformation Calculations.xls" SPREADSHEET
Marc = bf0 * (((1 + N + ((5 / 4) * (N ^ 2)) + ((5 / 4) * (N ^ 3))) * (phi - PHI0)) _
- (((3 * N) + (3 * (N ^ 2)) + ((21 /
* (N ^ 3))) * (sIn(phi - PHI0)) * (Cos(phi + PHI0))) _
+ ((((15 / * (N ^ 2)) + ((15 / * (N ^ 3))) * (sIn(2 * (phi - PHI0))) * (Cos(2 * (phi + PHI0)))) _
- (((35 / 24) * (N ^ 3)) * (sIn(3 * (phi - PHI0))) * (Cos(3 * (phi + PHI0)))))
End Function
Function Lat_Long_to_C(phi, lam, LAM0, a, b, f0)
'Compute convergence (in decimal degrees) from latitude and longitude
'Input: - _
latitude (PHI), longitude (LAM) and longitude (LAM0) of false origin in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
central meridian scale factor (f0).
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0 and e squared (e2)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
'Compute nu, rho, eta2 and p
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
'Compute Convergence
XIII = sIn(RadPHI)
XIV = ((sIn(RadPHI) * ((Cos(RadPHI)) ^ 2)) / 3) * (1 + (3 * eta2) + (2 * (eta2 ^ 2)))
XV = ((sIn(RadPHI) * ((Cos(RadPHI)) ^ 4)) / 15) * (2 - ((Tan(RadPHI)) ^ 2))
Lat_Long_to_C = (180 / Pi) * ((P * XIII) + ((P ^ 3) * XIV) + ((P ^ 5) * XV))
End Function
Function E_N_to_C(East, North, a, b, e0, n0, f0, PHI0)
'Compute convergence (in decimal degrees) from easting and northing
'Input: - _
Eastings (East) and Northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
easting (e0) and northing (n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Convergence
XVI = (Tan(PHId)) / nu
XVII = ((Tan(PHId)) / (3 * (nu ^ 3))) * (1 + ((Tan(PHId)) ^ 2) - eta2 - (2 * (eta2 ^ 2)))
XVIII = ((Tan(PHId)) / (15 * (nu ^ 5))) * (2 + (5 * ((Tan(PHId)) ^ 2)) + (3 * ((Tan(PHId)) ^ 4)))
E_N_to_C = (180 / Pi) * ((Et * XVI) - ((Et ^ 3) * XVII) + ((Et ^ 5) * XVIII))
End Function
Function Lat_Long_to_LSF(phi, lam, LAM0, a, b, f0)
'Compute local scale factor from latitude and longitude
'Input: - _
latitude (PHI), longitude (LAM) and longitude (LAM0) of false origin in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
central meridian scale factor (f0).
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0 and e squared (e2)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
'Compute nu, rho, eta2 and p
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
'Compute local scale factor
XIX = ((Cos(RadPHI) ^ 2) / 2) * (1 + eta2)
XX = ((Cos(RadPHI) ^ 4) / 24) * (5 - (4 * ((Tan(RadPHI)) ^ 2)) + (14 * eta2) - (28 * ((Tan(RadPHI * eta2)) ^ 2)))
Lat_Long_to_LSF = f0 * (1 + ((P ^ 2) * XIX) + ((P ^ 4) * XX))
End Function
Function E_N_to_LSF(East, North, a, b, e0, n0, f0, PHI0)
'Compute local scale factor from from easting and northing
'Input: - _
Eastings (East) and Northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
easting (e0) and northing (n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute local scale factor
XXI = 1 / (2 * rho * nu)
XXII = (1 + (4 * eta2)) / (24 * (rho ^ 2) * (nu ^ 2))
E_N_to_LSF = f0 * (1 + ((Et ^ 2) * XXI) + ((Et ^ 4) * XXII))
End Function
Function E_N_to_t_minus_T(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute (t-T) correction in decimal degrees at point (AtEast, AtNorth) to point (ToEast,ToNorth)
'Input: - _
Eastings (AtEast) and Northings (AtNorth) in meters, of point where (t-T) is being computed; _
Eastings (ToEast) and Northings (ToNorth) in meters, of point at other end of line to which (t-T) is being computed; _
ellipsoid axis dimensions (a & b) and easting & northing (e0 & n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Nm (Northing of mid point)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Nm = (AtNorth + ToNorth) / 2
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(Nm, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
'Compute (t-T)
XXIII = 1 / (6 * nu * rho)
E_N_to_t_minus_T = (180 / Pi) * ((2 * (AtEast - e0)) + (ToEast - e0)) * (AtNorth - ToNorth) * XXIII
End Function
Function TrueAzimuth(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute true azimuth in decimal degrees at point (AtEast, AtNorth) to point (ToEast,ToNorth)
'Input: - _
Eastings (AtEast) and Northings (AtNorth) in meters, of point where true azimuth is being computed; _
Eastings (ToEast) and Northings (ToNorth) in meters, of point at other end of line to which true azimuth is being computed; _
ellipsoid axis dimensions (a & b) and easting & northing (e0 & n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc", "InitialLat", "t_minus_T" and "E_N_to_C" FUNCTIONS
'Compute eastings and northings differences
Diffe = ToEast - AtEast
Diffn = ToNorth - AtNorth
'Compute grid bearing
If Diffe = 0 Then
If Diffn < 0 Then
GridBearing = 180
Else
GridBearing = 0
End If
GoTo EndOfComputeBearing
End If
Ratio = Diffn / Diffe
GridAngle = (180 / Pi) * Atn(Ratio)
If Diffe > 0 Then
GridBearing = 90 - GridAngle
End If
If Diffe < 0 Then
GridBearing = 270 - GridAngle
End If
EndOfComputeBearing:
'Compute convergence
Convergence = E_N_to_C(AtEast, AtNorth, a, b, e0, n0, f0, PHI0)
'Compute (t-T) correction
t_minus_T = E_N_to_t_minus_T(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute true azimuth
TrueAzimuth = GridBearing + Convergence - t_minus_T
End Function
schaut euch mal das an was ich gefunden habe.
--------------------------------------------------------------------------
'********************************************************************************************* _
THE FUNCTIONS IN THIS MODULE ARE WRITTEN TO BE "STAND ALONE" WITH AS LITTLE DEPENDANCE _
ON OTHER FUNCTIONS AS POSSIBLE. THIS MAKES THEM EASIER TO COPY TO OTHER VB APPLICATIONS. _
WHERE A FUNCTION DOES CALL ANOTHER FUNCTION THIS IS STATED IN THE COMMENTS AT THE START OF _
THE FUNCTION. _
*********************************************************************************************
Private Const Pi = 3.14159265358979
Function Lat_Long_H_to_X(phi, lam, H, a, b)
'1.Schritt ???
'Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian X coordinate.
'Input: - _
Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute X
Lat_Long_H_to_X = (V + H) * (Cos(RadPHI)) * (Cos(RadLAM))
End Function
Function Helmert_X(x, y, z, dX, Y_Rot, Z_Rot, S)
'2.Schritt
'Computed Helmert transformed X coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), X translation (DX) all in meters ; _
Y and Z rotations in seconds of arc (Y_Rot, Z_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadY_Rot = (Y_Rot / 3600) * (Pi / 180)
RadZ_Rot = (Z_Rot / 3600) * (Pi / 180)
'Compute transformed X coord
Helmert_X = x + (x * sfactor) - (y * RadZ_Rot) + (z * RadY_Rot) + dX
End Function
Function Helmert_Y(x, y, z, dY, X_Rot, Z_Rot, S)
'2a Schritt
'Computed Helmert transformed Y coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), Y translation (DY) all in meters ; _
X and Z rotations in seconds of arc (X_Rot, Z_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadX_Rot = (X_Rot / 3600) * (Pi / 180)
RadZ_Rot = (Z_Rot / 3600) * (Pi / 180)
'Compute transformed Y coord
Helmert_Y = (x * RadZ_Rot) + y + (y * sfactor) - (z * RadX_Rot) + dY
End Function
Function Helmert_Z(x, y, z, dZ, X_Rot, Y_Rot, S)
'2b Schritt
'Computed Helmert transformed Z coordinate.
'Input: - _
cartesian XYZ coords (X,Y,Z), Z translation (DZ) all in meters ; _
X and Y rotations in seconds of arc (X_Rot, Y_Rot) and scale in ppm (s).
'Convert rotations to radians and ppm scale to a factor
sfactor = S * 0.000001
RadX_Rot = (X_Rot / 3600) * (Pi / 180)
RadY_Rot = (Y_Rot / 3600) * (Pi / 180)
'Compute transformed Z coord
Helmert_Z = (-1 * x * RadY_Rot) + (y * RadX_Rot) + z + (z * sfactor) + dZ
End Function
Function XYZ_to_Lat(x, y, z, a, b)
'Convert XYZ to Latitude (PHI) in Dec Degrees.
'Input: - _
XYZ cartesian coords (X,Y,Z) and ellipsoid axis dimensions (a & b), all in meters.
'THIS FUNCTION REQUIRES THE "Iterate_XYZ_to_Lat" FUNCTION
'THIS FUNCTION IS CALLED BY THE "XYZ_to_H" FUNCTION
RootXYSqr = Sqr((x ^ 2) + (y ^ 2))
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
PHI1 = Atn(z / (RootXYSqr * (1 - e2)))
phi = Iterate_XYZ_to_Lat(a, e2, PHI1, z, RootXYSqr)
XYZ_to_Lat = phi * (180 / Pi)
End Function
Function Iterate_XYZ_to_Lat(a, e2, PHI1, z, RootXYSqr)
'Iteratively computes Latitude (PHI).
'Input: - _
ellipsoid semi major axis (a) in meters; _
eta squared (e2); _
estimated value for latitude (PHI1) in radians; _
cartesian Z coordinate (Z) in meters; _
RootXYSqr computed from X & Y in meters.
'THIS FUNCTION IS CALLED BY THE "XYZ_to_PHI" FUNCTION
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE _
"Projection and Transformation Calculations.xls" SPREADSHEET
V = a / (Sqr(1 - (e2 * ((sIn(PHI1)) ^ 2))))
phi2 = Atn((z + (e2 * V * (sIn(PHI1)))) / RootXYSqr)
Do While Abs(PHI1 - phi2) > 0.000000001
PHI1 = phi2
V = a / (Sqr(1 - (e2 * ((sIn(PHI1)) ^ 2))))
phi2 = Atn((z + (e2 * V * (sIn(PHI1)))) / RootXYSqr)
Loop
Iterate_XYZ_to_Lat = phi2
End Function
Function XYZ_to_Long(x, y)
'Convert XYZ to Longitude (LAM) in Dec Degrees.
'Input: - _
X and Y cartesian coords in meters.
XYZ_to_Long = (Atn(y / x)) * (180 / Pi)
End Function
Function XYZ_to_H(x, y, z, a, b)
'Convert XYZ to Ellipsoidal Height.
'Input: - _
XYZ cartesian coords (X,Y,Z) and ellipsoid axis dimensions (a & b), all in meters.
'REQUIRES THE "XYZ_to_Lat" FUNCTION
'Compute PHI (Dec Degrees) first
phi = XYZ_to_Lat(x, y, z, a, b)
'Convert PHI radians
RadPHI = phi * (Pi / 180)
'Compute H
RootXYSqr = Sqr((x ^ 2) + (y ^ 2))
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
H = (RootXYSqr / Cos(RadPHI)) - V
XYZ_to_H = H
End Function
Function Lat_Long_H_to_Y(phi, lam, H, a, b)
'Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian Y coordinate.
'Input: - _
Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute Y
Lat_Long_H_to_Y = (V + H) * (Cos(RadPHI)) * (sIn(RadLAM))
End Function
Function Lat_H_to_Z(phi, H, a, b)
'Convert geodetic coord components latitude (PHI) and height (H) to cartesian Z coordinate.
'Input: - _
Latitude (PHI) decimal degrees; _
Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
'Compute eccentricity squared and nu
e2 = ((a ^ 2) - (b ^ 2)) / (a ^ 2)
V = a / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
'Compute X
Lat_H_to_Z = ((V * (1 - e2)) + H) * (sIn(RadPHI))
End Function
Function Lat_Long_to_East(phi, lam, a, b, e0, f0, PHI0, LAM0)
'Project Latitude and longitude to Transverse Mercator eastings.
'Input: - _
Latitude (PHI) and Longitude (LAM) in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
eastings of false origin (e0) in meters; _
central meridian scale factor (f0); _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
IV = nu * (Cos(RadPHI))
V = (nu / 6) * ((Cos(RadPHI)) ^ 3) * ((nu / rho) - ((Tan(RadPHI) ^ 2)))
VI = (nu / 120) * ((Cos(RadPHI)) ^ 5) * (5 - (18 * ((Tan(RadPHI)) ^ 2)) + ((Tan(RadPHI)) ^ 4) + (14 * eta2) - (58 * ((Tan(RadPHI)) ^ 2) * eta2))
Lat_Long_to_East = e0 + (P * IV) + ((P ^ 3) * V) + ((P ^ 5) * VI)
End Function
Function Lat_Long_to_North(phi, lam, a, b, e0, n0, f0, PHI0, LAM0)
'Project Latitude and longitude to Transverse Mercator northings
'Input: - _
Latitude (PHI) and Longitude (LAM) in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0); _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" FUNCTION
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
M = Marc(bf0, N, RadPHI0, RadPHI)
i = M + n0
II = (nu / 2) * (sIn(RadPHI)) * (Cos(RadPHI))
III = ((nu / 24) * (sIn(RadPHI)) * ((Cos(RadPHI)) ^ 3)) * (5 - ((Tan(RadPHI)) ^ 2) + (9 * eta2))
IIIA = ((nu / 720) * (sIn(RadPHI)) * ((Cos(RadPHI)) ^ 5)) * (61 - (58 * ((Tan(RadPHI)) ^ 2)) + ((Tan(RadPHI)) ^ 4))
Lat_Long_to_North = i + ((P ^ 2) * II) + ((P ^ 4) * III) + ((P ^ 6) * IIIA)
End Function
Function E_N_to_Lat(East, North, a, b, e0, n0, f0, PHI0, LAM0)
'Un-project Transverse Mercator eastings and northings back to latitude.
'Input: - _
eastings (East) and northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0) and _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Latitude
VII = (Tan(PHId)) / (2 * rho * nu)
VIII = ((Tan(PHId)) / (24 * rho * (nu ^ 3))) * (5 + (3 * ((Tan(PHId)) ^ 2)) + eta2 - (9 * eta2 * ((Tan(PHId)) ^ 2)))
IX = ((Tan(PHId)) / (720 * rho * (nu ^ 5))) * (61 + (90 * ((Tan(PHId)) ^ 2)) + (45 * ((Tan(PHId)) ^ 4)))
E_N_to_Lat = (180 / Pi) * (PHId - ((Et ^ 2) * VII) + ((Et ^ 4) * VIII) - ((Et ^ 6) * IX))
End Function
Function E_N_to_Long(East, North, a, b, e0, n0, f0, PHI0, LAM0)
'Un-project Transverse Mercator eastings and northings back to longitude.
'Input: - _
eastings (East) and northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
eastings (e0) and northings (n0) of false origin in meters; _
central meridian scale factor (f0) and _
latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Longitude
x = ((Cos(PHId)) ^ -1) / nu
XI = (((Cos(PHId)) ^ -1) / (6 * (nu ^ 3))) * ((nu / rho) + (2 * ((Tan(PHId)) ^ 2)))
XII = (((Cos(PHId)) ^ -1) / (120 * (nu ^ 5))) * (5 + (28 * ((Tan(PHId)) ^ 2)) + (24 * ((Tan(PHId)) ^ 4)))
XIIA = (((Cos(PHId)) ^ -1) / (5040 * (nu ^ 7))) * (61 + (662 * ((Tan(PHId)) ^ 2)) + (1320 * ((Tan(PHId)) ^ 4)) + (720 * ((Tan(PHId)) ^ 6)))
E_N_to_Long = (180 / Pi) * (RadLAM0 + (Et * x) - ((Et ^ 3) * XI) + ((Et ^ 5) * XII) - ((Et ^ 7) * XIIA))
End Function
Function InitialLat(North, n0, afo, PHI0, N, bfo)
'Compute initial value for Latitude (PHI) IN RADIANS.
'Input: - _
northing of point (North) and northing of false origin (n0) in meters; _
semi major axis multiplied by central meridian scale factor (af0) in meters; _
latitude of false origin (PHI0) IN RADIANS; _
n (computed from a, b and f0) and _
ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters.
'REQUIRES THE "Marc" FUNCTION
'THIS FUNCTION IS CALLED BY THE "E_N_to_Lat", "E_N_to_Long" and "E_N_to_C" FUNCTIONS
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE "Projection and Transformation Calculations.xls" SPREADSHEET
'First PHI value (PHI1)
PHI1 = ((North - n0) / afo) + PHI0
'Calculate M
M = Marc(bfo, N, PHI0, PHI1)
'Calculate new PHI value (PHI2)
phi2 = ((North - n0 - M) / afo) + PHI1
'Iterate to get final value for InitialLat
Do While Abs(North - n0 - M) > 0.00001
phi2 = ((North - n0 - M) / afo) + PHI1
M = Marc(bfo, N, PHI0, phi2)
PHI1 = phi2
Loop
InitialLat = phi2
End Function
Function Marc(bf0, N, PHI0, phi)
'Compute meridional arc.
'Input: - _
ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters; _
n (computed from a, b and f0); _
lat of false origin (PHI0) and initial or final latitude of point (PHI) IN RADIANS.
'THIS FUNCTION IS CALLED BY THE - _
"Lat_Long_to_North" and "InitialLat" FUNCTIONS
'THIS FUNCTION IS ALSO USED ON IT'S OWN IN THE "Projection and Transformation Calculations.xls" SPREADSHEET
Marc = bf0 * (((1 + N + ((5 / 4) * (N ^ 2)) + ((5 / 4) * (N ^ 3))) * (phi - PHI0)) _
- (((3 * N) + (3 * (N ^ 2)) + ((21 /
* (N ^ 3))) * (sIn(phi - PHI0)) * (Cos(phi + PHI0))) _+ ((((15 /
* (N ^ 2)) + ((15 / * (N ^ 3))) * (sIn(2 * (phi - PHI0))) * (Cos(2 * (phi + PHI0)))) _- (((35 / 24) * (N ^ 3)) * (sIn(3 * (phi - PHI0))) * (Cos(3 * (phi + PHI0)))))
End Function
Function Lat_Long_to_C(phi, lam, LAM0, a, b, f0)
'Compute convergence (in decimal degrees) from latitude and longitude
'Input: - _
latitude (PHI), longitude (LAM) and longitude (LAM0) of false origin in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
central meridian scale factor (f0).
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0 and e squared (e2)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
'Compute nu, rho, eta2 and p
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
'Compute Convergence
XIII = sIn(RadPHI)
XIV = ((sIn(RadPHI) * ((Cos(RadPHI)) ^ 2)) / 3) * (1 + (3 * eta2) + (2 * (eta2 ^ 2)))
XV = ((sIn(RadPHI) * ((Cos(RadPHI)) ^ 4)) / 15) * (2 - ((Tan(RadPHI)) ^ 2))
Lat_Long_to_C = (180 / Pi) * ((P * XIII) + ((P ^ 3) * XIV) + ((P ^ 5) * XV))
End Function
Function E_N_to_C(East, North, a, b, e0, n0, f0, PHI0)
'Compute convergence (in decimal degrees) from easting and northing
'Input: - _
Eastings (East) and Northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
easting (e0) and northing (n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute Convergence
XVI = (Tan(PHId)) / nu
XVII = ((Tan(PHId)) / (3 * (nu ^ 3))) * (1 + ((Tan(PHId)) ^ 2) - eta2 - (2 * (eta2 ^ 2)))
XVIII = ((Tan(PHId)) / (15 * (nu ^ 5))) * (2 + (5 * ((Tan(PHId)) ^ 2)) + (3 * ((Tan(PHId)) ^ 4)))
E_N_to_C = (180 / Pi) * ((Et * XVI) - ((Et ^ 3) * XVII) + ((Et ^ 5) * XVIII))
End Function
Function Lat_Long_to_LSF(phi, lam, LAM0, a, b, f0)
'Compute local scale factor from latitude and longitude
'Input: - _
latitude (PHI), longitude (LAM) and longitude (LAM0) of false origin in decimal degrees; _
ellipsoid axis dimensions (a & b) in meters; _
central meridian scale factor (f0).
'Convert angle measures to radians
RadPHI = phi * (Pi / 180)
RadLAM = lam * (Pi / 180)
RadLAM0 = LAM0 * (Pi / 180)
'Compute af0, bf0 and e squared (e2)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
'Compute nu, rho, eta2 and p
nu = af0 / (Sqr(1 - (e2 * ((sIn(RadPHI)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(RadPHI)) ^ 2))
eta2 = (nu / rho) - 1
P = RadLAM - RadLAM0
'Compute local scale factor
XIX = ((Cos(RadPHI) ^ 2) / 2) * (1 + eta2)
XX = ((Cos(RadPHI) ^ 4) / 24) * (5 - (4 * ((Tan(RadPHI)) ^ 2)) + (14 * eta2) - (28 * ((Tan(RadPHI * eta2)) ^ 2)))
Lat_Long_to_LSF = f0 * (1 + ((P ^ 2) * XIX) + ((P ^ 4) * XX))
End Function
Function E_N_to_LSF(East, North, a, b, e0, n0, f0, PHI0)
'Compute local scale factor from from easting and northing
'Input: - _
Eastings (East) and Northings (North) in meters; _
ellipsoid axis dimensions (a & b) in meters; _
easting (e0) and northing (n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Et
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Et = East - e0
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(North, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
eta2 = (nu / rho) - 1
'Compute local scale factor
XXI = 1 / (2 * rho * nu)
XXII = (1 + (4 * eta2)) / (24 * (rho ^ 2) * (nu ^ 2))
E_N_to_LSF = f0 * (1 + ((Et ^ 2) * XXI) + ((Et ^ 4) * XXII))
End Function
Function E_N_to_t_minus_T(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute (t-T) correction in decimal degrees at point (AtEast, AtNorth) to point (ToEast,ToNorth)
'Input: - _
Eastings (AtEast) and Northings (AtNorth) in meters, of point where (t-T) is being computed; _
Eastings (ToEast) and Northings (ToNorth) in meters, of point at other end of line to which (t-T) is being computed; _
ellipsoid axis dimensions (a & b) and easting & northing (e0 & n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc" AND "InitialLat" FUNCTIONS
'Convert angle measures to radians
RadPHI0 = PHI0 * (Pi / 180)
'Compute af0, bf0, e squared (e2), n and Nm (Northing of mid point)
af0 = a * f0
bf0 = b * f0
e2 = ((af0 ^ 2) - (bf0 ^ 2)) / (af0 ^ 2)
N = (af0 - bf0) / (af0 + bf0)
Nm = (AtNorth + ToNorth) / 2
'Compute initial value for latitude (PHI) in radians
PHId = InitialLat(Nm, n0, af0, RadPHI0, N, bf0)
'Compute nu, rho and eta2 using value for PHId
nu = af0 / (Sqr(1 - (e2 * ((sIn(PHId)) ^ 2))))
rho = (nu * (1 - e2)) / (1 - (e2 * (sIn(PHId)) ^ 2))
'Compute (t-T)
XXIII = 1 / (6 * nu * rho)
E_N_to_t_minus_T = (180 / Pi) * ((2 * (AtEast - e0)) + (ToEast - e0)) * (AtNorth - ToNorth) * XXIII
End Function
Function TrueAzimuth(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute true azimuth in decimal degrees at point (AtEast, AtNorth) to point (ToEast,ToNorth)
'Input: - _
Eastings (AtEast) and Northings (AtNorth) in meters, of point where true azimuth is being computed; _
Eastings (ToEast) and Northings (ToNorth) in meters, of point at other end of line to which true azimuth is being computed; _
ellipsoid axis dimensions (a & b) and easting & northing (e0 & n0) of true origin in meters; _
central meridian scale factor (f0); _
latitude of central meridian (PHI0) in decimal degrees.
'REQUIRES THE "Marc", "InitialLat", "t_minus_T" and "E_N_to_C" FUNCTIONS
'Compute eastings and northings differences
Diffe = ToEast - AtEast
Diffn = ToNorth - AtNorth
'Compute grid bearing
If Diffe = 0 Then
If Diffn < 0 Then
GridBearing = 180
Else
GridBearing = 0
End If
GoTo EndOfComputeBearing
End If
Ratio = Diffn / Diffe
GridAngle = (180 / Pi) * Atn(Ratio)
If Diffe > 0 Then
GridBearing = 90 - GridAngle
End If
If Diffe < 0 Then
GridBearing = 270 - GridAngle
End If
EndOfComputeBearing:
'Compute convergence
Convergence = E_N_to_C(AtEast, AtNorth, a, b, e0, n0, f0, PHI0)
'Compute (t-T) correction
t_minus_T = E_N_to_t_minus_T(AtEast, AtNorth, ToEast, ToNorth, a, b, e0, n0, f0, PHI0)
'Compute true azimuth
TrueAzimuth = GridBearing + Convergence - t_minus_T
End Function
-
mactoolz
Hallo MacToolz,
ich schwanke hin und her.
Einerseits würde ich Dir gern helfen, da es hier um Kernfragen der Landesvermessung geht. Ich habe einige Unterlagen gefunden und entstaubt, meine Gehirnzellen noch nicht ...
Andererseits möchte ich Dich fragen, ob Du uns verarschen willst. Die zuletzt zitierten Formeln sehen wie eine 3D-Tranformation aus. Bei dem auf meinem Monitor erscheinenden Grinsgesicht gehört m.W. eine 8 gesetzt.
Bitte: Was soll das ?
Scheinbar hat sogar Hartmut inzwischen hingeschmissen.
Roland
ich schwanke hin und her.
Einerseits würde ich Dir gern helfen, da es hier um Kernfragen der Landesvermessung geht. Ich habe einige Unterlagen gefunden und entstaubt, meine Gehirnzellen noch nicht ...
Andererseits möchte ich Dich fragen, ob Du uns verarschen willst. Die zuletzt zitierten Formeln sehen wie eine 3D-Tranformation aus. Bei dem auf meinem Monitor erscheinenden Grinsgesicht gehört m.W. eine 8 gesetzt.
Bitte: Was soll das ?
Scheinbar hat sogar Hartmut inzwischen hingeschmissen.
Roland
Hallo macnetz,
Du hattest Dich aus dem Fenster gelehnt
http://de.wikipedia.org/wiki/Rauenberg% ... 5FPunkt%29
Dazu zitiere ich noch eine geodätische Koryphäe, Prof. Wolf, aus einem Beitrag von 1987:
"Umso weniger verständlich erscheint die für das Deutsche Hauptdreiecksnetz . . . beschlossene Datumsbezeichnung, nämlich "Potsdam-Datum (Zentralpunkt Rauenberg)", welche den grundlegenden Unterschied von "Rauenberg-Datum" und "Potsdam-Datum" verwischt und daher zu Unklarheiten bzw. Verwechslungen führen dürfte ..."
Die Landesvermessung des Ordnance Survey in Großbritannien bezieht sich auf einen Meridian 18 ft westlich des Greenwicher Meridians - und der WGS84-/"GPS"-Meridian liegt 338 ft östlich
(bei den kursiven Angaben könnte auch das Gegenteil richtig sein ).
http://www.hardwick-cambs.org.uk/milenium/meridian.htm
Grüße Roland
Du hattest Dich aus dem Fenster gelehnt
Also der Datumspunkt der deutschen Landesvermessung ist der ca. 1910 zerstörte TP Rauenberg in BerlinDie kartografische Vermessung des deutschen Reiches bezieht sich auf Potsdam, die italienische Kartografie auf die Sternwarte des Vatikanstaats (Monte Mario), die Kartografie der K&K-Monarchie bezieht sich auf die alte Westgrenze des Habsburgerreiches auf der Kanareninsel El Hierro, und das Britische Empire bezieht sich auf die Sternwarte von Greenwich.
http://de.wikipedia.org/wiki/Rauenberg% ... 5FPunkt%29
Dazu zitiere ich noch eine geodätische Koryphäe, Prof. Wolf, aus einem Beitrag von 1987:
"Umso weniger verständlich erscheint die für das Deutsche Hauptdreiecksnetz . . . beschlossene Datumsbezeichnung, nämlich "Potsdam-Datum (Zentralpunkt Rauenberg)", welche den grundlegenden Unterschied von "Rauenberg-Datum" und "Potsdam-Datum" verwischt und daher zu Unklarheiten bzw. Verwechslungen führen dürfte ..."
Die Landesvermessung des Ordnance Survey in Großbritannien bezieht sich auf einen Meridian 18 ft westlich des Greenwicher Meridians - und der WGS84-/"GPS"-Meridian liegt 338 ft östlich
(bei den kursiven Angaben könnte auch das Gegenteil richtig sein ).
http://www.hardwick-cambs.org.uk/milenium/meridian.htm
Grüße Roland