EPSG Dataset :: v12.054

Vertical Perspective

Coordinate Operation Method Details [VALID]

Name:

Vertical Perspective

Code:

9838

Operation is Reversible:

Formula:

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

This general case deals with a viewing point at a finite height hv above the origin. If the viewing point is at infinity, the formulas for the orthographic case (method code 9839) should be used.

The forward equations for the Vertical Perspective to convert geographical 3D coordinates (lat, lon, h) to Easting (E) and Northing (N) begin with the formulas of thje Geographic/topocentric conversions method (code 9836) to convert the geographical coordinates to topocentric coordinates U, V, W. The perspective projection origin is coincident with the topographic origin and has coordinates (latO, lonO, hO).

U = (nu + h) cos P sin (L – Lo)
V = (nu + h) [sin P cos Po – cos P sin Po cos (L – Lo)] + e^2 (nuO sin Po – nu sin P ) cos Po
W = (nu + h) [sin P sin Po + cos P cos Po cos (L – Lo)] + e^2 (nuO sin Po – nu sin P ) sin Po – (nuO – ho)

Then, given the height hv of the perspective viewing point above the origin, the perspective coordinates (E, N) are calculated from topocentric coordinates (U, V, W) as:

E = U * hv / (hv – W)
N = V * hv / (hv – W)

The reverse calculation from E,N to U,V,W and lat,lon,h is indeterminate.

Example:

See EPSG Guidance Note 7-2.

Method
Parameters:

Parameter Name	Parameter Code	Parameter Description
Latitude of topocentric origin	8834	For topocentric CSs, the latitude of the topocentric origin.
Longitude of topocentric origin	8835	For topocentric CSs, the longitude of the topocentric origin.
Ellipsoidal height of topocentric origin	8836	For topocentric CSs, the ellipsoidal height of the topocentric origin.
Viewpoint height	8840	For vertical perspective projections, the height of viewpoint above the topocentric origin.

Meta Data

Remarks:

For a viewing point height approaching or at infinity, see the Vertical Perspective (orthographic case) (method code 9839).

Information Source:

EPSG guidance note #7-2, http://www.epsg.org

Data Source:

EPSG

Revision Date:

June 13, 2017

Change ID:

[2017.018]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.