Finding the world position of the first point of a grid

Hello Lotfi

A grid by nature is a two-dimensional arrangement of point locations, with its own attached two-dimensional coordinate system, whose axes we will call X’ and Y’. Normally its rows line up with X’ and its columns with Y’.

In order to properly locate a grid in “real” three-dimensional XYZ space, we make use of an “orientation” object, which defines where the grid’s coordinate system origin is anchored, and where the grid axes point. In short, it defines the location and orientation of the infinite plane on which the grid is located.
The plane origin is the XYZ location in real-world coordinates of the plane origin point, that is (0, 0) in the grid coordinates. From this anchor point extend the grid coordinate axes.

In your example, this is the location X = 0, Y = 6678350, and Z = 0.

For (most) section grids, the grid’s X-coordinate axis runs parallel to the ground, and the direction it points is defined by the section azimuth, which is the angle the X-axis makes with the real-world Y (northing) axis, measured clockwise from north (the original version of this note was incorrect!).

Because your grid azimuth is 90°, the grid’s X’-axis is parallel to the world X-axis, and because the grid X’-origin is found at X = 0, all the grid X’ locations line up with the world X-axis (easting) values. This also means that the grid first point location X’ = 410.256 corresponds to X = 410.256.

The section swing is defined as the angle the grid’s Y’ axis makes with Z (vertical), measured counter-clock-wise looking along the grid’s X’ axis. For a vertical section, the swing is 0°. Because your grid is vertical, and because the grid Y’ axis origin is located at Z = 0, all the grid Y’ locations line up with the world Z-axis (elevation) values. This also means that the grid first point location Y’ = 4.125 corresponds to Z = 4.125.
Finally, because the grid is vertical and runs E-W, the entire grid coordinate plane has the same Y value, which is the same as the plane origin Y value, Y = 6678350.

So, in summary, for your grid, the first point is at (410.225, 6678350, 4.125).

For vertical section grids (swing = 0), we can use the following formula to find the first point location:

X = X0 + XG * sin ( azimuth )
Y = Y0 + XG * cos ( azimuth )
Z = Z0 + YG

Where

(X0, Y0, Z0) is the plane origin
(XG, YG) is the grid origin (first point location)

Note that in this context the grid “origin” is a confusing term, as it is not an origin in the (0, 0) sense, but in the sense that it is the start of the grid. In most cases the grid origin and the grid axis origin are two entirely different things.

For non-zero values of swing the level of complication increases substantially and deserves its own discussion. For instance, the Y’-axis is stretched so that grid Y-axis values continue to be able to represent real-world elevations.

You will notice that in the above discussion I never made reference to the grid rotation. The grid rotation is defined as a clock-wise rotation of the grid about its starting (origin) point. Because grid rotation introduces an additional complication on top of the grid-plane orientation, you will never find a Geosoft-produced grid that combines both a 3-dimensional orientation with a grid rotation. It is Geosoft practice, instead, to leave the grid rotation angle at zero and put all the grid location and orientation information into the orientation object. For your purposes you can simply ignore it.

Sincerely,

Stephen Cheesman
Senior Application Architect,
Geosoft Inc.

Hello Lotfi

1. Geosoft’s *.gi files contain projection and orientation information that cannot be stored in the file itself. So grids in any orientation – rotated or non-rotated, horizontal, vertical or angled, will usually have a *.gi file, and any grid to which a geographical or projected coordinate has been applied will certainly have one.

2. Geosoft grids can have their own "native" rotation angle, so even in the absence of a *.gi file they can show a rotation when displayed in a plan map. But using the grid rotation property to show rotation is really the “old” way of doing things, and using an orientation object (with or without an accompanying projection) is a much more general and powerful way to orient a grid in space, and that information requires the *.gi file for storage. We would discourage trying to combine the native grid rotation with an orientation definition, as the results may not be well-defined (which is a delicate way of stating we have not spent a great deal of time testing the combination throughout all aspects of the code). So create a grid without setting its rotation angle, determine which earth projection you are using, then orient the grid with respect to the projected coordinate system by defining an orientation, which is a local coordinate system defined with respect to the projected coordinate system.

You should never try to modify or deconstruct a *.gi file (which is not a text file anyway); always use the GX developer library methods to get and set projection and orientation information.

Sincerely,
Stephen