The Inverse option may be used to derive geodetic quantities for a single specified point, or for any two points and an imaginary or existing line between them. In the case of a plane projection, only the plane geometric values are displayed.

The required points are specified by point numbers; therefore the points must already exist in the database. The green fields indicate point values stored in the database (either grid or geographic coordinates). Note - some accuracy of derived coordinate values may be lost in the grid-to-geographic or geographic-to-grid conversions, depending on the form in which points are stored in the database.

NOTE - When deriving inverse details between points near the extreme northern or southern limits of a projection or where the points are separated by very large distances particularly in high latitudes, the distances and azimuths computed may sometimes appear to be incorrect. However the computation uses rigorous geodetic formulae and the quantities derived should nevertheless be correct - consideration of the relative positions of the points on the surface of the Earth's globe, should dispel any concerns.

The Inverse window is displayed when this option is selected.

Figure 1: Inverse option

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When Geoida is running, details of the purpose and use of each control in this window will be displayed in the bottom panel when the mouse is passed over any active object.


Azimuth, spheroidal distance, grid convergence and grid bearing

These values are derived from spheroidal grid coordinates using documented formulae for arc-to-chord and line-scale factor corrections, or from the Vincenty Inverse formulae for geographic coordinates. Normal-to-geodesic correction is not applied since the correction only becomes significant for azimuth at distances greater than about 1000 km and for distance after about 2500 km.

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Arc-to-chord and line-scale factor

Arc-to-chord and line-scale factor are computed from 'grid-formulae' which are not rigorous. Consequently, the displayed value for Arc-to-chord correction may be inconsistent in the 2nd decimal place of a second. Grid formulae for Transverse Mercator are quoted as being accurate to 0.02 second and 0.1 ppm over any 100 km line in a standard zone. Any discrepancies in the computed figures should be seen to be consistent with the stated accuracies.

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Points in different zones

If both points are located in different zones or the points are defined in the database as geographic coordinates, the Grid Bearing and Arc-to-Chord values cannot be determined and are not displayed, but the remaining values displayed are valid and correct as they are derived from the latitude and longitude values. Plane Bearing and Plane/Grid Distance values are still computed but are derived as purely plane values, hence caution is required as these may be quite meaningless.

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Geoid-spheroid separation (undulation)

Computations done on the spheroid require geoid-spheroid separation (N-value) correction for distance and height measurements which are based on geoidal (orthometric) heights. If a spheroidal height datum is used, the N-value can therefore be ignored by leaving blank or setting to 0.000. Values for the geoid-spheroid separation will usually be stated on permanent mark summary sheets obtainable from government geodetic authorities, may also be obtained from government authorities as digital data sets for specific locations (eg, in Australia, AUSGEOID98), or may be scaled from geoid-spheroid separation contour charts (eg, See References, The Australian Geodetic Datum - Technical Manual, Annex E).

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Inverse Distances

Where point heights used are spheroidal heights, the value for the geoid-spheroid separation (N) can be omitted, since the spheroidal distance computed between points will be correctly converted back to terrain distance. However, if the vertical datum on which point heights are based is related to the geoid or mean-sea-level and the value of N is not taken into consideration, then 'spheroidal' distances derived by the Inverse option will not be correctly converted back to terrain-height distances. For further details, refer to the heading Distances and Geoid-spheroid Separation in the topic Accuracy.

NOTE - Care should be exercised when extracting data where the coordinate system is set to Grid Projection and the grid selected is defined in the Projection option as a Special-area Project Grid, since terrain-height correction for distances may have been incorporated into the value for the central scale factor. If this is the case (usually), it is the quoted Spheroidal Distance that should be used in place of the Terrain Height distance for setout purposes since a correction for height is currently (v4.32) applied to all grid projection coordinates without distinction between Standard and Special-area Project grids. If height correction has not been incorporated into the value for the central scale factor for a Special-area grid and the distances have been reduced to spheroid height during survey processing, it is correct to use the quoted Terrain Distance. In any case, values computed in Geoida will be more accurate than coordinating and extracting the data using simple plane-geometry techniques as may still be appropriate for a Special-area Project grid. By comparing the listed Spheroidal and Terrain distances over any line, the differences may be assessed and should be found to be minimal or within the allowable tolerance. Refer to Projection and Job Configuration for more information.

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Terrain slope distance

Terrain Slope Distance is derived from Terrain Horizontal Distance and level difference between the points only - this value will be suitable for lines of limited length only.

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For further related details, refer to Accuracy.

Note - The Measure option also uses the Inverse window.

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