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Geodetic Surveying: Aligning Local Astronomical Axes with Conventional Terrestrial Axes

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This VRML module demonstrate the conversion of local vs. "universal" conventional terrestrial coordinates used in three-dimensional geodetic surveys.

3D Animation

You will need a VRML 2.0 viewer to see the illustration below. Please download the Cortona vrml plug-in.

Click here for the VRML Animation Within the animation you will see three buttons:

Conventional Terrestrial Coordinate System of the Earth

Conventional Terrestrial Coordinate System. Description in text.

Click on the image to enlarge.

When determining the position of a point on the Earth within a three-dimensional space, one method is to use the Conventional Terrestrial (CT) coordinate system: a Cartesian coordinate system with x, y, and z axes.

In this coordinate system,

The conventional terrestrial pole is commonly referred to as the Earth's North Pole.

Local Astronomical Coordinates

Local Astronomical Coordinate. Description in text.

Click on the image to enlarge.

Surveyors generally use a three-dimensional Cartesian system called the Local Astronomical (LA) coordinates to describe positions in reference to their own location.

In this coordinate system:

Note that unless the observer is at the North Pole, the direction of the U axis (local astronomical z axis) will not align with the Z axis in the CT coordinate system.

Aligning the Two Coordinate Systems

To align local astronomical coordinates (LA) with a conventional terrestrial coordinate system you will need to perform mathematical conversions which "rotate" the LA coordinates around two axes.

The first rotation is around the E axis (LA y axis) and "pushes" the N axis (x-axis) down until the NE plane is parallel with the Earth's equator. The U axis (z axis) is now parallel with the CTP (North pole) and the N axis in the LA system is now pointing into the earth.

The second rotation is around the U axis in the LA system and aligns the once-rotated LA N axis with the CT x-axis in equatorial plane.

Because the LA coordinate system is a left-handed coordinate system and the CT coordinate system is a right-handed coordinate system, the East axis will be pointing 180° away from the CT y-axis (that is, west from the observer).

To make the systems truly align, a negative sign is introduced in the LA y-axis.

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