**Theory**

The inverse of a spherical coordinate can be calculated by taking the inverse of the latitude (θ) and offsetting the longitude (Φ) by 180˚. The following formulas can be used to calculate these values.

The sgn function, known as the sign function and signum function, is a complex function that extracts the sign of a real number. This function has the following characteristics:

The inverse of a Cartesian coordinate can be calculated by taking the x, y, and z components of the coordinate and multiply them by -1.

**Application**

The function to calculate the inverse coordinate will take in a VELatLong object and will return a VELatLong object. There is not a *sgn* function in the JavaScript Math class but we can do this using simple logic.

function inverseSpherical(latlong)

{

var lat = -1*latlong.Latitude;

var lon = 180-Math.abs(latlong.Longitude);

if(latlong.Longitude>0)

lon *= -1;

return new VELatLong(lat,lon);

}

Listing 1 Inverse Spherical Coordinate

The following algorithm calculates the inverse coordinate of a Cartesian coordinate. This algorithm takes in a Cartesian coordinate and returns a Cartesian coordinate.

function inverseCartesian(p1)

{

return new Cartesian(-1*p1.X,-1*p1.Y,-1*p1.Z);

}

Listing 2 Inverse Cartesian Coordinate

The following post has additional information on the Cartesian object: http://rbrundritt.spaces.live.com/blog/cns!E7DBA9A4BFD458C5!280.entry

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