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/**
* Computes the fraction of a Web Wercator extent at which a given geodetic latitude is located.
*
* @name czm_latitudeToWebMercatorFraction
* @glslFunction
*
* @param {float} The geodetic latitude, in radians.
* @param {float} The low portion of the Web Mercator coordinate of the southern boundary of the extent.
* @param {float} The high portion of the Web Mercator coordinate of the southern boundary of the extent.
* @param {float} The total height of the extent in Web Mercator coordinates.
*
* @returns {float} The fraction of the extent at which the latitude occurs. If the latitude is the southern
* boundary of the extent, the return value will be zero. If it is the northern boundary, the return
* value will be 1.0. Latitudes in between are mapped according to the Web Mercator projection.
*/
float czm_latitudeToWebMercatorFraction(float latitude, float southMercatorYLow, float southMercatorYHigh, float oneOverMercatorHeight)
{
float sinLatitude = sin(latitude);
float mercatorY = 0.5 * log((1.0 + sinLatitude) / (1.0 - sinLatitude));
// mercatorY - southMercatorY in simulated double precision.
float t1 = 0.0 - southMercatorYLow;
float e = t1 - 0.0;
float t2 = ((-southMercatorYLow - e) + (0.0 - (t1 - e))) + mercatorY - southMercatorYHigh;
float highDifference = t1 + t2;
float lowDifference = t2 - (highDifference - t1);
return highDifference * oneOverMercatorHeight + lowDifference * oneOverMercatorHeight;
}
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