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// ----------------------------------------------------------------------------
// Copyright (c) 2014, Nicolas P. Rougier. All Rights Reserved.
// Distributed under the (new) BSD License.
// ----------------------------------------------------------------------------
// Constants
// ---------
const float k0 = 0.75;
const float a = 1.00;
// Helper functions
// ----------------
float cosh(float x) { return 0.5 * (exp(x)+exp(-x)); }
float sinh(float x) { return 0.5 * (exp(x)-exp(-x)); }
/* ---------------------------------------------------------
Transverse Mercator projection
-> http://en.wikipedia.org/wiki/Transverse_Mercator_projection
Parameters:
-----------
position : 2d position in (longitude,latitiude) coordinates
Return:
-------
2d position in cartesian coordinates
--------------------------------------------------------- */
vec2 transform_forward(vec2 P)
{
float lambda = P.x;
float phi = P.y;
float x = 0.5*k0*log((1.0+sin(lambda)*cos(phi)) / (1.0 - sin(lambda)*cos(phi)));
float y = k0*a*atan(tan(phi), cos(lambda));
return vec2(x,y);
}
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