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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)); }
/* ---------------------------------------------------------
Inverse Lambert azimuthal equal-area projection
-> http://en.wikipedia.org/wiki/Transverse_Mercator_projection
Parameters:
-----------
position : 2d position in cartesian coordinates
Return:
-------
2d position in (longitude,latitiude) coordinates
--------------------------------------------------------- */
vec2 transform_inverse(vec2 P)
{
float x = P.x;
float y = P.y;
float lambda = atan(sinh(x/(k0*a)),cos(y/(k0*a)));
float phi = asin(sin(y/(k0*a))/cosh(x/(k0*a)));
return vec2(lambda,phi);
}
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