/*****************************************************************************
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NAME GNOMONIC
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PURPOSE: Transforms input longitude and latitude to Easting and
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Northing for the Gnomonic Projection.
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Implementation based on the existing sterea and ortho
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implementations.
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PROGRAMMER DATE
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---------- ----
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Richard Marsden November 2009
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ALGORITHM REFERENCES
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1. Snyder, John P., "Flattening the Earth - Two Thousand Years of Map
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Projections", University of Chicago Press 1993
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2. Wolfram Mathworld "Gnomonic Projection"
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http://mathworld.wolfram.com/GnomonicProjection.html
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Accessed: 12th November 2009
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******************************************************************************/
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Proj4js.Proj.gnom = {
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/* Initialize the Gnomonic projection
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-------------------------------------*/
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init: function(def) {
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/* Place parameters in static storage for common use
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-------------------------------------------------*/
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this.sin_p14=Math.sin(this.lat0);
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this.cos_p14=Math.cos(this.lat0);
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// Approximation for projecting points to the horizon (infinity)
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this.infinity_dist = 1000 * this.a;
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this.rc = 1;
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},
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/* Gnomonic forward equations--mapping lat,long to x,y
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---------------------------------------------------*/
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forward: function(p) {
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var sinphi, cosphi; /* sin and cos value */
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var dlon; /* delta longitude value */
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var coslon; /* cos of longitude */
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var ksp; /* scale factor */
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var g;
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var x, y;
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var lon=p.x;
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var lat=p.y;
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/* Forward equations
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-----------------*/
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dlon = Proj4js.common.adjust_lon(lon - this.long0);
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sinphi=Math.sin(lat);
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cosphi=Math.cos(lat);
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coslon = Math.cos(dlon);
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g = this.sin_p14 * sinphi + this.cos_p14 * cosphi * coslon;
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ksp = 1.0;
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if ((g > 0) || (Math.abs(g) <= Proj4js.common.EPSLN)) {
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x = this.x0 + this.a * ksp * cosphi * Math.sin(dlon) / g;
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y = this.y0 + this.a * ksp * (this.cos_p14 * sinphi - this.sin_p14 * cosphi * coslon) / g;
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} else {
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Proj4js.reportError("orthoFwdPointError");
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// Point is in the opposing hemisphere and is unprojectable
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// We still need to return a reasonable point, so we project
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// to infinity, on a bearing
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// equivalent to the northern hemisphere equivalent
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// This is a reasonable approximation for short shapes and lines that
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// straddle the horizon.
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x = this.x0 + this.infinity_dist * cosphi * Math.sin(dlon);
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y = this.y0 + this.infinity_dist * (this.cos_p14 * sinphi - this.sin_p14 * cosphi * coslon);
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}
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p.x=x;
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p.y=y;
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return p;
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},
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inverse: function(p) {
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var rh; /* Rho */
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var z; /* angle */
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var sinc, cosc;
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var c;
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var lon , lat;
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/* Inverse equations
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-----------------*/
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p.x = (p.x - this.x0) / this.a;
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p.y = (p.y - this.y0) / this.a;
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p.x /= this.k0;
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p.y /= this.k0;
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if ( (rh = Math.sqrt(p.x * p.x + p.y * p.y)) ) {
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c = Math.atan2(rh, this.rc);
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sinc = Math.sin(c);
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cosc = Math.cos(c);
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lat = Proj4js.common.asinz(cosc*this.sin_p14 + (p.y*sinc*this.cos_p14) / rh);
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lon = Math.atan2(p.x*sinc, rh*this.cos_p14*cosc - p.y*this.sin_p14*sinc);
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lon = Proj4js.common.adjust_lon(this.long0+lon);
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} else {
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lat = this.phic0;
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lon = 0.0;
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}
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p.x=lon;
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p.y=lat;
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return p;
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}
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};
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