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#include <u.h>
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#include <libc.h>
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#include "map.h"
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int
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Xgilbert(struct place *p, double *x, double *y)
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{
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/* the interesting part - map the sphere onto a hemisphere */
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	struct place q;
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	q.nlat.s = tan(0.5*(p->nlat.l));
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	if(q.nlat.s > 1) q.nlat.s = 1;
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	if(q.nlat.s < -1) q.nlat.s = -1;
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	q.nlat.c = sqrt(1 - q.nlat.s*q.nlat.s);
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	q.wlon.l = p->wlon.l/2;
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	sincos(&q.wlon);
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/* the dull part: present the hemisphere orthogrpahically */
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	*y = q.nlat.s;
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	*x = -q.wlon.s*q.nlat.c;
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	return(1);
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}
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proj
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gilbert(void)
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{
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	return(Xgilbert);
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}
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/* derivation of the interesting part:
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   map the sphere onto the plane by stereographic projection;
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   map the plane onto a half plane by sqrt;
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   map the half plane back to the sphere by stereographic
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   projection
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   n,w are original lat and lon
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   r is stereographic radius
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   primes are transformed versions
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   r = cos(n)/(1+sin(n))
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   r' = sqrt(r) = cos(n')/(1+sin(n'))
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   r'^2 = (1-sin(n')^2)/(1+sin(n')^2) = cos(n)/(1+sin(n))
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   this is a linear equation for sin n', with solution
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   sin n' = (1+sin(n)-cos(n))/(1+sin(n)+cos(n))
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   use standard formula: tan x/2 = (1-cos x)/sin x = sin x/(1+cos x)
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   to show that the right side of the last equation is tan(n/2)
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*/
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