Why not?

src/cmd/map/libmap/aitoff.c

@@ -0,0 +1,26 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+#define Xaitwist Xaitpole.nlat
+static struct place Xaitpole;
+
+static int
+Xaitoff(struct place *place, double *x, double *y)
+{
+	struct place p;
+	copyplace(place,&p);
+	p.wlon.l /= 2.;
+	sincos(&p.wlon);
+	norm(&p,&Xaitpole,&Xaitwist);
+	Xazequalarea(&p,x,y);
+	*x *= 2.;
+	return(1);
+}
+
+proj
+aitoff(void)
+{
+	latlon(0.,0.,&Xaitpole);
+	return(Xaitoff);
+}

src/cmd/map/libmap/albers.c

@@ -0,0 +1,117 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+/* For Albers formulas see Deetz and Adams "Elements of Map Projection", */
+/* USGS Special Publication No. 68, GPO 1921 */
+
+static double r0sq, r1sq, d2, n, den, sinb1, sinb2;
+static struct coord plat1, plat2;
+static int southpole;
+
+static double num(double s)
+{
+	if(d2==0)
+		return(1);
+	s = d2*s*s;
+	return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9))));
+}
+
+/* Albers projection for a spheroid, good only when N pole is fixed */
+
+static int
+Xspalbers(struct place *place, double *x, double *y)
+{
+	double r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n);
+	double t = n*place->wlon.l;
+	*y = r*cos(t);
+	*x = -r*sin(t);
+	if(!southpole)
+		*y = -*y;
+	else
+		*x = -*x;
+	return(1);
+}
+
+/* lat1, lat2: std parallels; e2: squared eccentricity */
+
+static proj albinit(double lat1, double lat2, double e2)
+{
+	double r1;
+	double t;
+	for(;;) {
+		if(lat1 < -90)
+			lat1 = -180 - lat1;
+		if(lat2 > 90)
+			lat2 = 180 - lat2;
+		if(lat1 <= lat2)
+			break;
+		t = lat1; lat1 = lat2; lat2 = t;
+	}
+	if(lat2-lat1 < 1) {
+		if(lat1 > 89)
+			return(azequalarea());
+		return(0);
+	}
+	if(fabs(lat2+lat1) < 1)
+		return(cylequalarea(lat1));
+	d2 = e2;
+	den = num(1.);
+	deg2rad(lat1,&plat1);
+	deg2rad(lat2,&plat2);
+	sinb1 = plat1.s*num(plat1.s)/den;
+	sinb2 = plat2.s*num(plat2.s)/den;
+	n = (plat1.c*plat1.c/(1-e2*plat1.s*plat1.s) -
+	    plat2.c*plat2.c/(1-e2*plat2.s*plat2.s)) /
+	    (2*(1-e2)*den*(sinb2-sinb1));
+	r1 = plat1.c/(n*sqrt(1-e2*plat1.s*plat1.s));
+	r1sq = r1*r1;
+	r0sq = r1sq + 2*(1-e2)*den*sinb1/n;
+	southpole = lat1<0 && plat2.c>plat1.c;
+	return(Xspalbers);
+}
+
+proj
+sp_albers(double lat1, double lat2)
+{
+	return(albinit(lat1,lat2,EC2));
+}
+
+proj
+albers(double lat1, double lat2)
+{
+	return(albinit(lat1,lat2,0.));
+}
+
+static double scale = 1;
+static double twist = 0;
+
+void
+albscale(double x, double y, double lat, double lon)
+{
+	struct place place;
+	double alat, alon, x1,y1;
+	scale = 1;
+	twist = 0;
+	invalb(x,y,&alat,&alon);
+	twist = lon - alon;
+	deg2rad(lat,&place.nlat);
+	deg2rad(lon,&place.wlon);
+	Xspalbers(&place,&x1,&y1);
+	scale = sqrt((x1*x1+y1*y1)/(x*x+y*y));
+}
+
+void
+invalb(double x, double y, double *lat, double *lon)
+{
+	int i;
+	double sinb_den, sinp;
+	x *= scale;
+	y *= scale;
+	*lon = atan2(-x,fabs(y))/(RAD*n) + twist;
+	sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2));
+	sinp = sinb_den;
+	for(i=0; i<5; i++)
+		sinp = sinb_den/num(sinp);
+	*lat = asin(sinp)/RAD;
+}

src/cmd/map/libmap/azequalarea.c

@@ -0,0 +1,19 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xazequalarea(struct place *place, double *x, double *y)
+{
+	double r;
+	r = sqrt(1. - place->nlat.s);
+	*x = - r * place->wlon.s;
+	*y = - r * place->wlon.c;
+	return(1);
+}
+
+proj
+azequalarea(void)
+{
+	return(Xazequalarea);
+}

src/cmd/map/libmap/azequidist.c

@@ -0,0 +1,19 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xazequidistant(struct place *place, double *x, double *y)
+{
+	double colat;
+	colat = PI/2 - place->nlat.l;
+	*x = -colat * place->wlon.s;
+	*y = -colat * place->wlon.c;
+	return(1);
+}
+
+proj
+azequidistant(void)
+{
+	return(Xazequidistant);
+}

src/cmd/map/libmap/bicentric.c

@@ -0,0 +1,25 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord center;
+
+static int
+Xbicentric(struct place *place, double *x, double *y)
+{
+	if(place->wlon.c<=.01||place->nlat.c<=.01)
+		return(-1);
+	*x = -center.c*place->wlon.s/place->wlon.c;
+	*y = place->nlat.s/(place->nlat.c*place->wlon.c);
+	return(*x**x+*y**y<=9);
+}
+
+proj
+bicentric(double l)
+{
+	l = fabs(l);
+	if(l>89)
+		return(0);
+	deg2rad(l,&center);
+	return(Xbicentric);
+}

src/cmd/map/libmap/bonne.c

@@ -0,0 +1,36 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord stdpar;
+static double r0;
+
+static int
+Xbonne(struct place *place, double *x, double *y)
+{
+	double r, alpha;
+	r = r0 - place->nlat.l;
+	if(r<.001)
+		if(fabs(stdpar.c)<1e-10)
+			alpha = place->wlon.l;
+		else if(fabs(place->nlat.c)==0)
+			alpha = 0;
+		else 
+			alpha = place->wlon.l/(1+
+				stdpar.c*stdpar.c*stdpar.c/place->nlat.c/3);
+	else
+		alpha = place->wlon.l * place->nlat.c / r;
+	*x = - r*sin(alpha);
+	*y = - r*cos(alpha);
+	return(1);
+}
+
+proj
+bonne(double par)
+{
+	if(fabs(par*RAD) < .01)
+		return(Xsinusoidal);
+	deg2rad(par, &stdpar);
+	r0 = stdpar.c/stdpar.s + stdpar.l;
+	return(Xbonne);
+}

src/cmd/map/libmap/ccubrt.c

@@ -0,0 +1,13 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+void
+ccubrt(double zr, double zi, double *wr, double *wi)
+{
+	double r, theta;
+	theta = atan2(zi,zr);
+	r = cubrt(hypot(zr,zi));
+	*wr = r*cos(theta/3);
+	*wi = r*sin(theta/3);
+}

src/cmd/map/libmap/complex.c

@@ -0,0 +1,85 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+/*complex divide, defensive against overflow from
+ *	* and /, but not from + and -
+ *	assumes underflow yields 0.0
+ *	uses identities:
+ *	(a + bi)/(c + di) = ((a + bd/c) + (b - ad/c)i)/(c + dd/c)
+ *	(a + bi)/(c + di) = (b - ai)/(d - ci)
+*/
+void
+cdiv(double a, double b, double c, double d, double *u, double *v)
+{
+	double r,t;
+	if(fabs(c)<fabs(d)) {
+		t = -c; c = d; d = t;
+		t = -a; a = b; b = t;
+	}
+	r = d/c;
+	t = c + r*d;
+	*u = (a + r*b)/t;
+	*v = (b - r*a)/t;
+}
+
+void
+cmul(double c1, double c2, double d1, double d2, double *e1, double *e2)
+{
+	*e1 = c1*d1 - c2*d2;
+	*e2 = c1*d2 + c2*d1;
+}
+
+void
+csq(double c1, double c2, double *e1, double *e2)
+{
+	*e1 = c1*c1 - c2*c2;
+	*e2 = c1*c2*2;
+}
+
+/* complex square root
+ *	assumes underflow yields 0.0
+ *	uses these identities:
+ *	sqrt(x+_iy) = sqrt(r(cos(t)+_isin(t))
+ *	           = sqrt(r)(cos(t/2)+_isin(t/2))
+ *	cos(t/2) = sin(t)/2sin(t/2) = sqrt((1+cos(t)/2)
+ *	sin(t/2) = sin(t)/2cos(t/2) = sqrt((1-cos(t)/2)
+*/
+void
+csqrt(double c1, double c2, double *e1, double *e2)
+{
+	double r,s;
+	double x,y;
+	x = fabs(c1);
+	y = fabs(c2);
+	if(x>=y) {
+		if(x==0) {
+			*e1 = *e2 = 0;
+			return;
+		}
+		r = x;
+		s = y/x;
+	} else {
+		r = y;
+		s = x/y;
+	}
+	r *= sqrt(1+ s*s);
+	if(c1>0) {
+		*e1 = sqrt((r+c1)/2);
+		*e2 = c2/(2* *e1);
+	} else {
+		*e2 = sqrt((r-c1)/2);
+		if(c2<0)
+			*e2 = -*e2;
+		*e1 = c2/(2* *e2);
+	}
+}
+
+
+void cpow(double c1, double c2, double *d1, double *d2, double pwr)
+{
+	double theta = pwr*atan2(c2,c1);
+	double r = pow(hypot(c1,c2), pwr);
+	*d1 = r*cos(theta);
+	*d2 = r*sin(theta);
+}

src/cmd/map/libmap/conic.c

@@ -0,0 +1,27 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord stdpar;
+
+static int
+Xconic(struct place *place, double *x, double *y)
+{
+	double r;
+	if(fabs(place->nlat.l-stdpar.l) > 80.*RAD)
+		return(-1);
+	r = stdpar.c/stdpar.s - tan(place->nlat.l - stdpar.l);
+	*x = - r*sin(place->wlon.l * stdpar.s);
+	*y = - r*cos(place->wlon.l * stdpar.s);
+	if(r>3) return(0);
+	return(1);
+}
+
+proj
+conic(double par)
+{
+	if(fabs(par) <.1)
+		return(Xcylindrical);
+	deg2rad(par, &stdpar);
+	return(Xconic);
+}

src/cmd/map/libmap/cubrt.c

@@ -0,0 +1,30 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+double
+cubrt(double a)
+{
+	double x,y,x1;
+	if(a==0) 
+		return(0.);
+	y = 1;
+	if(a<0) {
+		y = -y;
+		a = -a;
+	}
+	while(a<1) {
+		a *= 8;
+		y /= 2;
+	}
+	while(a>1) {
+		a /= 8;
+		y *= 2;
+	}
+	x = 1;
+	do {
+		x1 = x;
+		x = (2*x1+a/(x1*x1))/3;
+	} while(fabs(x-x1)>10.e-15);
+	return(x*y);
+}

src/cmd/map/libmap/cuts.c

@@ -0,0 +1,39 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+extern void abort(void);
+
+/* these routines duplicate names found in map.c.  they are
+called from routines in hex.c, guyou.c, and tetra.c, which
+are in turn invoked directly from map.c.  this bad organization
+arises from data hiding; only these three files know stuff
+that's necessary for the proper handling of the unusual cuts
+involved in these projections.
+
+the calling routines are not advertised as part of the library,
+and the library duplicates should never get loaded, however they
+are included to make the libary self-standing.*/
+
+int
+picut(struct place *g, struct place *og, double *cutlon)
+{
+	g; og; cutlon;
+	abort();
+	return 0;
+}
+
+int
+ckcut(struct place *g1, struct place *g2, double lon)
+{
+	g1; g2; lon;
+	abort();
+	return 0;
+}
+
+double
+reduce(double x)
+{
+	x;
+	abort();
+	return 0;
+}

src/cmd/map/libmap/cylequalarea.c

@@ -0,0 +1,24 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double a;
+
+static int
+Xcylequalarea(struct place *place, double *x, double *y)
+{
+	*x = - place->wlon.l * a;
+	*y = place->nlat.s;
+	return(1);
+}
+
+proj
+cylequalarea(double par)
+{
+	struct coord stdp0;
+	if(par > 89.0)
+		return(0);
+	deg2rad(par, &stdp0);
+	a = stdp0.c*stdp0.c;
+	return(Xcylequalarea);
+}

src/cmd/map/libmap/cylindrical.c

@@ -0,0 +1,19 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xcylindrical(struct place *place, double *x, double *y)
+{
+	if(fabs(place->nlat.l) > 80.*RAD)
+		return(-1);
+	*x = - place->wlon.l;
+	*y = place->nlat.s / place->nlat.c;
+	return(1);
+}
+
+proj
+cylindrical(void)
+{
+	return(Xcylindrical);
+}

src/cmd/map/libmap/elco2.c

@@ -0,0 +1,132 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+/* elliptic integral routine, R.Bulirsch,
+ *	Numerische Mathematik 7(1965) 78-90
+ *	calculate integral from 0 to x+iy of
+ *	(a+b*t^2)/((1+t^2)*sqrt((1+t^2)*(1+kc^2*t^2)))
+ *	yields about D valid figures, where CC=10e-D
+ *	for a*b>=0, except at branchpoints x=0,y=+-i,+-i/kc;
+ *	there the accuracy may be reduced.
+ *	fails for kc=0 or x<0
+ *	return(1) for success, return(0) for fail
+ *
+ *	special case a=b=1 is equivalent to
+ *	standard elliptic integral of first kind
+ *	from 0 to atan(x+iy) of
+ *	1/sqrt(1-k^2*(sin(t))^2) where k^2=1-kc^2
+*/
+
+#define ROOTINF 10.e18
+#define CC 1.e-6
+
+int
+elco2(double x, double y, double kc, double a, double b, double *u, double *v)
+{
+	double c,d,dn1,dn2,e,e1,e2,f,f1,f2,h,k,m,m1,m2,sy;
+	double d1[13],d2[13];
+	int i,l;
+	if(kc==0||x<0)
+		return(0);
+	sy = y>0? 1: y==0? 0: -1;
+	y = fabs(y);
+	csq(x,y,&c,&e2);
+	d = kc*kc;
+	k = 1-d;
+	e1 = 1+c;
+	cdiv2(1+d*c,d*e2,e1,e2,&f1,&f2);
+	f2 = -k*x*y*2/f2;
+	csqr(f1,f2,&dn1,&dn2);
+	if(f1<0) {
+		f1 = dn1;
+		dn1 = -dn2;
+		dn2 = -f1;
+	}
+	if(k<0) {
+		dn1 = fabs(dn1);
+		dn2 = fabs(dn2);
+	}
+	c = 1+dn1;
+	cmul(e1,e2,c,dn2,&f1,&f2);
+	cdiv(x,y,f1,f2,&d1[0],&d2[0]);
+	h = a-b;
+	d = f = m = 1;
+	kc = fabs(kc);
+	e = a;
+	a += b;
+	l = 4;
+	for(i=1;;i++) {
+		m1 = (kc+m)/2;
+		m2 = m1*m1;
+		k *= f/(m2*4);
+		b += e*kc;
+		e = a;
+		cdiv2(kc+m*dn1,m*dn2,c,dn2,&f1,&f2);
+		csqr(f1/m1,k*dn2*2/f2,&dn1,&dn2);
+		cmul(dn1,dn2,x,y,&f1,&f2);
+		x = fabs(f1);
+		y = fabs(f2);
+		a += b/m1;
+		l *= 2;
+		c = 1 +dn1;
+		d *= k/2;
+		cmul(x,y,x,y,&e1,&e2);
+		k *= k;
+
+		cmul(c,dn2,1+e1*m2,e2*m2,&f1,&f2);
+		cdiv(d*x,d*y,f1,f2,&d1[i],&d2[i]);
+		if(k<=CC) 
+			break;
+		kc = sqrt(m*kc);
+		f = m2;
+		m = m1;
+	}
+	f1 = f2 = 0;
+	for(;i>=0;i--) {
+		f1 += d1[i];
+		f2 += d2[i];
+	}
+	x *= m1;
+	y *= m1;
+	cdiv2(1-y,x,1+y,-x,&e1,&e2);
+	e2 = x*2/e2;
+	d = a/(m1*l);
+	*u = atan2(e2,e1);
+	if(*u<0)
+		*u += PI;
+	a = d*sy/2;
+	*u = d*(*u) + f1*h;
+	*v = (-1-log(e1*e1+e2*e2))*a + f2*h*sy + a;
+	return(1);
+}
+
+void
+cdiv2(double c1, double c2, double d1, double d2, double *e1, double *e2)
+{
+	double t;
+	if(fabs(d2)>fabs(d1)) {
+		t = d1, d1 = d2, d2 = t;
+		t = c1, c1 = c2, c2 = t;
+	}
+	if(fabs(d1)>ROOTINF)
+		*e2 = ROOTINF*ROOTINF;
+	else
+		*e2 = d1*d1 + d2*d2;
+	t = d2/d1;
+	*e1 = (c1+t*c2)/(d1+t*d2); /* (c1*d1+c2*d2)/(d1*d1+d2*d2) */
+}
+
+/* complex square root of |x|+iy */
+void
+csqr(double c1, double c2, double *e1, double *e2)
+{
+	double r2;
+	r2 = c1*c1 + c2*c2;
+	if(r2<=0) {
+		*e1 = *e2 = 0;
+		return;
+	}
+	*e1 = sqrt((sqrt(r2) + fabs(c1))/2);
+	*e2 = c2/(*e1*2);
+}

src/cmd/map/libmap/elliptic.c

@@ -0,0 +1,35 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+struct coord center;
+
+static int
+Xelliptic(struct place *place, double *x, double *y)
+{
+	double r1,r2;
+	r1 = acos(place->nlat.c*(place->wlon.c*center.c
+		- place->wlon.s*center.s));
+	r2 = acos(place->nlat.c*(place->wlon.c*center.c
+		+ place->wlon.s*center.s));
+	*x = -(r1*r1 - r2*r2)/(4*center.l);
+	*y = (r1*r1+r2*r2)/2 - (center.l*center.l+*x**x);
+	if(*y < 0)
+		*y = 0;
+	*y = sqrt(*y);
+	if(place->nlat.l<0)
+		*y = -*y;
+	return(1);
+}
+
+proj
+elliptic(double l)
+{
+	l = fabs(l);
+	if(l>89)
+		return(0);
+	if(l<1)
+		return(Xazequidistant);
+	deg2rad(l,&center);
+	return(Xelliptic);
+}

src/cmd/map/libmap/fisheye.c

@@ -0,0 +1,26 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+/* refractive fisheye, not logarithmic */
+
+static double n;
+
+static int
+Xfisheye(struct place *place, double *x, double *y)
+{
+	double r;
+	double u = sin(PI/4-place->nlat.l/2)/n;
+	if(fabs(u) > .97)
+		return -1;
+	r = tan(asin(u));
+	*x = -r*place->wlon.s;
+	*y = -r*place->wlon.c;
+	return 1;
+}
+
+proj
+fisheye(double par)
+{
+	n = par;
+	return n<.1? 0: Xfisheye;
+}

src/cmd/map/libmap/gall.c

@@ -0,0 +1,29 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double scale;
+
+static int
+Xgall(struct place *place, double *x, double *y)
+{
+	/* two ways to compute tan(place->nlat.l/2) */
+	if(fabs(place->nlat.s)<.1)
+		*y = sin(place->nlat.l/2)/cos(place->nlat.l/2);
+	else
+		*y = (1-place->nlat.c)/place->nlat.s;
+	*x = -scale*place->wlon.l;
+	return 1;
+}
+
+proj
+gall(double par)
+{
+	double coshalf;
+	if(fabs(par)>80)
+		return 0;
+	par *= RAD;
+	coshalf = cos(par/2);
+	scale = cos(par)/(2*coshalf*coshalf);
+	return Xgall;
+}

src/cmd/map/libmap/gilbert.c

@@ -0,0 +1,51 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xgilbert(struct place *p, double *x, double *y)
+{
+/* the interesting part - map the sphere onto a hemisphere */
+	struct place q;
+	q.nlat.s = tan(0.5*(p->nlat.l));
+	if(q.nlat.s > 1) q.nlat.s = 1;
+	if(q.nlat.s < -1) q.nlat.s = -1;
+	q.nlat.c = sqrt(1 - q.nlat.s*q.nlat.s);
+	q.wlon.l = p->wlon.l/2;
+	sincos(&q.wlon);
+/* the dull part: present the hemisphere orthogrpahically */
+	*y = q.nlat.s;
+	*x = -q.wlon.s*q.nlat.c;
+	return(1);
+}
+
+proj
+gilbert(void)
+{
+	return(Xgilbert);
+}
+
+/* derivation of the interesting part:
+   map the sphere onto the plane by stereographic projection;
+   map the plane onto a half plane by sqrt;
+   map the half plane back to the sphere by stereographic
+   projection
+
+   n,w are original lat and lon
+   r is stereographic radius
+   primes are transformed versions
+
+   r = cos(n)/(1+sin(n))
+   r' = sqrt(r) = cos(n')/(1+sin(n'))
+
+   r'^2 = (1-sin(n')^2)/(1+sin(n')^2) = cos(n)/(1+sin(n))
+
+   this is a linear equation for sin n', with solution
+
+   sin n' = (1+sin(n)-cos(n))/(1+sin(n)+cos(n))
+
+   use standard formula: tan x/2 = (1-cos x)/sin x = sin x/(1+cos x)
+   to show that the right side of the last equation is tan(n/2)
+*/
+
+

src/cmd/map/libmap/guyou.c

@@ -0,0 +1,101 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct place gywhem, gyehem;
+static struct coord gytwist;
+static double gyconst, gykc, gyside;
+
+
+static void
+dosquare(double z1, double z2, double *x, double *y)
+{
+	double w1,w2;
+	w1 = z1 -1;
+	if(fabs(w1*w1+z2*z2)>.000001) {
+		cdiv(z1+1,z2,w1,z2,&w1,&w2);
+		w1 *= gyconst;
+		w2 *= gyconst;
+		if(w1<0)
+			w1 = 0;
+		elco2(w1,w2,gykc,1.,1.,x,y);
+	} else {
+		*x = gyside;
+		*y = 0;
+	}
+}
+
+int
+Xguyou(struct place *place, double *x, double *y)
+{
+	int ew;		/*which hemisphere*/
+	double z1,z2;
+	struct place pl;
+	ew = place->wlon.l<0;
+	copyplace(place,&pl);
+	norm(&pl,ew?&gyehem:&gywhem,&gytwist);
+	Xstereographic(&pl,&z1,&z2);
+	dosquare(z1/2,z2/2,x,y);
+	if(!ew)
+		*x -= gyside;
+	return(1);
+}
+
+proj
+guyou(void)
+{
+	double junk;
+	gykc = 1/(3+2*sqrt(2.));
+	gyconst = -(1+sqrt(2.));
+	elco2(-gyconst,0.,gykc,1.,1.,&gyside,&junk);
+	gyside *= 2;
+	latlon(0.,90.,&gywhem);
+	latlon(0.,-90.,&gyehem);
+	deg2rad(0.,&gytwist);
+	return(Xguyou);
+}
+
+int
+guycut(struct place *g, struct place *og, double *cutlon)
+{
+	int c;
+	c = picut(g,og,cutlon);
+	if(c!=1)
+		return(c);
+	*cutlon = 0.;
+	if(g->nlat.c<.7071||og->nlat.c<.7071)
+		return(ckcut(g,og,0.));
+	return(1);
+}
+
+static int
+Xsquare(struct place *place, double *x, double *y)
+{
+	double z1,z2;
+	double r, theta;
+	struct place p;
+	copyplace(place,&p);
+	if(place->nlat.l<0) {
+		p.nlat.l = -p.nlat.l;
+		p.nlat.s = -p.nlat.s;
+	}
+	if(p.nlat.l<FUZZ && fabs(p.wlon.l)>PI-FUZZ){
+		*y = -gyside/2;
+		*x = p.wlon.l>0?0:gyside;
+		return(1);
+	}
+	Xstereographic(&p,&z1,&z2);
+	r = sqrt(sqrt(hypot(z1,z2)/2));
+	theta = atan2(z1,-z2)/4;
+	dosquare(r*sin(theta),-r*cos(theta),x,y);
+	if(place->nlat.l<0)
+		*y = -gyside - *y;
+	return(1);
+}
+
+proj
+square(void)
+{
+	guyou();
+	return(Xsquare);
+}

src/cmd/map/libmap/harrison.c

@@ -0,0 +1,40 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double v3,u2,u3,a,b; /*v=view,p=obj,u=unit.y*/
+
+static int
+Xharrison(struct place *place, double *x, double *y)
+{
+	double p1 = -place->nlat.c*place->wlon.s;
+	double p2 = -place->nlat.c*place->wlon.c;
+	double p3 = place->nlat.s;
+	double d = b + u3*p2 - u2*p3;
+	double t;
+	if(d < .01)
+		return -1;
+	t = a/d;
+	if(v3*place->nlat.s < 1.)
+		return -1;
+	*y = t*p2*u2 + (v3-t*(v3-p3))*u3;
+	*x = t*p1;
+	if(t < 0)
+		return 0;
+	if(*x * *x + *y * *y > 16)
+		return -1;
+	return 1;
+}
+
+proj
+harrison(double r, double alpha)
+{
+	u2 = cos(alpha*RAD);
+	u3 = sin(alpha*RAD);
+	v3 = r;
+	b = r*u2;
+	a = 1 + b;
+	if(r<1.001 || a<sqrt(r*r-1))
+		return 0;
+	return Xharrison;
+}

src/cmd/map/libmap/hex.c

@@ -0,0 +1,122 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+#define BIG 1.e15
+#define HFUZZ .0001
+
+static double hcut[3] ;
+static double kr[3] = { .5, -1., .5 };
+static double ki[3] = { -1., 0., 1. }; 	/*to multiply by sqrt(3)/2*/
+static double cr[3];
+static double ci[3];
+static struct place hem;
+static struct coord twist;
+static double  rootroot3, hkc;
+static double w2;
+static double rootk;
+
+static void
+reflect(int i, double wr, double wi, double *x, double *y)
+{
+	double pr,pi,l;
+	pr = cr[i]-wr;
+	pi = ci[i]-wi;
+	l = 2*(kr[i]*pr + ki[i]*pi);
+	*x = wr + l*kr[i];
+	*y = wi + l*ki[i];
+}
+
+static int
+Xhex(struct place *place, double *x, double *y)
+{
+	int ns;
+	int i;
+	double zr,zi;
+	double sr,si,tr,ti,ur,ui,vr,vi,yr,yi;
+	struct place p;
+	copyplace(place,&p);
+	ns = place->nlat.l >= 0;
+	if(!ns) {
+		p.nlat.l = -p.nlat.l;
+		p.nlat.s = -p.nlat.s;
+	}
+	if(p.nlat.l<HFUZZ) {
+		for(i=0;i<3;i++)
+			if(fabs(reduce(p.wlon.l-hcut[i]))<HFUZZ) {
+				if(i==2) {
+					*x = 2*cr[0] - cr[1];
+					*y = 0;
+				} else {
+					*x = cr[1];
+					*y = 2*ci[2*i];
+				}
+				return(1);
+			}
+		p.nlat.l = HFUZZ;
+		sincos(&p.nlat);
+	}
+	norm(&p,&hem,&twist);
+	Xstereographic(&p,&zr,&zi);
+	zr /= 2;
+	zi /= 2;
+	cdiv(1-zr,-zi,1+zr,zi,&sr,&si);
+	csq(sr,si,&tr,&ti);
+	ccubrt(1+3*tr,3*ti,&ur,&ui);
+	csqrt(ur-1,ui,&vr,&vi);
+	cdiv(rootroot3+vr,vi,rootroot3-vr,-vi,&yr,&yi);
+	yr /= rootk;
+	yi /= rootk;
+	elco2(fabs(yr),yi,hkc,1.,1.,x,y);
+	if(yr < 0)
+		*x = w2 - *x;
+	if(!ns) reflect(hcut[0]>place->wlon.l?0:
+			hcut[1]>=place->wlon.l?1:
+			2,*x,*y,x,y);
+	return(1);
+}
+
+proj
+hex(void)
+{
+	int i;
+	double t;
+	double root3;
+	double c,d;
+	struct place p;
+	hcut[2] = PI;
+	hcut[1] = hcut[2]/3;
+	hcut[0] = -hcut[1];
+	root3 = sqrt(3.);
+	rootroot3 = sqrt(root3);
+	t = 15 -8*root3;
+	hkc = t*(1-sqrt(1-1/(t*t)));
+	elco2(BIG,0.,hkc,1.,1.,&w2,&t);
+	w2 *= 2;
+	rootk = sqrt(hkc);
+	latlon(90.,90.,&hem);
+	latlon(90.,0.,&p);
+	Xhex(&p,&c,&t);
+	latlon(0.,0.,&p);
+	Xhex(&p,&d,&t);
+	for(i=0;i<3;i++) {
+		ki[i] *= root3/2;
+		cr[i] = c + (c-d)*kr[i];
+		ci[i] = (c-d)*ki[i];
+	}
+	deg2rad(0.,&twist);
+	return(Xhex);
+}
+
+int
+hexcut(struct place *g, struct place *og, double *cutlon)
+{
+	int t,i;
+	if(g->nlat.l>=-HFUZZ&&og->nlat.l>=-HFUZZ)
+		return(1);
+	for(i=0;i<3;i++) {
+		t = ckcut(g,og,*cutlon=hcut[i]);
+		if(t!=1) return(t);
+	}
+	return(1);
+}

src/cmd/map/libmap/homing.c

@@ -0,0 +1,121 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord p0;		/* standard parallel */
+
+int first;
+
+static double
+trigclamp(double x)
+{
+	return x>1? 1: x<-1? -1: x;
+}
+
+static struct coord az;		/* azimuth of p0 seen from place */
+static struct coord rad;	/* angular dist from place to p0 */
+
+static int
+azimuth(struct place *place)
+{
+	if(place->nlat.c < FUZZ) {
+		az.l = PI/2 + place->nlat.l - place->wlon.l;
+		sincos(&az);
+		rad.l = fabs(place->nlat.l - p0.l);
+		if(rad.l > PI)
+			rad.l = 2*PI - rad.l;
+		sincos(&rad);
+		return 1;
+	}
+	rad.c = trigclamp(p0.s*place->nlat.s +	/* law of cosines */
+		p0.c*place->nlat.c*place->wlon.c);
+	rad.s = sqrt(1 - rad.c*rad.c);
+	if(fabs(rad.s) < .001) {
+		az.s = 0;
+		az.c = 1;
+	} else {
+		az.s = trigclamp(p0.c*place->wlon.s/rad.s); /* sines */
+		az.c = trigclamp((p0.s - rad.c*place->nlat.s)
+				/(rad.s*place->nlat.c));
+	}
+	rad.l = atan2(rad.s, rad.c);
+	return 1;
+}
+
+static int
+Xmecca(struct place *place, double *x, double *y)
+{
+	if(!azimuth(place))
+		return 0;
+	*x = -place->wlon.l;
+	*y = fabs(az.s)<.02? -az.c*rad.s/p0.c: *x*az.c/az.s;
+	return fabs(*y)>2? -1:
+	       rad.c<0? 0:
+	       1;
+}
+
+proj
+mecca(double par)
+{
+	first = 1;
+	if(fabs(par)>80.)
+		return(0);
+	deg2rad(par,&p0);
+	return(Xmecca);
+}
+
+static int
+Xhoming(struct place *place, double *x, double *y)
+{
+	if(!azimuth(place))
+		return 0;
+	*x = -rad.l*az.s;
+	*y = -rad.l*az.c;
+	return place->wlon.c<0? 0: 1;
+}
+
+proj
+homing(double par)
+{
+	first = 1;
+	if(fabs(par)>80.)
+		return(0);
+	deg2rad(par,&p0);
+	return(Xhoming);
+}
+
+int
+hlimb(double *lat, double *lon, double res)
+{
+	if(first) {
+		*lon = -90;
+		*lat = -90;
+		first = 0;
+		return 0;
+	}
+	*lat += res;
+	if(*lat <= 90) 
+		return 1;
+	if(*lon == 90)
+		return -1;
+	*lon = 90;
+	*lat = -90;
+	return 0;
+}
+
+int
+mlimb(double *lat, double *lon, double res)
+{
+	int ret = !first;
+	if(fabs(p0.s) < .01)
+		return -1;
+	if(first) {
+		*lon = -180;
+		first = 0;
+	} else
+		*lon += res;
+	if(*lon > 180)
+		return -1;
+	*lat = atan(-cos(*lon*RAD)/p0.s*p0.c)/RAD;
+	return ret;
+}

src/cmd/map/libmap/lagrange.c

@@ -0,0 +1,30 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static int
+Xlagrange(struct place *place, double *x, double *y)
+{
+	double z1,z2;
+	double w1,w2,t1,t2;
+	struct place p;
+	copyplace(place,&p);
+	if(place->nlat.l<0) {
+		p.nlat.l = -p.nlat.l;
+		p.nlat.s = -p.nlat.s;
+	}
+	Xstereographic(&p,&z1,&z2);
+	csqrt(-z2/2,z1/2,&w1,&w2);
+	cdiv(w1-1,w2,w1+1,w2,&t1,&t2);
+	*y = -t1;
+	*x = t2;
+	if(place->nlat.l<0)
+		*y = -*y;
+	return(1);
+}
+
+proj
+lagrange(void)
+{
+	return(Xlagrange);
+}

src/cmd/map/libmap/lambert.c

@@ -0,0 +1,46 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord stdp0, stdp1;
+static double k;
+
+static int
+Xlambert(struct place *place, double *x, double *y)
+{
+	double r;
+	if(place->nlat.l < -80.*RAD)
+		return(-1);
+	if(place->nlat.l > 89.*RAD)
+		r = 0;	/* slovenly */
+	else
+		r = stdp0.c*exp(0.5*k*log(
+		   (1+stdp0.s)*(1-place->nlat.s)/((1-stdp0.s)*(1+place->nlat.s))));
+	if(stdp1.l<0.)
+		r = -r;
+	*x = - r*sin(k * place->wlon.l);
+	*y = - r*cos(k * place->wlon.l);
+	return(1);
+}
+
+proj
+lambert(double par0, double par1)
+{
+	double temp;
+	if(fabs(par0)>fabs(par1)){
+		temp = par0;
+		par0 = par1;
+		par1 = temp;
+	}
+	deg2rad(par0, &stdp0);
+	deg2rad(par1, &stdp1);
+	if(fabs(par1+par0)<.1) 
+		return(mercator());
+	if(fabs(par1-par0)<.1)
+		return(perspective(-1.));
+	if(fabs(par0)>89.5||fabs(par1)>89.5)
+		return(0);
+	k = 2*log(stdp1.c/stdp0.c)/log(
+		(1+stdp0.s)*(1-stdp1.s)/((1-stdp0.s)*(1+stdp1.s)));
+	return(Xlambert);
+}

src/cmd/map/libmap/laue.c

@@ -0,0 +1,24 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+
+static int
+Xlaue(struct place *place, double *x, double *y)
+{
+	double r;
+	if(place->nlat.l<PI/4+FUZZ)
+		return(-1);
+	r = tan(PI-2*place->nlat.l);
+	if(r>3)
+		return(-1);
+	*x = - r * place->wlon.s;
+	*y = - r * place->wlon.c;
+	return(1);
+}
+
+proj
+laue(void)
+{
+	return(Xlaue);
+}

src/cmd/map/libmap/lune.c

@@ -0,0 +1,62 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int Xstereographic(struct place *place, double *x, double *y);
+
+static struct place eastpole;
+static struct place westpole;
+static double eastx, easty;
+static double westx, westy;
+static double scale;
+static double pwr;
+
+/* conformal map w = ((1+z)^A - (1-z)^A)/((1+z)^A + (1-z)^A),
+   where A<1, maps unit circle onto a convex lune with x= +-1
+   mapping to vertices of angle A*PI at w = +-1 */
+
+/* there are cuts from E and W poles to S pole,
+   in absence of a cut routine, error is returned for
+   points outside a polar cap through E and W poles */
+
+static int Xlune(struct place *place, double *x, double *y)
+{
+	double stereox, stereoy;
+	double z1x, z1y, z2x, z2y;
+	double w1x, w1y, w2x, w2y;
+	double numx, numy, denx, deny;
+	if(place->nlat.l < eastpole.nlat.l-FUZZ)
+		return	-1;
+	Xstereographic(place, &stereox, &stereoy);
+	stereox *= scale;
+	stereoy *= scale;
+	z1x = 1 + stereox;
+	z1y = stereoy;
+	z2x = 1 - stereox;
+	z2y = -stereoy;
+	cpow(z1x,z1y,&w1x,&w1y,pwr);
+	cpow(z2x,z2y,&w2x,&w2y,pwr);
+	numx = w1x - w2x;
+	numy = w1y - w2y;
+	denx = w1x + w2x;
+	deny = w1y + w2y;
+	cdiv(numx, numy, denx, deny, x, y);
+	return 1;
+}	
+
+proj
+lune(double lat, double theta)
+{
+	deg2rad(lat, &eastpole.nlat);
+	deg2rad(-90.,&eastpole.wlon);
+	deg2rad(lat, &westpole.nlat);
+	deg2rad(90. ,&westpole.wlon);
+	Xstereographic(&eastpole, &eastx, &easty);
+	Xstereographic(&westpole, &westx, &westy);
+	if(fabs(easty)>FUZZ || fabs(westy)>FUZZ ||
+	   fabs(eastx+westx)>FUZZ)
+		abort();
+	scale = 1/eastx;
+	pwr = theta/180;
+	return Xlune;
+}

src/cmd/map/libmap/mercator.c

@@ -0,0 +1,36 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static int
+Xmercator(struct place *place, double *x, double *y)
+{
+	if(fabs(place->nlat.l) > 80.*RAD)
+		return(-1);
+	*x = -place->wlon.l;
+	*y = 0.5*log((1+place->nlat.s)/(1-place->nlat.s));
+	return(1);
+}
+
+proj
+mercator(void)
+{
+	return(Xmercator);
+}
+
+static double ecc = ECC;
+
+static int
+Xspmercator(struct place *place, double *x, double *y)
+{
+	if(Xmercator(place,x,y) < 0)
+		return(-1);
+	*y += 0.5*ecc*log((1-ecc*place->nlat.s)/(1+ecc*place->nlat.s));
+	return(1);
+}
+
+proj
+sp_mercator(void)
+{
+	return(Xspmercator);
+}

src/cmd/map/libmap/mkfile

@@ -0,0 +1,50 @@
+<$PLAN9/src/mkhdr
+
+LIB=libmap.a
+OFILES=aitoff.$O\
+	albers.$O\
+	azequalarea.$O\
+	azequidist.$O\
+	bicentric.$O\
+	bonne.$O\
+	ccubrt.$O\
+	complex.$O\
+	conic.$O\
+	cubrt.$O\
+	cylequalarea.$O\
+	cylindrical.$O\
+	elco2.$O\
+	elliptic.$O\
+	fisheye.$O\
+	gall.$O\
+	gilbert.$O\
+	guyou.$O\
+	harrison.$O\
+	hex.$O\
+	homing.$O\
+	lagrange.$O\
+	lambert.$O\
+	laue.$O\
+	lune.$O\
+	mercator.$O\
+	mollweide.$O\
+	newyorker.$O\
+	orthographic.$O\
+	perspective.$O\
+	polyconic.$O\
+	rectangular.$O\
+	simpleconic.$O\
+	sinusoidal.$O\
+	tetra.$O\
+	trapezoidal.$O\
+	twocirc.$O\
+	zcoord.$O\
+
+HFILES=../map.h\
+
+<$PLAN9/src/mklib
+CFLAGS=$CFLAGS -I..
+
+nuke:V:
+	mk clean
+	rm -f libmap.a[$OS]

src/cmd/map/libmap/mollweide.c

@@ -0,0 +1,25 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static int
+Xmollweide(struct place *place, double *x, double *y)
+{
+	double z;
+	double w;
+	z = place->nlat.l;
+	if(fabs(z)<89.9*RAD)
+		do {	/*newton for 2z+sin2z=pi*sin(lat)*/
+			w = (2*z+sin(2*z)-PI*place->nlat.s)/(2+2*cos(2*z));
+			z -= w;
+		} while(fabs(w)>=.00001);
+	*y = sin(z);
+	*x = - (2/PI)*cos(z)*place->wlon.l;
+	return(1);
+}
+
+proj
+mollweide(void)
+{
+	return(Xmollweide);
+}

src/cmd/map/libmap/newyorker.c

@@ -0,0 +1,28 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double a;
+
+static int
+Xnewyorker(struct place *place, double *x, double *y)
+{
+	double r = PI/2 - place->nlat.l;
+	double s;
+	if(r<.001)	/* cheat to plot center */
+		s = 0;
+	else if(r<a)
+		return -1;
+	else
+		s = log(r/a);
+	*x = -s * place->wlon.s;
+	*y = -s * place->wlon.c;
+	return(1);
+}
+
+proj
+newyorker(double a0)
+{
+	a = a0*RAD;
+	return(Xnewyorker);
+}

src/cmd/map/libmap/orthographic.c

@@ -0,0 +1,35 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+
+int
+Xorthographic(struct place *place, double *x, double *y)
+{
+	*x = - place->nlat.c * place->wlon.s;
+	*y = - place->nlat.c * place->wlon.c;
+	return(place->nlat.l<0.? 0 : 1);
+}
+
+proj
+orthographic(void)
+{
+	return(Xorthographic);
+}
+
+int
+olimb(double *lat, double *lon, double res)
+{
+	static int first  = 1;
+	if(first) {
+		*lat = 0;
+		*lon = -180;
+		first = 0;
+		return 0;
+	}
+	*lon += res;
+	if(*lon <= 180)
+		return 1;
+	first = 1;
+	return -1;
+}

src/cmd/map/libmap/perspective.c

@@ -0,0 +1,84 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+#define ORTHRAD 1000
+static double viewpt;
+
+static int
+Xperspective(struct place *place, double *x, double *y)
+{
+	double r;
+	if(viewpt<=1+FUZZ && fabs(place->nlat.s<=viewpt+.01))
+		return(-1);
+	r = place->nlat.c*(viewpt - 1.)/(viewpt - place->nlat.s);
+	*x = - r*place->wlon.s;
+	*y = - r*place->wlon.c;
+	if(r>4.)
+		return(-1);
+	if(fabs(viewpt)>1 && place->nlat.s<1/viewpt ||
+	   fabs(viewpt)<=1 && place->nlat.s<viewpt)
+			return 0;
+	return(1);
+}
+
+proj
+perspective(double radius)
+{
+	viewpt = radius;
+	if(viewpt >= ORTHRAD)
+		return(Xorthographic);
+	if(fabs(viewpt-1.)<.0001)
+		return(0);
+	return(Xperspective);
+}
+
+	/* called from various conformal projections,
+           but not from stereographic itself */
+int
+Xstereographic(struct place *place, double *x, double *y)
+{
+	double v = viewpt;
+	int retval;
+	viewpt = -1;
+	retval = Xperspective(place, x, y);
+	viewpt = v;
+	return retval;
+}
+
+proj
+stereographic(void)
+{
+	viewpt = -1.;
+	return(Xperspective);
+}
+
+proj
+gnomonic(void)
+{
+	viewpt = 0.;
+	return(Xperspective);
+}
+
+int
+plimb(double *lat, double *lon, double res)
+{
+	static int first = 1;
+	if(viewpt >= ORTHRAD)
+		return olimb(lat, lon, res);
+	if(first) {
+		first = 0;
+		*lon = -180;
+		if(fabs(viewpt) < .01)
+			*lat = 0;
+		else if(fabs(viewpt)<=1)
+			*lat = asin(viewpt)/RAD;
+		else
+			*lat = asin(1/viewpt)/RAD;
+	} else
+		*lon += res;
+	if(*lon <= 180)
+		return 1;
+	first = 1;
+	return -1;
+}

src/cmd/map/libmap/polyconic.c

@@ -0,0 +1,28 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xpolyconic(struct place *place, double *x, double *y)
+{
+	double r, alpha;
+	double lat2, lon2;
+	if(fabs(place->nlat.l) > .01) {
+		r = place->nlat.c / place->nlat.s;
+		alpha = place->wlon.l * place->nlat.s;
+		*y = place->nlat.l + r*(1 - cos(alpha));
+		*x = - r*sin(alpha);
+	} else {
+		lon2 = place->wlon.l * place->wlon.l;
+		lat2 = place->nlat.l * place->nlat.l;
+		*y = place->nlat.l * (1+(lon2/2)*(1-(8+lon2)*lat2/12));
+		*x = - place->wlon.l * (1-lat2*(3+lon2)/6);
+	}
+	return(1);
+}
+
+proj
+polyconic(void)
+{
+	return(Xpolyconic);
+}

src/cmd/map/libmap/rectangular.c

@@ -0,0 +1,22 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double scale;
+
+static int
+Xrectangular(struct place *place, double *x, double *y)
+{
+	*x = -scale*place->wlon.l;
+	*y = place->nlat.l;
+	return(1);
+}
+
+proj
+rectangular(double par)
+{
+	scale = cos(par*RAD);
+	if(scale<.1)
+		return 0;
+	return(Xrectangular);
+}

src/cmd/map/libmap/simpleconic.c

@@ -0,0 +1,34 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double r0, a;
+
+static int
+Xsimpleconic(struct place *place, double *x, double *y)
+{
+	double r = r0 - place->nlat.l;
+	double t = a*place->wlon.l;
+	*x = -r*sin(t);
+	*y = -r*cos(t);
+	return 1;
+}
+
+proj
+simpleconic(double par0, double par1)
+{
+	struct coord lat0;
+	struct coord lat1;
+	deg2rad(par0,&lat0);
+	deg2rad(par1,&lat1);
+	if(fabs(lat0.l+lat1.l)<.01)
+		return rectangular(par0);
+	if(fabs(lat0.l-lat1.l)<.01) {
+		a = lat0.s/lat0.l;
+		r0 = lat0.c/lat0.s + lat0.l;
+	} else {
+		a = (lat1.c-lat0.c)/(lat0.l-lat1.l);
+		r0 = ((lat0.c+lat1.c)/a + lat1.l + lat0.l)/2;
+	}
+	return Xsimpleconic;
+}

src/cmd/map/libmap/sinusoidal.c

@@ -0,0 +1,17 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+int
+Xsinusoidal(struct place *place, double *x, double *y)
+{
+	*x = - place->wlon.l * place->nlat.c;
+	*y = place->nlat.l;
+	return(1);
+}
+
+proj
+sinusoidal(void)
+{
+	return(Xsinusoidal);
+}

src/cmd/map/libmap/tetra.c

@@ -0,0 +1,206 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+/*
+ *	conformal map of earth onto tetrahedron
+ *	the stages of mapping are
+ *	(a) stereo projection of tetrahedral face onto
+ *	    isosceles curvilinear triangle with 3 120-degree
+ *	    angles and one straight side
+ *	(b) map of this triangle onto half plane cut along
+ *	    3 rays from the roots of unity to infinity
+ *		formula (z^4+2*3^.5*z^2-1)/(z^4-2*3^.5*z^2-1)
+ *	(c) do 3 times for  each sector of plane:
+ *	    map of |arg z|<=pi/6, cut along z>1 into
+ *	    triangle |arg z|<=pi/6, Re z<=const,
+ *	    with upper side of cut going into upper half of
+ *	    of vertical side of triangle and lowere into lower
+ *		formula int from 0 to z dz/sqrt(1-z^3)
+ *
+ *	int from u to 1 3^.25*du/sqrt(1-u^3) =
+		F(acos((rt3-1+u)/(rt3+1-u)),sqrt(1/2+rt3/4))
+ *	int from 1 to u 3^.25*du/sqrt(u^3-1) =
+ *		F(acos((rt3+1-u)/(rt3-1+u)),sqrt(1/2-rt3/4))
+ *	this latter formula extends analytically down to
+ *	u=0 and is the basis of this routine, with the
+ *	argument of complex elliptic integral elco2
+ *	being tan(acos...)
+ *	the formula F(pi-x,k) = 2*F(pi/2,k)-F(x,k) is
+ *	used to cross over into the region where Re(acos...)>pi/2
+ *		f0 and fpi are suitably scaled complete integrals
+*/
+
+#define TFUZZ 0.00001
+
+static struct place tpole[4];	/* point of tangency of tetrahedron face*/
+static double tpoleinit[4][2] = {
+	1.,	0.,
+	1.,	180.,
+	-1.,	90.,
+	-1.,	-90.
+};
+static struct tproj {
+	double tlat,tlon;	/* center of stereo projection*/
+	double ttwist;		/* rotatn before stereo*/
+	double trot;		/*rotate after projection*/
+	struct place projpl;	/*same as tlat,tlon*/
+	struct coord projtw;	/*same as ttwist*/
+	struct coord postrot;	/*same as trot*/
+} tproj[4][4] = {
+{/*00*/	{0.},
+ /*01*/	{90.,	0.,	90.,	-90.},
+ /*02*/	{0.,	45.,	-45.,	150.},
+ /*03*/	{0.,	-45.,	-135.,	30.}
+},
+{/*10*/	{90.,	0.,	-90.,	90.},
+ /*11*/ {0.},
+ /*12*/ {0.,	135.,	-135.,	-150.},
+ /*13*/	{0.,	-135.,	-45.,	-30.}
+},
+{/*20*/	{0.,	45.,	135.,	-30.},
+ /*21*/	{0.,	135.,	45.,	-150.},
+ /*22*/	{0.},
+ /*23*/	{-90.,	0.,	180.,	90.}
+},
+{/*30*/	{0.,	-45.,	45.,	-150.},
+ /*31*/ {0.,	-135.,	135.,	-30.},
+ /*32*/	{-90.,	0.,	0.,	90.},
+ /*33*/ {0.} 
+}};
+static double tx[4] = {	/*where to move facet after final rotation*/
+	0.,	0.,	-1.,	1.	/*-1,1 to be sqrt(3)*/
+};
+static double ty[4] = {
+	0.,	2.,	-1.,	-1.
+};
+static double root3;
+static double rt3inv;
+static double two_rt3;
+static double tkc,tk,tcon;
+static double f0r,f0i,fpir,fpii;
+
+static void
+twhichp(struct place *g, int *p, int *q)
+{
+	int i,j,k;
+	double cosdist[4];
+	struct place *tp;
+	for(i=0;i<4;i++) {
+		tp = &tpole[i];
+		cosdist[i] = g->nlat.s*tp->nlat.s +
+			  g->nlat.c*tp->nlat.c*(
+			  g->wlon.s*tp->wlon.s +
+			  g->wlon.c*tp->wlon.c);
+	}
+	j = 0;
+	for(i=1;i<4;i++)
+		if(cosdist[i] > cosdist[j])
+			j = i;
+	*p = j;
+	k = j==0?1:0;
+	for(i=0;i<4;i++)
+		if(i!=j&&cosdist[i]>cosdist[k])
+			k = i;
+	*q = k;
+}
+
+int
+Xtetra(struct place *place, double *x, double *y)
+{
+	int i,j;
+	struct place pl;
+	register struct tproj *tpp;
+	double vr, vi;
+	double br, bi;
+	double zr,zi,z2r,z2i,z4r,z4i,sr,si,tr,ti;
+	twhichp(place,&i,&j);
+	copyplace(place,&pl);
+	norm(&pl,&tproj[i][j].projpl,&tproj[i][j].projtw);
+	Xstereographic(&pl,&vr,&vi);
+	zr = vr/2;
+	zi = vi/2;
+	if(zr<=TFUZZ)
+		zr = TFUZZ;
+	csq(zr,zi,&z2r,&z2i);
+	csq(z2r,z2i,&z4r,&z4i);
+	z2r *= two_rt3;
+	z2i *= two_rt3;
+	cdiv(z4r+z2r-1,z4i+z2i,z4r-z2r-1,z4i-z2i,&sr,&si);
+	csqrt(sr-1,si,&tr,&ti);
+	cdiv(tcon*tr,tcon*ti,root3+1-sr,-si,&br,&bi);
+	if(br<0) {
+		br = -br;
+		bi = -bi;
+		if(!elco2(br,bi,tk,1.,1.,&vr,&vi))
+			return 0;
+		vr = fpir - vr;
+		vi = fpii - vi;
+	} else 
+		if(!elco2(br,bi,tk,1.,1.,&vr,&vi))
+			return 0;
+	if(si>=0) {
+		tr = f0r - vi;
+		ti = f0i + vr;
+	} else {
+		tr = f0r + vi;
+		ti = f0i - vr;
+	}
+	tpp = &tproj[i][j];
+	*x = tr*tpp->postrot.c +
+	     ti*tpp->postrot.s + tx[i];
+	*y = ti*tpp->postrot.c -
+	     tr*tpp->postrot.s + ty[i];
+	return(1);
+}
+
+int
+tetracut(struct place *g, struct place *og, double *cutlon)
+{
+	int i,j,k;
+	if((g->nlat.s<=-rt3inv&&og->nlat.s<=-rt3inv) && 
+	   (ckcut(g,og,*cutlon=0.)==2||ckcut(g,og,*cutlon=PI)==2))
+		return(2);
+	twhichp(g,&i,&k);
+	twhichp(og,&j,&k);
+	if(i==j||i==0||j==0)
+		return(1);
+	return(0);
+}
+
+proj
+tetra(void)
+{
+	int i;
+	int j;
+	register struct place *tp;
+	register struct tproj *tpp;
+	double t;
+	root3 = sqrt(3.);
+	rt3inv = 1/root3;
+	two_rt3 = 2*root3;
+	tkc = sqrt(.5-.25*root3);
+	tk = sqrt(.5+.25*root3);
+	tcon = 2*sqrt(root3);
+	elco2(tcon/(root3-1),0.,tkc,1.,1.,&f0r,&f0i);
+	elco2(1.e15,0.,tk,1.,1.,&fpir,&fpii);
+	fpir *= 2;
+	fpii *= 2;
+	for(i=0;i<4;i++) {
+		tx[i] *= f0r*root3;
+		ty[i] *= f0r;
+		tp = &tpole[i];
+		t = tp->nlat.s = tpoleinit[i][0]/root3;
+		tp->nlat.c = sqrt(1 - t*t);
+		tp->nlat.l = atan2(tp->nlat.s,tp->nlat.c);
+		deg2rad(tpoleinit[i][1],&tp->wlon);
+		for(j=0;j<4;j++) {
+			tpp = &tproj[i][j];
+			latlon(tpp->tlat,tpp->tlon,&tpp->projpl);
+			deg2rad(tpp->ttwist,&tpp->projtw);
+			deg2rad(tpp->trot,&tpp->postrot);
+		}
+	}
+	return(Xtetra);
+}
+

src/cmd/map/libmap/trapezoidal.c

@@ -0,0 +1,30 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static struct coord stdpar0, stdpar1;
+static double k;
+static double yeq;
+
+static int
+Xtrapezoidal(struct place *place, double *x, double *y)
+{
+	*y = yeq + place->nlat.l;
+	*x = *y*k*place->wlon.l;
+	return 1;
+}
+
+proj
+trapezoidal(double par0, double par1)
+{
+	if(fabs(fabs(par0)-fabs(par1))<.1)
+		return rectangular(par0);
+	deg2rad(par0,&stdpar0);
+	deg2rad(par1,&stdpar1);
+	if(fabs(par1-par0) < .1)
+		k = stdpar1.s;
+	else
+		k = (stdpar1.c-stdpar0.c)/(stdpar0.l-stdpar1.l);
+	yeq = -stdpar1.l - stdpar1.c/k;
+	return Xtrapezoidal;
+}

src/cmd/map/libmap/twocirc.c

@@ -0,0 +1,80 @@
+#include <u.h>
+#include <libc.h>
+#include "map.h"
+
+static double
+quadratic(double a, double b, double c)
+{
+	double disc = b*b - 4*a*c;
+	return disc<0? 0: (-b-sqrt(disc))/(2*a);
+}
+
+/* for projections with meridians being circles centered
+on the x axis and parallels being circles centered on the y
+axis.  Find the intersection of the meridian thru (m,0), (90,0),
+with the parallel thru (0,p), (p1,p2) */
+
+static int
+twocircles(double m, double p, double p1, double p2, double *x, double *y)
+{
+	double a;	/* center of meridian circle, a>0 */
+	double b;	/* center of parallel circle, b>0 */
+	double t,bb;
+	if(m > 0) {
+		twocircles(-m,p,p1,p2,x,y);
+		*x = -*x;
+	} else if(p < 0) {
+		twocircles(m,-p,p1,-p2,x,y);
+		*y = -*y;
+	} else if(p < .01) {
+		*x = m;
+		t = m/p1;
+		*y = p + (p2-p)*t*t;
+	} else if(m > -.01) {
+		*y = p;
+		*x = m - m*p*p;
+	} else {
+		b = p>=1? 1: p>.99? 0.5*(p+1 + p1*p1/(1-p)):
+			0.5*(p*p-p1*p1-p2*p2)/(p-p2);
+		a = .5*(m - 1/m);
+		t = m*m-p*p+2*(b*p-a*m);
+		bb = b*b;
+		*x = quadratic(1+a*a/bb, -2*a + a*t/bb,
+			t*t/(4*bb) - m*m + 2*a*m);
+		*y = (*x*a+t/2)/b;
+	}
+	return 1;
+}		
+
+static int
+Xglobular(struct place *place, double *x, double *y)
+{
+	twocircles(-2*place->wlon.l/PI,
+		2*place->nlat.l/PI, place->nlat.c, place->nlat.s, x, y);
+	return 1;
+}	
+
+proj
+globular(void)
+{
+	return Xglobular;
+}
+
+static int
+Xvandergrinten(struct place *place, double *x, double *y)
+{
+	double t = 2*place->nlat.l/PI;
+	double abst = fabs(t);
+	double pval = abst>=1? 1: abst/(1+sqrt(1-t*t));
+	double p2 = 2*pval/(1+pval);
+	twocircles(-place->wlon.l/PI, pval, sqrt(1-p2*p2), p2, x, y);
+	if(t < 0) 
+		*y = -*y;
+	return 1;
+}
+
+proj
+vandergrinten(void)
+{
+	return Xvandergrinten;
+}

src/cmd/map/libmap/zcoord.c

@@ -0,0 +1,143 @@
+#include <u.h>
+#include <libc.h>
+#include <stdio.h>
+#include "map.h"
+
+static double cirmod(double);
+
+static struct place pole;	/* map pole is tilted to here */
+static struct coord twist;	/* then twisted this much */
+static struct place ipole;	/* inverse transfrom */
+static struct coord itwist;
+
+void
+orient(double lat, double lon, double theta)
+{
+	lat = cirmod(lat);
+	if(lat>90.) {
+		lat = 180. - lat;
+		lon -= 180.;
+		theta -= 180.;
+	} else if(lat < -90.) {
+		lat = -180. - lat;
+		lon -= 180.;
+		theta -= 180;
+	}
+	latlon(lat,lon,&pole);
+	deg2rad(theta, &twist);
+	latlon(lat,180.-theta,&ipole);
+	deg2rad(180.-lon, &itwist);
+}
+
+void
+latlon(double lat, double lon, struct place *p)
+{
+	lat = cirmod(lat);
+	if(lat>90.) {
+		lat = 180. - lat;
+		lon -= 180.;
+	} else if(lat < -90.) {
+		lat = -180. - lat;
+		lon -= 180.;
+	}
+	deg2rad(lat,&p->nlat);
+	deg2rad(lon,&p->wlon);
+}
+
+void
+deg2rad(double theta, struct coord *coord)
+{
+	theta = cirmod(theta);
+	coord->l = theta*RAD;
+	if(theta==90) {
+		coord->s = 1;
+		coord->c = 0;
+	} else if(theta== -90) {
+		coord->s = -1;
+		coord->c = 0;
+	} else
+		sincos(coord);
+}
+
+static double
+cirmod(double theta)
+{
+	while(theta >= 180.)
+		theta -= 360;
+	while(theta<-180.)
+		theta += 360.;
+	return(theta);
+}
+
+void
+sincos(struct coord *coord)
+{
+	coord->s = sin(coord->l);
+	coord->c = cos(coord->l);
+}
+
+void
+normalize(struct place *gg)
+{
+	norm(gg,&pole,&twist);
+}
+
+void
+invert(struct place *g)
+{
+	norm(g,&ipole,&itwist);
+}
+
+void
+norm(struct place *gg, struct place *pp, struct coord *tw)
+{
+	register struct place *g;	/*geographic coords */
+	register struct place *p;	/* new pole in old coords*/
+	struct place m;			/* standard map coords*/
+	g = gg;
+	p = pp;
+	if(p->nlat.s == 1.) {
+		if(p->wlon.l+tw->l == 0.)
+			return;
+		g->wlon.l -= p->wlon.l+tw->l;
+	} else {
+		if(p->wlon.l != 0) {
+			g->wlon.l -= p->wlon.l;
+			sincos(&g->wlon);
+		}
+		m.nlat.s = p->nlat.s * g->nlat.s
+			+ p->nlat.c * g->nlat.c * g->wlon.c;
+		m.nlat.c = sqrt(1. - m.nlat.s * m.nlat.s);
+		m.nlat.l = atan2(m.nlat.s, m.nlat.c);
+		m.wlon.s = g->nlat.c * g->wlon.s;
+		m.wlon.c = p->nlat.c * g->nlat.s
+			- p->nlat.s * g->nlat.c * g->wlon.c;
+		m.wlon.l = atan2(m.wlon.s, - m.wlon.c)
+			- tw->l;
+		*g = m;
+	}
+	sincos(&g->wlon);
+	if(g->wlon.l>PI)
+		g->wlon.l -= 2*PI;
+	else if(g->wlon.l<-PI)
+		g->wlon.l += 2*PI;
+}
+
+double
+tan(double x)
+{
+	return(sin(x)/cos(x));
+}
+
+void
+printp(struct place *g)
+{
+printf("%.3f %.3f %.3f %.3f %.3f %.3f\n",
+g->nlat.l,g->nlat.s,g->nlat.c,g->wlon.l,g->wlon.s,g->wlon.c);
+}
+
+void
+copyplace(struct place *g1, struct place *g2)
+{
+	*g2 = *g1;
+}