ref: 3e0e77a8521331412c96b6371622aa2f76d7aefc
dir: /sys/src/cmd/map/libmap/twocirc.c/
#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; }