1 #include "map.h" 2 3 static double 4 quadratic(double a, double b, double c) 5 { 6 double disc = b*b - 4*a*c; 7 return disc<0? 0: (-b-sqrt(disc))/(2*a); 8 } 9 10 /* for projections with meridians being circles centered 11 on the x axis and parallels being circles centered on the y 12 axis. Find the intersection of the meridian thru (m,0), (90,0), 13 with the parallel thru (0,p), (p1,p2) */ 14 15 static int 16 twocircles(double m, double p, double p1, double p2, double *x, double *y) 17 { 18 double a; /* center of meridian circle, a>0 */ 19 double b; /* center of parallel circle, b>0 */ 20 double t,bb; 21 if(m > 0) { 22 twocircles(-m,p,p1,p2,x,y); 23 *x = -*x; 24 } else if(p < 0) { 25 twocircles(m,-p,p1,-p2,x,y); 26 *y = -*y; 27 } else if(p < .01) { 28 *x = m; 29 t = m/p1; 30 *y = p + (p2-p)*t*t; 31 } else if(m > -.01) { 32 *y = p; 33 *x = m - m*p*p; 34 } else { 35 b = p>=1? 1: p>.99? 0.5*(p+1 + p1*p1/(1-p)): 36 0.5*(p*p-p1*p1-p2*p2)/(p-p2); 37 a = .5*(m - 1/m); 38 t = m*m-p*p+2*(b*p-a*m); 39 bb = b*b; 40 *x = quadratic(1+a*a/bb, -2*a + a*t/bb, 41 t*t/(4*bb) - m*m + 2*a*m); 42 *y = (*x*a+t/2)/b; 43 } 44 return 1; 45 } 46 47 static int 48 Xglobular(struct place *place, double *x, double *y) 49 { 50 twocircles(-2*place->wlon.l/PI, 51 2*place->nlat.l/PI, place->nlat.c, place->nlat.s, x, y); 52 return 1; 53 } 54 55 proj 56 globular(void) 57 { 58 return Xglobular; 59 } 60 61 static int 62 Xvandergrinten(struct place *place, double *x, double *y) 63 { 64 double t = 2*place->nlat.l/PI; 65 double abst = fabs(t); 66 double pval = abst>=1? 1: abst/(1+sqrt(1-t*t)); 67 double p2 = 2*pval/(1+pval); 68 twocircles(-place->wlon.l/PI, pval, sqrt(1-p2*p2), p2, x, y); 69 if(t < 0) 70 *y = -*y; 71 return 1; 72 } 73 74 proj 75 vandergrinten(void) 76 { 77 return Xvandergrinten; 78 } 79