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/* determine latitude from authalic latitude */
#include <math.h>
#include <stddef.h>
#include "proj.h"
#include "projects.h"
# define P00 .33333333333333333333 /* 1 / 3 */
# define P01 .17222222222222222222 /* 31 / 180 */
# define P02 .10257936507936507937 /* 517 / 5040 */
# define P10 .06388888888888888888 /* 23 / 360 */
# define P11 .06640211640211640212 /* 251 / 3780 */
# define P20 .01677689594356261023 /* 761 / 45360 */
#define APA_SIZE 3
double *
pj_authset(double es) {
double t, *APA;
if ((APA = (double *)pj_malloc(APA_SIZE * sizeof(double))) != nullptr) {
APA[0] = es * P00;
t = es * es;
APA[0] += t * P01;
APA[1] = t * P10;
t *= es;
APA[0] += t * P02;
APA[1] += t * P11;
APA[2] = t * P20;
}
return APA;
}
double
pj_authlat(double beta, double *APA) {
double t = beta+beta;
return(beta + APA[0] * sin(t) + APA[1] * sin(t+t) + APA[2] * sin(t+t+t));
}
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