1 files changed, 106 insertions, 0 deletions
diff --git a/src/projections/PJ_vandg.cpp b/src/projections/PJ_vandg.cpp
new file mode 100644
index 00000000..d148e210
--- /dev/null
+++ b/src/projections/PJ_vandg.cpp
@@ -0,0 +1,106 @@
+#define PJ_LIB__
+#include "proj.h"
+#include "projects.h"
+
+PROJ_HEAD(vandg, "van der Grinten (I)") "\n\tMisc Sph";
+
+# define TOL        1.e-10
+# define THIRD      .33333333333333333333
+# define C2_27      .07407407407407407407
+# define PI4_3      4.18879020478639098458
+# define PISQ       9.86960440108935861869
+# define TPISQ      19.73920880217871723738
+# define HPISQ      4.93480220054467930934
+
+
+static XY s_forward (LP lp, PJ *P) {           /* Spheroidal, forward */
+    XY xy = {0.0,0.0};
+    double  al, al2, g, g2, p2;
+
+    p2 = fabs(lp.phi / M_HALFPI);
+    if ((p2 - TOL) > 1.) {
+        proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
+        return xy;
+    }
+    if (p2 > 1.)
+        p2 = 1.;
+    if (fabs(lp.phi) <= TOL) {
+        xy.x = lp.lam;
+        xy.y = 0.;
+    } else if (fabs(lp.lam) <= TOL || fabs(p2 - 1.) < TOL) {
+        xy.x = 0.;
+        xy.y = M_PI * tan(.5 * asin(p2));
+        if (lp.phi < 0.) xy.y = -xy.y;
+    } else {
+        al = .5 * fabs(M_PI / lp.lam - lp.lam / M_PI);
+        al2 = al * al;
+        g = sqrt(1. - p2 * p2);
+        g = g / (p2 + g - 1.);
+        g2 = g * g;
+        p2 = g * (2. / p2 - 1.);
+        p2 = p2 * p2;
+        xy.x = g - p2; g = p2 + al2;
+        xy.x = M_PI * (al * xy.x + sqrt(al2 * xy.x * xy.x - g * (g2 - p2))) / g;
+        if (lp.lam < 0.) xy.x = -xy.x;
+        xy.y = fabs(xy.x / M_PI);
+        xy.y = 1. - xy.y * (xy.y + 2. * al);
+        if (xy.y < -TOL) {
+            proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
+            return xy;
+        }
+        if (xy.y < 0.)
+            xy.y = 0.;
+        else
+            xy.y = sqrt(xy.y) * (lp.phi < 0. ? -M_PI : M_PI);
+    }
+
+    return xy;
+}
+
+
+static LP s_inverse (XY xy, PJ *P) {           /* Spheroidal, inverse */
+    LP lp = {0.0,0.0};
+    double t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
+
+    x2 = xy.x * xy.x;
+    if ((ay = fabs(xy.y)) < TOL) {
+        lp.phi = 0.;
+        t = x2 * x2 + TPISQ * (x2 + HPISQ);
+        lp.lam = fabs(xy.x) <= TOL ? 0. :
+           .5 * (x2 - PISQ + sqrt(t)) / xy.x;
+        return (lp);
+    }
+    y2 = xy.y * xy.y;
+    r = x2 + y2;    r2 = r * r;
+    c1 = - M_PI * ay * (r + PISQ);
+    c3 = r2 + M_TWOPI * (ay * r + M_PI * (y2 + M_PI * (ay + M_HALFPI)));
+    c2 = c1 + PISQ * (r - 3. *  y2);
+    c0 = M_PI * ay;
+    c2 /= c3;
+    al = c1 / c3 - THIRD * c2 * c2;
+    m = 2. * sqrt(-THIRD * al);
+    d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
+    if (((t = fabs(d = 3. * d / (al * m))) - TOL) <= 1.) {
+        d = t > 1. ? (d > 0. ? 0. : M_PI) : acos(d);
+        lp.phi = M_PI * (m * cos(d * THIRD + PI4_3) - THIRD * c2);
+        if (xy.y < 0.) lp.phi = -lp.phi;
+        t = r2 + TPISQ * (x2 - y2 + HPISQ);
+        lp.lam = fabs(xy.x) <= TOL ? 0. :
+           .5 * (r - PISQ + (t <= 0. ? 0. : sqrt(t))) / xy.x;
+    } else {
+        proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
+        return lp;
+    }
+
+    return lp;
+}
+
+
+PJ *PROJECTION(vandg) {
+    P->es = 0.;
+    P->inv = s_inverse;
+    P->fwd = s_forward;
+
+    return P;
+}
+