Added hill

CHANGELOG.md

@@ -1,3 +1,6 @@
+v0.0.33
+* Added Hill Eucyclic projection.
+
 v0.0.32
 * Bug fix
 

package.json

@@ -1,6 +1,6 @@
 {
 	"name": "mproj",
-	"version": "0.0.32",
+	"version": "0.0.33",
 	"description": "A JavaScript port of the Proj.4 cartographic projections library",
 	"keywords": [
 		"projections",

src/projections/bertin1953.js

@@ -9,7 +9,7 @@
   Port to PROJ by Philippe Rivière, 21 September 2018
   Port to JavaScript by Matthew Bloch October 2018
 */
-pj_add(pj_bertin1953, 'bertin1953', 'Bertin 1953', 'Misc Sph no inv.');
+pj_add(pj_bertin1953, 'bertin1953', 'Bertin 1953', 'Misc., Sph., NoInv.');
 
 function pj_bertin1953(P) {
   var cos_delta_phi, sin_delta_phi, cos_delta_gamma, sin_delta_gamma;

src/projections/cupola.js

@@ -1,4 +1,4 @@
-pj_add(pj_cupola, 'cupola', 'Cupola', 'Misc., Sph., NoInv.');
+pj_add(pj_cupola, 'cupola', 'Cupola', 'PCyl., Sph., NoInv.');
 
 // Source: https://www.tandfonline.com/eprint/EE7Y8RK4GXA4ITWUTQPY/full?target=10.1080/23729333.2020.1862962
 // See also: http://www.at-a-lanta.nl/weia/cupola.html

src/projections/hill.js

@@ -0,0 +1,58 @@
+pj_add(pj_hill, 'hill', 'Hill Eucyclic', 'PCyl., Sph., NoInv.');
+
+// Adapted from: https://github.com/d3/d3-geo-projection/blob/master/src/hill.js
+// License: https://github.com/d3/d3-geo-projection/blob/master/LICENSE
+
+function pj_hill(P) {
+  var K = 1, // TODO: expose as parameter
+      L = 1 + K,
+      sinBt = sin(1 / L),
+      Bt = asin(sinBt),
+      A = 2 * sqrt(M_PI / (B = M_PI + 4 * Bt * L)),
+      B,
+      rho0 = 0.5 * A * (L + sqrt(K * (2 + K))),
+      K2 = K * K,
+      L2 = L * L,
+      EPS = 1e-12;
+
+  P.es = 0;
+  P.fwd = s_fwd;
+  P.inv = s_inv;
+
+  function s_fwd(lp, xy) {
+    var t = 1 - sin(lp.phi),
+        rho, omega;
+    if (t && t < 2) {
+      var theta = M_HALFPI - lp.phi,
+          i = 25,
+          delta, sinTheta, cosTheta, C, Bt_Bt1;
+      do {
+        sinTheta = sin(theta);
+        cosTheta = cos(theta);
+        Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta);
+        C = 1 + L2 - 2 * L * cosTheta;
+        theta -= delta = (theta - K2 * Bt - L * sinTheta + C * Bt_Bt1 -0.5 * t * B) / (2 * L * sinTheta * Bt_Bt1);
+      } while (fabs(delta) > EPS && --i > 0);
+      rho = A * sqrt(C);
+      omega = lp.lam * Bt_Bt1 / M_PI;
+    } else {
+      rho = A * (K + t);
+      omega = lp.lam * Bt / M_PI;
+    }
+
+    xy.x = rho * sin(omega);
+    xy.y = rho0 - rho * cos(omega);
+  }
+
+  function s_inv(xy, lp) {
+    var x = xy.x,
+        y = xy.y,
+        rho2 = x * x + (y -= rho0) * y,
+        cosTheta = (1 + L2 - rho2 / (A * A)) / (2 * L),
+        theta = acos(cosTheta),
+        sinTheta = sin(theta),
+        Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta);
+    lp.lam = asin(x / sqrt(rho2)) * M_PI / Bt_Bt1,
+    lp.phi = asin(1 - 2 * (theta - K2 * Bt - L * sinTheta + (1 + L2 - 2 * L * cosTheta) * Bt_Bt1) / B);
+  }
+}