d3-geo-projection - npm Package Compare versions

Comparing version 0.2.7 to 0.2.8

d3.geo.projection.min.js

@@ -1,2 +0,2 @@
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M=Math.tan(e),s=1/Math.cos(e),c=r-2*n*e+e*e;e-=a=(M*c+2*(e-n))/(2+c*s*s+2*(e-n)*M)}while(Math.abs(a)>sa&&--o>0);return M=Math.tan(e),[(Math.abs(n)<Math.abs(e+1/M)?h(t*M):i(t)*(u(Math.abs(t*M))+va))/Math.sin(e),e]},(d3.geo.polyconic=function(){return ba(Cn)}).raw=Cn,(d3.geo.rectangularPolyconic=function(){return x(Dn)}).raw=Dn;var Ga=[[.9986,-.062],[1,0],[.9986,.062],[.9954,.124],[.99,.186],[.9822,.248],[.973,.31],[.96,.372],[.9427,.434],[.9216,.4958],[.8962,.5571],[.8679,.6176],[.835,.6769],[.7986,.7346],[.7597,.7903],[.7186,.8435],[.6732,.8936],[.6213,.9394],[.5722,.9761],[.5322,1]];Ga.forEach(function(t){t[1]*=1.0144}),Ln.invert=function(t,n){var a=n/va,r=90*a,e=Math.min(18,Math.abs(r/5)),o=Math.max(0,Math.floor(e));do{var i=Ga[o][1],h=Ga[o+1][1],u=Ga[Math.min(19,o+2)][1],M=u-i,s=u-2*h+i,c=2*(Math.abs(a)-h)/M,f=s/M,v=c*(1-f*c*(1-2*f*c));if(v>=0||1===o){r=(n>=0?5:-5)*(v+e);var l,g=50;do e=Math.min(18,Math.abs(r)/5),o=Math.floor(e),v=e-o,i=Ga[o][1],h=Ga[o+1][1],u=Ga[Math.min(19,o+2)][1],r-=(l=(n>=0?va:-va)*(h+v*(u-i)/2+v*v*(u-2*h+i)/2)-n)*da;while(Math.abs(l)>ca&&--g>0);break}}while(--o>=0);var d=Ga[o][0],b=Ga[o+1][0],p=Ga[Math.min(19,o+2)][0];return[t/(b+v*(p-d)/2+v*v*(p-2*b+d)/2),r*ga]},(d3.geo.robinson=function(){return ba(Ln)}).raw=Ln,(d3.geo.satellite=In).raw=Hn,Jn.invert=function(t,n){var a=n/1.70711,r=Math.sin(fa/4*a);return[t/(.74482-.34588*r*r),2*Math.atan(a)]},(d3.geo.times=function(){return ba(Jn)}).raw=Jn,(d3.geo.twoPointEquidistant=Nn).raw=Kn,(d3.geo.twoPointAzimuthal=Vn).raw=Un,Wn.invert=function(t,n){if(Math.abs(n)<sa)return[t,0];if(Math.abs(t)<sa)return[0,va*Math.sin(2*Math.atan(n/fa))];var a=(t/=fa)*t,r=(n/=fa)*n,e=a+r,o=e*e,h=-Math.abs(n)*(1+e),M=h-2*r+a,s=-2*h+1+2*r+o,c=r/s+(2*M*M*M/(s*s*s)-9*h*M/(s*s))/27,f=(h-M*M/(3*s))/s,v=2*Math.sqrt(-f/3),l=u(3*c/(f*v))/3;return[fa*(e-1+Math.sqrt(1+2*(a-r)+o))/(2*t),i(n)*fa*(-v*Math.cos(l+fa/3)-M/(3*s))]},(d3.geo.vanDerGrinten=function(){return ba(Wn)}).raw=Wn,Xn.invert=function(t,n){if(!t)return[0,va*Math.sin(2*Math.atan(n/fa))];var a=Math.abs(t/fa),r=(1-a*a-(n/=fa)*n)/(2*a),e=r*r,o=Math.sqrt(e+1);return[i(t)*fa*(o-r),i(n)*va*Math.sin(2*Math.atan2(Math.sqrt((1-2*r*a)*(r+o)-a),Math.sqrt(o+r+a)))]},(d3.geo.vanDerGrinten2=function(){return ba(Xn)}).raw=Xn,Yn.invert=function(t,n){if(!n)return[t,0];var a=n/fa,r=(fa*fa*(1-a*a)-t*t)/(2*fa*t);return[t?fa*(i(t)*Math.sqrt(r*r+1)-r):0,va*Math.sin(2*Math.atan(a))]},(d3.geo.vanDerGrinten3=function(){return ba(Yn)}).raw=Yn,Zn.invert=function(t,n){if(!t||!n)return[t,n];n/=fa;var a=i(t)*t/va,r=(a*a-1+4*n*n)/Math.abs(a),e=r*r,o=2*n,h=50;do{var u=o*o,M=(8*o-u*(u+2)-5)/(2*u*(o-1)),s=(3*o-u*o-10)/(2*u*o),c=M*M,f=o*M,v=o+M,l=v*v,g=o+3*M,d=l*(u+c*e-1)+(1-u)*(u*(g*g+4*c)+c*(12*f+4*c)),b=-2*v*(4*f*c+(1-4*u+3*u*u)*(1+s)+c*(-6+14*u-e+(-8+8*u-2*e)*s)+f*(-8+12*u+(-10+10*u-e)*s)),p=Math.sqrt(d),w=r*(l+c-1)+2*p-a*(4*l+e),q=r*(2*M*s+2*v*(1+s))+b/p-8*v*(r*(-1+c+l)+2*p)*(1+s)/(e+4*l);o-=δ=w/q}while(δ>sa&&--h>0);return[i(t)*(Math.sqrt(r*r+4)+r)*fa/4,va*o]},(d3.geo.vanDerGrinten4=function(){return ba(Zn)}).raw=Zn;var ja=function(){var t=4*fa+3*Math.sqrt(3),n=2*Math.sqrt(2*fa*Math.sqrt(3)/t);return R(n*Math.sqrt(3)/fa,n,t/6)}();(d3.geo.wagner4=function(){return ba(ja)}).raw=ja,$n.invert=function(t,n){return[t/Math.sqrt(1-3*n*n/(fa*fa)),n]},(d3.geo.wagner6=function(){return ba($n)}).raw=$n,ta.invert=function(t,n){var a=t/2.66723,r=n/1.24104,e=Math.sqrt(a*a+r*r),o=2*h(e/2);return[3*Math.atan2(t*Math.tan(o),2.66723*e),e&&h(n*Math.sin(o)/(1.24104*.90631*e))]},(d3.geo.wagner7=function(){return ba(ta)}).raw=ta,na.invert=function(t,n){var a=-.5*(t*t+n*n),r=Math.sqrt(-a*(2+a)),e=n*a+t*r,o=t*a-n*r,i=Math.sqrt(o*o+e*e);return[Math.atan2(r*e,i*(1+a)),i?-h(r*o/i):0]},(d3.geo.wiechel=function(){return ba(na)}).raw=na,aa.invert=function(t,n){var a=t,r=n,e=25;do{var o,i=Math.cos(r),h=Math.sin(r),M=Math.sin(2*r),s=h*h,c=i*i,f=Math.sin(a),v=Math.cos(a/2),l=Math.sin(a/2),g=l*l,d=1-c*v*v,b=d?u(i*v)*Math.sqrt(o=1/d):o=0,p=.5*(2*b*i*l+a/va)-t,w=.5*(b*h+r)-n,q=.5*o*(c*g+b*i*v*s)+.5/va,m=o*(f*M/4-b*h*l),y=.125*o*(M*l-b*h*c*f),S=.5*o*(s*v+b*g*i)+.5,Q=m*y-S*q,R=(w*m-p*S)/Q,T=(p*y-w*q)/Q;a-=R,r-=T}while((Math.abs(R)>sa||Math.abs(T)>sa)&&--e>0);return[a,r]},(d3.geo.winkel3=function(){return ba(aa)}).raw=aa}();

package.json

 {
   "name": "d3-geo-projection",
-  "version": "0.2.7",
+  "version": "0.2.8",
   "description": "Extended geographic projections for D3.js.",
@@ -5,0 +5,0 @@ "keywords": [

src/airy.js

@@ -43,3 +43,3 @@ import "projection";
 function airyProjection() {
-  var β = π / 2,
+  var β = halfπ,
       m = projectionMutator(airy),
@@ -46,0 +46,0 @@ p = m(β);

src/aitoff.js

@@ -13,2 +13,6 @@ import "projection";
 aitoff.invert = function(x, y) {
+  // Abort if [x, y] is not within an ellipse centered at [0, 0] with
+  // semi-major axis π and semi-minor axis π/2.
+  if (x * x + 4 * y * y > π * π + ε) return;
+
   var λ = x, φ = y, i = 25;
@@ -15,0 +19,0 @@ do {

src/baker.js

@@ -16,3 +16,3 @@ import "projection";
 baker.invert = function(x, y) {
-  if ((y0 = Math.abs(y)) < bakerφ) return [x, 2 * Math.atan(Math.exp(y)) - π / 2];
+  if ((y0 = Math.abs(y)) < bakerφ) return [x, 2 * Math.atan(Math.exp(y)) - halfπ];
   var sqrt8 = Math.sqrt(8),
@@ -19,0 +19,0 @@ φ = π / 4, i = 25, δ, y0;

src/berghaus.js

@@ -10,6 +10,6 @@ import "projection";
     var p = berghausAzimuthalEquidistant(λ, φ);
-    if (Math.abs(λ) > π / 2) { // back hemisphere
+    if (Math.abs(λ) > halfπ) { // back hemisphere
       var θ = Math.atan2(p[1], p[0]),
           r = Math.sqrt(p[0] * p[0] + p[1] * p[1]),
-          θ0 = k * Math.round((θ - π / 2) / k) + π / 2,
+          θ0 = k * Math.round((θ - halfπ) / k) + halfπ,
           α = Math.atan2(Math.sin(θ -= θ0), 2 - Math.cos(θ)); // angle relative to lobe end
@@ -25,5 +25,5 @@ θ = θ0 + asin(π / r * Math.sin(α)) - α;
     var r = Math.sqrt(x * x + y * y);
-    if (r > π / 2) {
+    if (r > halfπ) {
       var θ = Math.atan2(y, x),
-          θ0 = k * Math.round((θ - π / 2) / k) + π / 2,
+          θ0 = k * Math.round((θ - halfπ) / k) + halfπ,
           s = θ > θ0 ? -1 : 1,
@@ -45,3 +45,6 @@ A = r * Math.cos(θ0 - θ),
       p = m(n),
-      stream_ = p.stream;
+      stream_ = p.stream,
+      ε = 1e-2,
+      cr = -Math.cos(ε * radians),
+      sr = Math.sin(ε * radians);
 
@@ -60,8 +63,7 @@ p.lobes = function(_) {
       sphereStream.polygonStart(), sphereStream.lineStart();
-      var ε = 1e-2;
-      for (var i = 0, δ = 360 / n, φ = 90 - 180 / n; i < n; ++i, φ -= δ) {
-        sphereStream.point(180, 0);
+      for (var i = 0, δ = 360 / n, δ0 = 2 * π / n, φ = 90 - 180 / n, φ0 = halfπ ; i < n; ++i, φ -= δ, φ0 -= δ0) {
+        sphereStream.point(Math.atan2(sr * Math.cos(φ0), cr) * degrees, asin(sr * Math.sin(φ0)) * degrees);
         if (φ < -90) {
-          sphereStream.point(-90, 180 - φ - ε);
-          sphereStream.point(-90, 180 - φ + ε);
+          sphereStream.point(-90, -180 - φ - ε);
+          sphereStream.point(-90, -180 - φ + ε);
         } else {
@@ -68,0 +70,0 @@ sphereStream.point(90, φ + ε);

src/eckert4.js

 import "projection";
 
 function eckert4(λ, φ) {
-  var k = (2 + π / 2) * Math.sin(φ);
+  var k = (2 + halfπ) * Math.sin(φ);
   φ /= 2;
@@ -22,3 +22,3 @@ for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) {
     x / (2 / Math.sqrt(π * (4 + π)) * (1 + c)),
-    asin((k + A * (c + 2)) / (2 + π / 2))
+    asin((k + A * (c + 2)) / (2 + halfπ))
   ];
@@ -25,0 +25,0 @@ };

src/eckert6.js

 import "projection";
 
 function eckert6(λ, φ) {
-  var k = (1 + π / 2) * Math.sin(φ);
+  var k = (1 + halfπ) * Math.sin(φ);
   for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) {
@@ -16,3 +16,3 @@ φ -= δ = (φ + Math.sin(φ) - k) / (1 + Math.cos(φ));
 eckert6.invert = function(x, y) {
-  var j = 1 + π / 2,
+  var j = 1 + halfπ,
       k = Math.sqrt(j / 2);
@@ -19,0 +19,0 @@ return [

src/eisenlohr.js

@@ -69,5 +69,5 @@ import "projection";
     λ -= δλ;
-    φ = Math.max(-π / 2, Math.min(π / 2, φ - δφ));
+    φ = Math.max(-halfπ, Math.min(halfπ, φ - δφ));
   } while ((Math.abs(δλ) > ε || Math.abs(δφ) > ε) && --i > 0);
-  return Math.abs(Math.abs(φ) - π / 2) < ε
+  return Math.abs(Math.abs(φ) - halfπ) < ε
       ? [0, φ]
@@ -74,0 +74,0 @@ : i && [λ, φ];

src/elliptic.js

@@ -49,3 +49,3 @@ import "math";
       φ + ai * t * φ * (twon + u),
-      2 * Math.atan(Math.exp(u)) - π / 2 + ai * (twon - u) / b
+      2 * Math.atan(Math.exp(u)) - halfπ + ai * (twon - u) / b
     ];
@@ -52,0 +52,0 @@ }

src/gringorten.js

@@ -15,4 +15,4 @@ import "projection";
 
-  if (Math.abs(λ - π / 2) > ε) λ %= π / 2;
-  var point = gringortenHexadecant(λ > π / 4 ? π / 2 - λ : λ, φ);
+  if (Math.abs(λ - halfπ) > ε) λ %= halfπ;
+  var point = gringortenHexadecant(λ > π / 4 ? halfπ - λ : λ, φ);
 
@@ -34,3 +34,3 @@ if (λ > π / 4) z = point[0], point[0] = -point[1], point[1] = -z;
 
-  if (t) λ = -π / 2 - λ;
+  if (t) λ = -halfπ - λ;
 
@@ -46,3 +46,3 @@ var cosφ = Math.cos(φ),
 function gringortenHexadecant(λ, φ) {
-  if (φ === π / 2) return [0, 0];
+  if (φ === halfπ) return [0, 0];
 
@@ -49,0 +49,0 @@ var sinφ = Math.sin(φ),

src/guyou.js

@@ -10,3 +10,3 @@ import "projection";
       k = Math.sqrt(1 - k_ * k_),
-      K = ellipticF(π / 2, k * k),
+      K = ellipticF(halfπ, k * k),
       f = -1;
@@ -43,3 +43,3 @@
       k = Math.sqrt(1 - k_ * k_),
-      K = ellipticF(π / 2, k * k),
+      K = ellipticF(halfπ, k * k),
       f = -1;
@@ -53,3 +53,3 @@
     λ,
-    2 * Math.atan(Math.exp(.5 / f * Math.log(k_ * tn[0] * tn[0] + k_ * tn[1] * tn[1]))) - π / 2
+    2 * Math.atan(Math.exp(.5 / f * Math.log(k_ * tn[0] * tn[0] + k_ * tn[1] * tn[1]))) - halfπ
   ];
@@ -56,0 +56,0 @@ };

src/hammer-retroazimuthal.js

@@ -20,3 +20,3 @@ import "projection";
       K * cosφ0 * Math.sin(λ),
-      (Math.abs(λ) > π / 2 ? K : -K) // rotate for back hemisphere
+      (Math.abs(λ) > halfπ ? K : -K) // rotate for back hemisphere
         * (sinφ0 * cosφ - cosφ0 * sinφ * cosλ)
@@ -35,3 +35,3 @@ ];
         φ = Math.atan2(a * c + b * d, b * c - a * d),
-        λ = (ρ > π / 2 ? -1 : 1) * Math.atan2(x * sinz, ρ * Math.cos(φ) * cosz + y * Math.sin(φ) * sinz);
+        λ = (ρ > halfπ ? -1 : 1) * Math.atan2(x * sinz, ρ * Math.cos(φ) * cosz + y * Math.sin(φ) * sinz);
     return rotate.invert(λ, φ);
@@ -38,0 +38,0 @@ };

src/hatano.js

@@ -17,3 +17,3 @@ import "projection";
   var θ = Math.abs(θ = y * (y < 0 ? .51799515156538134803 : .56863737426006061674)) > 1 - ε
-      ? θ > 0 ? π / 2 : -π / 2
+      ? θ > 0 ? halfπ : -halfπ
       : asin(θ);
@@ -23,3 +23,3 @@ return [
     Math.abs(θ = ((θ += θ) + Math.sin(θ)) * (y < 0 ? .41023453108141924738 : .37369906014686373063)) > 1 - ε
-      ? θ > 0 ? π / 2 : -π / 2
+      ? θ > 0 ? halfπ : -halfπ
       : asin(θ)
@@ -26,0 +26,0 @@ ];

src/healpix.js

@@ -14,3 +14,3 @@ import "projection";
       y1 = d3.geo.collignon.raw(0, φ0)[1],
-      dy1 = d3.geo.collignon.raw(0, π / 2)[1] - y1,
+      dy1 = d3.geo.collignon.raw(0, halfπ)[1] - y1,
       k = 2 * π / h;
@@ -17,0 +17,0 @@

src/hill.js

@@ -18,3 +18,3 @@ import "projection";
     if (t && t < 2) {
-      var θ = π / 2 - φ, i = 25, δ;
+      var θ = halfπ - φ, i = 25, δ;
       do {
@@ -21,0 +21,0 @@ var sinθ = Math.sin(θ),

src/interrupt.js

@@ -6,4 +6,4 @@ import "projection";
   var lobes = [
-    [[[-π, 0], [0,  π / 2], [π, 0]]],
-    [[[-π, 0], [0, -π / 2], [π, 0]]]
+    [[[-π, 0], [0,  halfπ], [π, 0]]],
+    [[[-π, 0], [0, -halfπ], [π, 0]]]
   ];
@@ -10,0 +10,0 @@

src/lagrange.js

@@ -5,3 +5,3 @@ import "projection";
   function forward(λ, φ) {
-    if (Math.abs(Math.abs(φ) - π / 2) < ε) return [0, φ < 0 ? -2 : 2];
+    if (Math.abs(Math.abs(φ) - halfπ) < ε) return [0, φ < 0 ? -2 : 2];
     var sinφ = Math.sin(φ),
@@ -18,3 +18,3 @@ v = Math.pow((1 + sinφ) / (1 - sinφ), n / 2),
     var y0 = Math.abs(y);
-    if (Math.abs(y0 - 2) < ε) return x ? null : [0, sgn(y) * π / 2];
+    if (Math.abs(y0 - 2) < ε) return x ? null : [0, sgn(y) * halfπ];
     if (y0 > 2) return null;
@@ -21,0 +21,0 @@

src/larrivee.js

@@ -15,3 +15,3 @@ import "projection";
       λ = ε,
-      φ = π / 2;
+      φ = halfπ;
   if (y0 < π_sqrt2) φ *= y0 / π_sqrt2;
@@ -18,0 +18,0 @@ else λ += 6 * acos(π_sqrt2 / y0);

src/loximuthal.js

@@ -11,3 +11,3 @@ import "projection";
         x = Math.abs(y) < ε ? λ * cosφ0
-        : Math.abs(x = π / 4 + φ / 2) < ε || Math.abs(Math.abs(x) - π / 2) < ε
+        : Math.abs(x = π / 4 + φ / 2) < ε || Math.abs(Math.abs(x) - halfπ) < ε
         ? 0 : λ * y / Math.log(Math.tan(x) / tanφ0);
@@ -22,3 +22,3 @@ return [x, y];
       Math.abs(y) < ε ? x / cosφ0
-        : (Math.abs(λ = π / 4 + φ / 2) < ε || Math.abs(Math.abs(λ) - π / 2) < ε) ? 0
+        : (Math.abs(λ = π / 4 + φ / 2) < ε || Math.abs(Math.abs(λ) - halfπ) < ε) ? 0
         : x * Math.log(Math.tan(λ) / tanφ0) / y,
@@ -25,0 +25,0 @@ φ

src/math.js

 var ε = 1e-6,
     ε2 = ε * ε,
     π = Math.PI,
+    halfπ = π / 2,
     sqrtπ = Math.sqrt(π),
@@ -17,3 +18,3 @@ radians = π / 180,
 function asin(x) {
-  return x > 1 ? π / 2 : x < -1 ? -π / 2 : Math.asin(x);
+  return x > 1 ? halfπ : x < -1 ? -halfπ : Math.asin(x);
 }
@@ -20,0 +21,0 @@

src/mollweide.js

@@ -35,4 +35,4 @@ import "projection";
 var mollweideθ = mollweideBromleyθ(π),
-    mollweide = mollweideBromley(2 * Math.SQRT2 / π, Math.SQRT2, π);
+    mollweide = mollweideBromley(Math.SQRT2 / halfπ, Math.SQRT2, π);
 
 (d3.geo.mollweide = function() { return projection(mollweide); }).raw = mollweide;

src/mt-flat-polar-sinusoidal.js

@@ -20,3 +20,3 @@ import "projection";
       θ = y / A;
-  if (Math.abs(Math.abs(θ) - π / 2) < ε) θ = θ < 0 ? -π / 2 : π / 2;
+  if (Math.abs(Math.abs(θ) - halfπ) < ε) θ = θ < 0 ? -halfπ : halfπ;
   return [
@@ -23,0 +23,0 @@ 1.5 * x / (A * (.5 + Math.cos(θ))),

src/polyconic.js

@@ -26,3 +26,3 @@ import "projection";
   return [
-    (Math.abs(y) < Math.abs(φ + 1 / tanφ) ? asin(x * tanφ) : sgn(x) * (acos(Math.abs(x * tanφ)) + π / 2)) / Math.sin(φ),
+    (Math.abs(y) < Math.abs(φ + 1 / tanφ) ? asin(x * tanφ) : sgn(x) * (acos(Math.abs(x * tanφ)) + halfπ)) / Math.sin(φ),
     φ
@@ -29,0 +29,0 @@ ];

src/quincuncial.js

 import "projection";
 
 function quincuncialProjection(projectHemisphere) {
-  var dx = projectHemisphere(π / 2, 0)[0] - projectHemisphere(-π / 2, 0)[0];
+  var dx = projectHemisphere(halfπ, 0)[0] - projectHemisphere(-halfπ, 0)[0];
 
@@ -21,3 +21,3 @@ function projection() {
     var forward = quincuncial ? function(λ, φ) {
-      var t = Math.abs(λ) < π / 2,
+      var t = Math.abs(λ) < halfπ,
           p = projectHemisphere(t ? λ : λ > 0 ? λ - π : λ + π, φ);
@@ -24,0 +24,0 @@

src/robinson.js

@@ -43,3 +43,3 @@ import "projection";
     λ * (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2),
-    (φ > 0 ? π : -π) / 2 * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2)
+    (φ > 0 ? halfπ : -halfπ) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2)
   ];
@@ -49,3 +49,3 @@ }
 robinson.invert = function(x, y) {
-  var yy = 2 * y / π,
+  var yy = y / halfπ,
       φ = yy * 90,
@@ -73,3 +73,3 @@ i = Math.min(18, Math.abs(φ / 5)),
         cy = robinsonConstants[Math.min(19, i0 + 2)][1];
-        φ -= (δ = (y >= 0 ? π : -π) / 2 * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2) - y) * degrees;
+        φ -= (δ = (y >= 0 ? halfπ : -halfπ) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2) - y) * degrees;
       } while (Math.abs(δ) > ε2 && --j > 0);
@@ -76,0 +76,0 @@ break;

src/van-der-grinten.js

@@ -5,5 +5,5 @@ import "projection";
   if (Math.abs(φ) < ε) return [λ, 0];
-  var sinθ = Math.abs(2 * φ / π),
+  var sinθ = Math.abs(φ / halfπ),
       θ = asin(sinθ);
-  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - π / 2) < ε) return [0, sgn(φ) * π * Math.tan(θ / 2)];
+  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - halfπ) < ε) return [0, sgn(φ) * π * Math.tan(θ / 2)];
   var cosθ = Math.cos(θ),
@@ -26,3 +26,3 @@ A = Math.abs(π / λ - λ / π) / 2,
   if (Math.abs(y) < ε) return [x, 0];
-  if (Math.abs(x) < ε) return [0, π / 2 * Math.sin(2 * Math.atan(y / π))];
+  if (Math.abs(x) < ε) return [0, halfπ * Math.sin(2 * Math.atan(y / π))];
   var x2 = (x /= π) * x,
@@ -29,0 +29,0 @@ y2 = (y /= π) * y,

src/van-der-grinten2.js

@@ -5,5 +5,5 @@ import "projection";
   if (Math.abs(φ) < ε) return [λ, 0];
-  var sinθ = Math.abs(2 * φ / π),
+  var sinθ = Math.abs(φ / halfπ),
       θ = asin(sinθ);
-  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - π / 2) < ε) return [0, sgn(φ) * π * Math.tan(θ / 2)];
+  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - halfπ) < ε) return [0, sgn(φ) * π * Math.tan(θ / 2)];
   var cosθ = Math.cos(θ),
@@ -20,3 +20,3 @@ A = Math.abs(π / λ - λ / π) / 2,
 vanDerGrinten2.invert = function(x, y) {
-  if (!x) return [0, π / 2 * Math.sin(2 * Math.atan(y / π))];
+  if (!x) return [0, halfπ * Math.sin(2 * Math.atan(y / π))];
   var x1 = Math.abs(x / π),
@@ -28,3 +28,3 @@ A = (1 - x1 * x1 - (y /= π) * y) / (2 * x1),
     sgn(x) * π * (B - A),
-    sgn(y) * π / 2 * Math.sin(2 * Math.atan2(Math.sqrt((1 - 2 * A * x1) * (A + B) - x1), Math.sqrt(B + A + x1)))
+    sgn(y) * halfπ * Math.sin(2 * Math.atan2(Math.sqrt((1 - 2 * A * x1) * (A + B) - x1), Math.sqrt(B + A + x1)))
   ];
@@ -31,0 +31,0 @@ };

src/van-der-grinten3.js

@@ -5,5 +5,5 @@ import "projection";
   if (Math.abs(φ) < ε) return [λ, 0];
-  var sinθ = 2 * φ / π,
+  var sinθ = φ / halfπ,
       θ = asin(sinθ);
-  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - π / 2) < ε) return [0, π * Math.tan(θ / 2)];
+  if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - halfπ) < ε) return [0, π * Math.tan(θ / 2)];
   var A = (π / λ - λ / π) / 2,
@@ -23,3 +23,3 @@ y1 = sinθ / (1 + Math.cos(θ));
     x ? π * (sgn(x) * Math.sqrt(A * A + 1) - A) : 0,
-    π / 2 * Math.sin(2 * Math.atan(y1))
+    halfπ * Math.sin(2 * Math.atan(y1))
   ];
@@ -26,0 +26,0 @@ };

src/van-der-grinten4.js

@@ -6,4 +6,4 @@ import "projection";
   var φ0 = Math.abs(φ);
-  if (!λ || φ0 === π / 2) return [0, φ];
-  var B = 2 * φ0 / π,
+  if (!λ || φ0 === halfπ) return [0, φ];
+  var B = φ0 / halfπ,
       B2 = B * B,
@@ -15,5 +15,5 @@ C = (8 * B - B2 * (B2 + 2) - 5) / (2 * B2 * (B - 1)),
       B_3C = B + 3 * C,
-      λ0 = 2 * λ / π,
+      λ0 = λ / halfπ,
       λ1 = λ0 + 1 / λ0,
-      D = sgn(Math.abs(λ) - π / 2) * Math.sqrt(λ1 * λ1 - 4),
+      D = sgn(Math.abs(λ) - halfπ) * Math.sqrt(λ1 * λ1 - 4),
       D2 = D * D,
@@ -23,4 +23,4 @@ F = B_C2 * (B2 + C2 * D2 - 1) + (1 - B2) * (B2 * (B_3C * B_3C + 4 * C2) + 12 * BC * C2 + 4 * C2 * C2),
   return [
-    sgn(λ) * π * x1 / 2,
-    sgn(φ) * π / 2 * asqrt(1 + D * Math.abs(x1) - x1 * x1)
+    sgn(λ) * halfπ * x1,
+    sgn(φ) * halfπ * asqrt(1 + D * Math.abs(x1) - x1 * x1)
   ];
@@ -32,3 +32,3 @@ }
   y /= π;
-  var x1 = sgn(x) * x * 2 / π,
+  var x1 = sgn(x) * x / halfπ,
       D = (x1 * x1 - 1 + 4 * y * y) / Math.abs(x1),
@@ -56,3 +56,3 @@ D2 = D * D,
     sgn(x) * (Math.sqrt(D * D + 4) + D) * π / 4,
-    π / 2 * B
+    halfπ * B
   ];
@@ -59,0 +59,0 @@ };

src/winkel3.js

@@ -7,3 +7,3 @@ import "projection";
   return [
-    (coordinates[0] + λ * 2 / π) / 2,
+    (coordinates[0] + λ / halfπ) / 2,
     (coordinates[1] + φ) / 2
@@ -28,5 +28,5 @@ ];
         F,
-        fx = .5 * (2 * E * cosφ * sinλ_2 + λ * 2 / π) - x,
+        fx = .5 * (2 * E * cosφ * sinλ_2 + λ / halfπ) - x,
         fy = .5 * (E * sinφ + φ) - y,
-        δxδλ = .5 * F * (cos2φ * sin2λ_2 + E * cosφ * cosλ_2 * sin2φ) + .5 * 2 / π,
+        δxδλ = .5 * F * (cos2φ * sin2λ_2 + E * cosφ * cosλ_2 * sin2φ) + .5 / halfπ,
         δxδφ = F * (sinλ * sin_2φ / 4 - E * sinφ * sinλ_2),
@@ -33,0 +33,0 @@ δyδλ = .125 * F * (sin_2φ * sinλ_2 - E * sinφ * cos2φ * sinλ),

test/aitoff-test.js

@@ -23,2 +23,5 @@ var vows = require("vows"),
         assert.equalInverse(aitoff, [  45,  87], [489.158099, 21.6821110]);
+      },
+      "the inverse projection of points outside the target region are falsey": function(aitoff) {
+        assert.ok(!aitoff.invert([0, 0]));
       }
@@ -25,0 +28,0 @@ }

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