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Merge branch 'gnomonic' of https://github.com/jasondavies/d3 into gno…
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@mbostock
mbostock committed Sep 26, 2011
2 parents c974d3a + d832335 commit b678e08
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1 change: 1 addition & 0 deletions Makefile
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Expand Up @@ -188,6 +188,7 @@ d3.geo.js: \
src/geo/path.js \
src/geo/bounds.js \
src/geo/greatCircle.js \
src/geo/clip.js \
src/end.js

d3.csv.js: \
Expand Down
245 changes: 191 additions & 54 deletions d3.geo.js
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@@ -1,7 +1,10 @@
(function(){d3.geo = {};

var d3_radians = Math.PI / 180,
d3_geo_earthRadius = 6371; // Mean radius of Earth, in km.
// TODO clip input coordinates on opposite hemisphere
d3.geo.azimuthal = function() {
var mode = "orthographic", // or stereographic
var mode = "orthographic", // or stereographic, gnomonic, equidistant or equalarea
origin,
scale = 200,
translate = [480, 250],
Expand All @@ -17,7 +20,13 @@ d3.geo.azimuthal = function() {
sx1 = Math.sin(x1),
cy1 = Math.cos(y1),
sy1 = Math.sin(y1),
k = mode === "stereographic" ? 1 / (1 + sy0 * sy1 + cy0 * cy1 * cx1) : 1,
cc = mode !== "orthographic" ? sy0 * sy1 + cy0 * cy1 * cx1 : null,
c,
k = mode === "stereographic" ? 1 / (1 + cc)
: mode === "gnomonic" ? 1 / cc
: mode === "equidistant" ? (c = Math.acos(cc), c ? c / Math.sin(c) : 0)
: mode === "equalarea" ? Math.sqrt(2 / (1 + cc))
: 1,
x = k * cy1 * sx1,
y = k * (sy0 * cy1 * cx1 - cy0 * sy1);
return [
Expand All @@ -30,12 +39,16 @@ d3.geo.azimuthal = function() {
var x = (coordinates[0] - translate[0]) / scale,
y = (coordinates[1] - translate[1]) / scale,
p = Math.sqrt(x * x + y * y),
c = mode === "stereographic" ? 2 * Math.atan(p) : Math.asin(p),
c = mode === "stereographic" ? 2 * Math.atan(p)
: mode === "gnomonic" ? Math.atan(p)
: mode === "equidistant" ? p
: mode === "equalarea" ? 2 * Math.asin(.5 * p)
: Math.asin(p),
sc = Math.sin(c),
cc = Math.cos(c);
return [
(x0 + Math.atan2(x * sc, p * cy0 * cc + y * sy0 * sc)) / d3_radians,
Math.asin(cc * sy0 - (y * sc * cy0) / p) / d3_radians
Math.asin(cc * sy0 - (p ? (y * sc * cy0) / p : 0)) / d3_radians
];
};

Expand Down Expand Up @@ -195,8 +208,6 @@ d3.geo.albersUsa = function() {

return albersUsa.scale(lower48.scale());
};

var d3_radians = Math.PI / 180;
d3.geo.equirectangular = function() {
var scale = 500,
translate = [480, 250];
Expand Down Expand Up @@ -279,7 +290,8 @@ d3.geo.mercator = function() {
d3.geo.path = function() {
var pointRadius = 4.5,
pointCircle = d3_path_circle(pointRadius),
projection = d3.geo.albersUsa();
projection = d3.geo.albersUsa(),
clip = Object;

function path(d, i) {
if (typeof pointRadius === "function") {
Expand Down Expand Up @@ -308,12 +320,14 @@ d3.geo.path = function() {
},

Point: function(o) {
return "M" + project(o.coordinates) + pointCircle;
var coordinates = clip.call(this, [o.coordinates]);
return coordinates.length
? "M" + project(coordinates[0]) + pointCircle : "";
},

MultiPoint: function(o) {
var path = [],
coordinates = o.coordinates,
coordinates = clip.call(this, o.coordinates),
i = -1, // coordinates.index
n = coordinates.length;
while (++i < n) path.push("M", project(coordinates[i]), pointCircle);
Expand All @@ -322,7 +336,7 @@ d3.geo.path = function() {

LineString: function(o) {
var path = ["M"],
coordinates = o.coordinates,
coordinates = clip.call(this, o.coordinates),
i = -1, // coordinates.index
n = coordinates.length;
while (++i < n) path.push(project(coordinates[i]), "L");
Expand All @@ -339,7 +353,7 @@ d3.geo.path = function() {
j, // subcoordinates.index
m; // subcoordinates.length
while (++i < n) {
subcoordinates = coordinates[i];
subcoordinates = clip.call(this, coordinates[i]);
j = -1;
m = subcoordinates.length;
path.push("M");
Expand All @@ -358,9 +372,10 @@ d3.geo.path = function() {
j, // subcoordinates.index
m; // subcoordinates.length
while (++i < n) {
subcoordinates = coordinates[i];
subcoordinates = clip.call(this, coordinates[i]);
j = -1;
m = subcoordinates.length;
m = subcoordinates.length - 1;
if (m < 1) continue;
path.push("M");
while (++j < m) path.push(project(subcoordinates[j]), "L");
path[path.length - 1] = "Z";
Expand All @@ -384,9 +399,10 @@ d3.geo.path = function() {
j = -1;
m = subcoordinates.length;
while (++j < m) {
subsubcoordinates = subcoordinates[j];
subsubcoordinates = clip.call(this, subcoordinates[j]);
k = -1;
p = subsubcoordinates.length - 1;
if (p < 1) continue;
path.push("M");
while (++k < p) path.push(project(subsubcoordinates[k]), "L");
path[path.length - 1] = "Z";
Expand Down Expand Up @@ -524,6 +540,12 @@ d3.geo.path = function() {
return path;
};

path.clip = function(x) {
if (!arguments.length) return clip;
clip = x;
return path;
}

path.area = function(d) {
return d3_geo_pathType(areaTypes, d);
};
Expand Down Expand Up @@ -638,59 +660,38 @@ function d3_geo_boundsPolygon(o, f) {
d3.geo.greatCircle = function() {
var source = d3_geo_greatCircleSource,
target = d3_geo_greatCircleTarget,
coordinates = Object, // for use with polyline
precision = null,
n = 100,
radius = 6371; // Mean radius of Earth, in km.
radius = d3_geo_earthRadius;
// TODO: breakAtDateLine?

function greatCircle(d, i) {
var from = source.call(this, d, i),
to = target.call(this, d, i),
x0 = from[0] * d3_radians,
y0 = from[1] * d3_radians,
x1 = to[0] * d3_radians,
y1 = to[1] * d3_radians,
cx0 = Math.cos(x0), sx0 = Math.sin(x0),
cy0 = Math.cos(y0), sy0 = Math.sin(y0),
cx1 = Math.cos(x1), sx1 = Math.sin(x1),
cy1 = Math.cos(y1), sy1 = Math.sin(y1),
d = Math.acos(sy0 * sy1 + cy0 * cy1 * Math.cos(x1 - x0)),
sd = Math.sin(d),
f = d / (n - 1),
e = -f,
path = [],
i = -1;

while (++i < n) {
e += f;
var A = Math.sin(d - e) / sd,
B = Math.sin(e) / sd,
x = A * cy0 * cx0 + B * cy1 * cx1,
y = A * cy0 * sx0 + B * cy1 * sx1,
z = A * sy0 + B * sy1;
path[i] = [
Math.atan2(y, x) / d3_radians,
Math.atan2(z, Math.sqrt(x * x + y * y)) / d3_radians
];
}

return path;
return d3_geo_greatCirclePath([
source.call(this, d, i), target.call(this, d, i)], precision, n);
}

greatCircle.source = function(x) {
if (!arguments.length) return source;
source = x;
return greatCircle;
greatCircle.polyline = function(d, i) {
return d3_geo_greatCirclePath(coordinates.call(this, d, i), precision, n);
};

greatCircle.target = function(x) {
if (!arguments.length) return target;
target = x;
greatCircle.coordinates = function(x) {
if (!arguments.length) return coordinates;
coordinates = x;
return greatCircle;
};

greatCircle.n = function(x) {
if (!arguments.length) return n;
n = +x;
precision = null;
return greatCircle;
};

greatCircle.precision = function(x) {
if (!arguments.length) return precision;
precision = +x;
n = null;
return greatCircle;
};

Expand All @@ -711,18 +712,154 @@ d3.geo.greatCircle = function() {
sy = Math.sin((y1 - y0) / 2),
sx = Math.sin((x1 - x0) / 2),
a = sy * sy + Math.cos(y0) * Math.cos(y1) * sx * sx;

return radius * 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
};

return greatCircle;
};

function d3_geo_greatCirclePath(coordinates, precision, segments) {
var m = coordinates.length;
if (m < 2) return coordinates;

var i = 0,
p = precision * d3_radians,
from = coordinates[0],
to,
x0 = from[0] * d3_radians,
y0 = from[1] * d3_radians,
cx0 = Math.cos(x0), sx0 = Math.sin(x0),
cy0 = Math.cos(y0), sy0 = Math.sin(y0),
path = [from];

while (++i < m) {
to = coordinates[i];
var x1 = to[0] * d3_radians,
y1 = to[1] * d3_radians,
cx1 = Math.cos(x1), sx1 = Math.sin(x1),
cy1 = Math.cos(y1), sy1 = Math.sin(y1),
d = Math.acos(Math.max(-1, Math.min(1, sy0 * sy1 + cy0 * cy1 * Math.cos(x1 - x0)))),
sd = Math.sin(d),
n = segments != null ? segments - 1 : Math.ceil(d / p),
f = d / n,
e = 0,
j = 0;

while (++j < n) {
e += f;
var A = Math.sin(d - e) / sd,
B = Math.sin(e) / sd,
x = A * cy0 * cx0 + B * cy1 * cx1,
y = A * cy0 * sx0 + B * cy1 * sx1,
z = A * sy0 + B * sy1;
path.push([
Math.atan2(y, x) / d3_radians,
Math.atan2(z, Math.sqrt(x * x + y * y)) / d3_radians
]);
}
path.push(to);
x0 = x1;
y0 = y1;
cx0 = cx1; sx0 = sx1;
cy0 = cy1; sy0 = sy1;
}

return path;
}

function d3_geo_greatCircleSource(d) {
return d.source;
}

function d3_geo_greatCircleTarget(d) {
return d.target;
}
d3.geo.clip = function() {
var origin = [0, 0],
angle = 90,
r = d3_geo_earthRadius * angle / 180 * Math.PI,
coordinates = Object;

function clip(d, i) {
var d = coordinates.call(this, d, i),
o = {source: origin, target: null},
n = d.length,
i = -1,
path,
clipped = [],
p = null,
q = null,
distance,
oldDistance;
while (++i < n) {
o.target = d[i];
distance = d3_geo_clipGreatCircle.distance(o);
if (distance < r) {
if (q) clipped.push(d3_geo_clipIntersect(q, o.target, (oldDistance - r) / (oldDistance - distance)));
clipped.push(d[i]);
p = q = null;
} else {
q = o.target;
if (!p && clipped.length) {
clipped.push(d3_geo_clipIntersect(clipped[clipped.length - 1], q, (r - oldDistance) / (distance - oldDistance)));
p = q;
}
}
oldDistance = distance;
}
if (q && clipped.length) {
o.target = clipped[0];
distance = d3_geo_clipGreatCircle.distance(o);
clipped.push(d3_geo_clipIntersect(q, o.target, (oldDistance - r) / (oldDistance - distance)));
}
return clipped;
}

clip.coordinates = function(x) {
if (!arguments.length) return coordinates;
coordinates = x;
return clip;
};

clip.origin = function(x) {
if (!arguments.length) return origin;
origin = x;
return clip;
};

clip.angle = function(x) {
if (!arguments.length) return angle;
angle = +x;
r = d3_geo_earthRadius * angle / 180 * Math.PI;
return clip;
};

return clip;
}

var d3_geo_clipGreatCircle = d3.geo.greatCircle();

function d3_geo_clipIntersect(from, to, f) {
var x0 = from[0] * d3_radians,
y0 = from[1] * d3_radians,
x1 = to[0] * d3_radians,
y1 = to[1] * d3_radians,
cx0 = Math.cos(x0), sx0 = Math.sin(x0),
cy0 = Math.cos(y0), sy0 = Math.sin(y0),
cx1 = Math.cos(x1), sx1 = Math.sin(x1),
cy1 = Math.cos(y1), sy1 = Math.sin(y1),
d = Math.acos(Math.max(-1, Math.min(1, sy0 * sy1 + cy0 * cy1 * Math.cos(x1 - x0)))),
e = f * d,
sd = Math.sin(d),
A = Math.sin(d - e) / sd,
B = Math.sin(e) / sd,
x = A * cy0 * cx0 + B * cy1 * cx1,
y = A * cy0 * sx0 + B * cy1 * sx1,
z = A * sy0 + B * sy1;

return [
Math.atan2(y, x) / d3_radians,
Math.atan2(z, Math.sqrt(x * x + y * y)) / d3_radians
];
}
})();
2 changes: 1 addition & 1 deletion d3.geo.min.js
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