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3103 lines
86 KiB
3103 lines
86 KiB
// https://d3js.org/d3-geo/ v1.11.1 Copyright 2018 Mike Bostock |
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(function (global, factory) { |
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typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('d3-array')) : |
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typeof define === 'function' && define.amd ? define(['exports', 'd3-array'], factory) : |
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(factory((global.d3 = global.d3 || {}),global.d3)); |
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}(this, (function (exports,d3Array) { 'use strict'; |
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|
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// Adds floating point numbers with twice the normal precision. |
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// Reference: J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and |
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// Fast Robust Geometric Predicates, Discrete & Computational Geometry 18(3) |
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// 305–363 (1997). |
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// Code adapted from GeographicLib by Charles F. F. Karney, |
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// http://geographiclib.sourceforge.net/ |
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function adder() { |
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return new Adder; |
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} |
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function Adder() { |
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this.reset(); |
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} |
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Adder.prototype = { |
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constructor: Adder, |
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reset: function() { |
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this.s = // rounded value |
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this.t = 0; // exact error |
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}, |
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add: function(y) { |
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add(temp, y, this.t); |
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add(this, temp.s, this.s); |
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if (this.s) this.t += temp.t; |
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else this.s = temp.t; |
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}, |
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valueOf: function() { |
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return this.s; |
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} |
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}; |
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var temp = new Adder; |
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function add(adder, a, b) { |
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var x = adder.s = a + b, |
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bv = x - a, |
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av = x - bv; |
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adder.t = (a - av) + (b - bv); |
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} |
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var epsilon = 1e-6; |
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var epsilon2 = 1e-12; |
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var pi = Math.PI; |
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var halfPi = pi / 2; |
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var quarterPi = pi / 4; |
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var tau = pi * 2; |
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var degrees = 180 / pi; |
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var radians = pi / 180; |
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var abs = Math.abs; |
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var atan = Math.atan; |
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var atan2 = Math.atan2; |
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var cos = Math.cos; |
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var ceil = Math.ceil; |
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var exp = Math.exp; |
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var log = Math.log; |
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var pow = Math.pow; |
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var sin = Math.sin; |
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var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }; |
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var sqrt = Math.sqrt; |
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var tan = Math.tan; |
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function acos(x) { |
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return x > 1 ? 0 : x < -1 ? pi : Math.acos(x); |
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} |
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function asin(x) { |
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return x > 1 ? halfPi : x < -1 ? -halfPi : Math.asin(x); |
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} |
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function haversin(x) { |
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return (x = sin(x / 2)) * x; |
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} |
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function noop() {} |
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function streamGeometry(geometry, stream) { |
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if (geometry && streamGeometryType.hasOwnProperty(geometry.type)) { |
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streamGeometryType[geometry.type](geometry, stream); |
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} |
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} |
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var streamObjectType = { |
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Feature: function(object, stream) { |
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streamGeometry(object.geometry, stream); |
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}, |
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FeatureCollection: function(object, stream) { |
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var features = object.features, i = -1, n = features.length; |
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while (++i < n) streamGeometry(features[i].geometry, stream); |
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} |
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}; |
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var streamGeometryType = { |
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Sphere: function(object, stream) { |
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stream.sphere(); |
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}, |
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Point: function(object, stream) { |
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object = object.coordinates; |
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stream.point(object[0], object[1], object[2]); |
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}, |
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MultiPoint: function(object, stream) { |
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var coordinates = object.coordinates, i = -1, n = coordinates.length; |
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while (++i < n) object = coordinates[i], stream.point(object[0], object[1], object[2]); |
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}, |
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LineString: function(object, stream) { |
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streamLine(object.coordinates, stream, 0); |
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}, |
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MultiLineString: function(object, stream) { |
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var coordinates = object.coordinates, i = -1, n = coordinates.length; |
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while (++i < n) streamLine(coordinates[i], stream, 0); |
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}, |
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Polygon: function(object, stream) { |
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streamPolygon(object.coordinates, stream); |
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}, |
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MultiPolygon: function(object, stream) { |
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var coordinates = object.coordinates, i = -1, n = coordinates.length; |
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while (++i < n) streamPolygon(coordinates[i], stream); |
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}, |
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GeometryCollection: function(object, stream) { |
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var geometries = object.geometries, i = -1, n = geometries.length; |
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while (++i < n) streamGeometry(geometries[i], stream); |
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} |
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}; |
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function streamLine(coordinates, stream, closed) { |
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var i = -1, n = coordinates.length - closed, coordinate; |
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stream.lineStart(); |
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while (++i < n) coordinate = coordinates[i], stream.point(coordinate[0], coordinate[1], coordinate[2]); |
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stream.lineEnd(); |
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} |
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function streamPolygon(coordinates, stream) { |
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var i = -1, n = coordinates.length; |
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stream.polygonStart(); |
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while (++i < n) streamLine(coordinates[i], stream, 1); |
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stream.polygonEnd(); |
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} |
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function geoStream(object, stream) { |
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if (object && streamObjectType.hasOwnProperty(object.type)) { |
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streamObjectType[object.type](object, stream); |
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} else { |
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streamGeometry(object, stream); |
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} |
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} |
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var areaRingSum = adder(); |
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var areaSum = adder(), |
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lambda00, |
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phi00, |
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lambda0, |
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cosPhi0, |
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sinPhi0; |
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var areaStream = { |
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point: noop, |
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lineStart: noop, |
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lineEnd: noop, |
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polygonStart: function() { |
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areaRingSum.reset(); |
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areaStream.lineStart = areaRingStart; |
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areaStream.lineEnd = areaRingEnd; |
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}, |
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polygonEnd: function() { |
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var areaRing = +areaRingSum; |
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areaSum.add(areaRing < 0 ? tau + areaRing : areaRing); |
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this.lineStart = this.lineEnd = this.point = noop; |
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}, |
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sphere: function() { |
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areaSum.add(tau); |
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} |
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}; |
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function areaRingStart() { |
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areaStream.point = areaPointFirst; |
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} |
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function areaRingEnd() { |
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areaPoint(lambda00, phi00); |
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} |
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function areaPointFirst(lambda, phi) { |
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areaStream.point = areaPoint; |
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lambda00 = lambda, phi00 = phi; |
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lambda *= radians, phi *= radians; |
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lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi); |
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} |
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function areaPoint(lambda, phi) { |
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lambda *= radians, phi *= radians; |
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phi = phi / 2 + quarterPi; // half the angular distance from south pole |
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// Spherical excess E for a spherical triangle with vertices: south pole, |
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// previous point, current point. Uses a formula derived from Cagnoli’s |
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// theorem. See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2). |
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var dLambda = lambda - lambda0, |
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sdLambda = dLambda >= 0 ? 1 : -1, |
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adLambda = sdLambda * dLambda, |
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cosPhi = cos(phi), |
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sinPhi = sin(phi), |
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k = sinPhi0 * sinPhi, |
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u = cosPhi0 * cosPhi + k * cos(adLambda), |
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v = k * sdLambda * sin(adLambda); |
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areaRingSum.add(atan2(v, u)); |
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// Advance the previous points. |
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lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi; |
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} |
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function area(object) { |
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areaSum.reset(); |
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geoStream(object, areaStream); |
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return areaSum * 2; |
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} |
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function spherical(cartesian) { |
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return [atan2(cartesian[1], cartesian[0]), asin(cartesian[2])]; |
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} |
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function cartesian(spherical) { |
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var lambda = spherical[0], phi = spherical[1], cosPhi = cos(phi); |
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return [cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)]; |
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} |
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function cartesianDot(a, b) { |
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return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; |
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} |
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function cartesianCross(a, b) { |
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return [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]]; |
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} |
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// TODO return a |
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function cartesianAddInPlace(a, b) { |
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a[0] += b[0], a[1] += b[1], a[2] += b[2]; |
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} |
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function cartesianScale(vector, k) { |
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return [vector[0] * k, vector[1] * k, vector[2] * k]; |
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} |
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// TODO return d |
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function cartesianNormalizeInPlace(d) { |
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var l = sqrt(d[0] * d[0] + d[1] * d[1] + d[2] * d[2]); |
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d[0] /= l, d[1] /= l, d[2] /= l; |
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} |
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var lambda0$1, phi0, lambda1, phi1, // bounds |
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lambda2, // previous lambda-coordinate |
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lambda00$1, phi00$1, // first point |
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p0, // previous 3D point |
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deltaSum = adder(), |
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ranges, |
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range; |
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var boundsStream = { |
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point: boundsPoint, |
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lineStart: boundsLineStart, |
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lineEnd: boundsLineEnd, |
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polygonStart: function() { |
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boundsStream.point = boundsRingPoint; |
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boundsStream.lineStart = boundsRingStart; |
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boundsStream.lineEnd = boundsRingEnd; |
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deltaSum.reset(); |
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areaStream.polygonStart(); |
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}, |
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polygonEnd: function() { |
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areaStream.polygonEnd(); |
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boundsStream.point = boundsPoint; |
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boundsStream.lineStart = boundsLineStart; |
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boundsStream.lineEnd = boundsLineEnd; |
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if (areaRingSum < 0) lambda0$1 = -(lambda1 = 180), phi0 = -(phi1 = 90); |
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else if (deltaSum > epsilon) phi1 = 90; |
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else if (deltaSum < -epsilon) phi0 = -90; |
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range[0] = lambda0$1, range[1] = lambda1; |
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} |
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}; |
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function boundsPoint(lambda, phi) { |
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ranges.push(range = [lambda0$1 = lambda, lambda1 = lambda]); |
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if (phi < phi0) phi0 = phi; |
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if (phi > phi1) phi1 = phi; |
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} |
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function linePoint(lambda, phi) { |
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var p = cartesian([lambda * radians, phi * radians]); |
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if (p0) { |
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var normal = cartesianCross(p0, p), |
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equatorial = [normal[1], -normal[0], 0], |
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inflection = cartesianCross(equatorial, normal); |
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cartesianNormalizeInPlace(inflection); |
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inflection = spherical(inflection); |
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var delta = lambda - lambda2, |
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sign$$1 = delta > 0 ? 1 : -1, |
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lambdai = inflection[0] * degrees * sign$$1, |
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phii, |
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antimeridian = abs(delta) > 180; |
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if (antimeridian ^ (sign$$1 * lambda2 < lambdai && lambdai < sign$$1 * lambda)) { |
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phii = inflection[1] * degrees; |
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if (phii > phi1) phi1 = phii; |
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} else if (lambdai = (lambdai + 360) % 360 - 180, antimeridian ^ (sign$$1 * lambda2 < lambdai && lambdai < sign$$1 * lambda)) { |
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phii = -inflection[1] * degrees; |
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if (phii < phi0) phi0 = phii; |
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} else { |
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if (phi < phi0) phi0 = phi; |
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if (phi > phi1) phi1 = phi; |
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} |
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if (antimeridian) { |
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if (lambda < lambda2) { |
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if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda; |
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} else { |
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if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda; |
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} |
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} else { |
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if (lambda1 >= lambda0$1) { |
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if (lambda < lambda0$1) lambda0$1 = lambda; |
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if (lambda > lambda1) lambda1 = lambda; |
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} else { |
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if (lambda > lambda2) { |
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if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda; |
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} else { |
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if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda; |
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} |
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} |
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} |
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} else { |
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ranges.push(range = [lambda0$1 = lambda, lambda1 = lambda]); |
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} |
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if (phi < phi0) phi0 = phi; |
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if (phi > phi1) phi1 = phi; |
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p0 = p, lambda2 = lambda; |
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} |
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function boundsLineStart() { |
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boundsStream.point = linePoint; |
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} |
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function boundsLineEnd() { |
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range[0] = lambda0$1, range[1] = lambda1; |
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boundsStream.point = boundsPoint; |
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p0 = null; |
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} |
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function boundsRingPoint(lambda, phi) { |
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if (p0) { |
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var delta = lambda - lambda2; |
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deltaSum.add(abs(delta) > 180 ? delta + (delta > 0 ? 360 : -360) : delta); |
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} else { |
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lambda00$1 = lambda, phi00$1 = phi; |
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} |
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areaStream.point(lambda, phi); |
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linePoint(lambda, phi); |
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} |
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function boundsRingStart() { |
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areaStream.lineStart(); |
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} |
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function boundsRingEnd() { |
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boundsRingPoint(lambda00$1, phi00$1); |
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areaStream.lineEnd(); |
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if (abs(deltaSum) > epsilon) lambda0$1 = -(lambda1 = 180); |
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range[0] = lambda0$1, range[1] = lambda1; |
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p0 = null; |
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} |
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// Finds the left-right distance between two longitudes. |
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// This is almost the same as (lambda1 - lambda0 + 360°) % 360°, except that we want |
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// the distance between ±180° to be 360°. |
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function angle(lambda0, lambda1) { |
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return (lambda1 -= lambda0) < 0 ? lambda1 + 360 : lambda1; |
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} |
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function rangeCompare(a, b) { |
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return a[0] - b[0]; |
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} |
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function rangeContains(range, x) { |
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return range[0] <= range[1] ? range[0] <= x && x <= range[1] : x < range[0] || range[1] < x; |
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} |
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function bounds(feature) { |
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var i, n, a, b, merged, deltaMax, delta; |
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phi1 = lambda1 = -(lambda0$1 = phi0 = Infinity); |
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ranges = []; |
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geoStream(feature, boundsStream); |
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// First, sort ranges by their minimum longitudes. |
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if (n = ranges.length) { |
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ranges.sort(rangeCompare); |
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// Then, merge any ranges that overlap. |
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for (i = 1, a = ranges[0], merged = [a]; i < n; ++i) { |
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b = ranges[i]; |
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if (rangeContains(a, b[0]) || rangeContains(a, b[1])) { |
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if (angle(a[0], b[1]) > angle(a[0], a[1])) a[1] = b[1]; |
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if (angle(b[0], a[1]) > angle(a[0], a[1])) a[0] = b[0]; |
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} else { |
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merged.push(a = b); |
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} |
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} |
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// Finally, find the largest gap between the merged ranges. |
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// The final bounding box will be the inverse of this gap. |
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for (deltaMax = -Infinity, n = merged.length - 1, i = 0, a = merged[n]; i <= n; a = b, ++i) { |
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b = merged[i]; |
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if ((delta = angle(a[1], b[0])) > deltaMax) deltaMax = delta, lambda0$1 = b[0], lambda1 = a[1]; |
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} |
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} |
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ranges = range = null; |
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return lambda0$1 === Infinity || phi0 === Infinity |
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? [[NaN, NaN], [NaN, NaN]] |
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: [[lambda0$1, phi0], [lambda1, phi1]]; |
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} |
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var W0, W1, |
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X0, Y0, Z0, |
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X1, Y1, Z1, |
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X2, Y2, Z2, |
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lambda00$2, phi00$2, // first point |
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x0, y0, z0; // previous point |
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var centroidStream = { |
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sphere: noop, |
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point: centroidPoint, |
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lineStart: centroidLineStart, |
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lineEnd: centroidLineEnd, |
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polygonStart: function() { |
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centroidStream.lineStart = centroidRingStart; |
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centroidStream.lineEnd = centroidRingEnd; |
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}, |
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polygonEnd: function() { |
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centroidStream.lineStart = centroidLineStart; |
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centroidStream.lineEnd = centroidLineEnd; |
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} |
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}; |
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// Arithmetic mean of Cartesian vectors. |
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function centroidPoint(lambda, phi) { |
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lambda *= radians, phi *= radians; |
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var cosPhi = cos(phi); |
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centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)); |
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} |
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function centroidPointCartesian(x, y, z) { |
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++W0; |
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X0 += (x - X0) / W0; |
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Y0 += (y - Y0) / W0; |
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Z0 += (z - Z0) / W0; |
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} |
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function centroidLineStart() { |
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centroidStream.point = centroidLinePointFirst; |
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} |
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function centroidLinePointFirst(lambda, phi) { |
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lambda *= radians, phi *= radians; |
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var cosPhi = cos(phi); |
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x0 = cosPhi * cos(lambda); |
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y0 = cosPhi * sin(lambda); |
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z0 = sin(phi); |
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centroidStream.point = centroidLinePoint; |
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centroidPointCartesian(x0, y0, z0); |
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} |
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function centroidLinePoint(lambda, phi) { |
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lambda *= radians, phi *= radians; |
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var cosPhi = cos(phi), |
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x = cosPhi * cos(lambda), |
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y = cosPhi * sin(lambda), |
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z = sin(phi), |
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w = atan2(sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z); |
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W1 += w; |
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X1 += w * (x0 + (x0 = x)); |
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Y1 += w * (y0 + (y0 = y)); |
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Z1 += w * (z0 + (z0 = z)); |
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centroidPointCartesian(x0, y0, z0); |
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} |
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|
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function centroidLineEnd() { |
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centroidStream.point = centroidPoint; |
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} |
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|
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// See J. E. Brock, The Inertia Tensor for a Spherical Triangle, |
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// J. Applied Mechanics 42, 239 (1975). |
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function centroidRingStart() { |
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centroidStream.point = centroidRingPointFirst; |
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} |
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|
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function centroidRingEnd() { |
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centroidRingPoint(lambda00$2, phi00$2); |
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centroidStream.point = centroidPoint; |
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} |
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|
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function centroidRingPointFirst(lambda, phi) { |
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lambda00$2 = lambda, phi00$2 = phi; |
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lambda *= radians, phi *= radians; |
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centroidStream.point = centroidRingPoint; |
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var cosPhi = cos(phi); |
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x0 = cosPhi * cos(lambda); |
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y0 = cosPhi * sin(lambda); |
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z0 = sin(phi); |
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centroidPointCartesian(x0, y0, z0); |
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} |
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|
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function centroidRingPoint(lambda, phi) { |
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lambda *= radians, phi *= radians; |
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var cosPhi = cos(phi), |
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x = cosPhi * cos(lambda), |
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y = cosPhi * sin(lambda), |
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z = sin(phi), |
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cx = y0 * z - z0 * y, |
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cy = z0 * x - x0 * z, |
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cz = x0 * y - y0 * x, |
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m = sqrt(cx * cx + cy * cy + cz * cz), |
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w = asin(m), // line weight = angle |
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v = m && -w / m; // area weight multiplier |
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X2 += v * cx; |
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Y2 += v * cy; |
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Z2 += v * cz; |
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W1 += w; |
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X1 += w * (x0 + (x0 = x)); |
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Y1 += w * (y0 + (y0 = y)); |
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Z1 += w * (z0 + (z0 = z)); |
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centroidPointCartesian(x0, y0, z0); |
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} |
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|
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function centroid(object) { |
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W0 = W1 = |
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X0 = Y0 = Z0 = |
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X1 = Y1 = Z1 = |
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X2 = Y2 = Z2 = 0; |
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geoStream(object, centroidStream); |
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|
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var x = X2, |
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y = Y2, |
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z = Z2, |
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m = x * x + y * y + z * z; |
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|
|
// If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid. |
|
if (m < epsilon2) { |
|
x = X1, y = Y1, z = Z1; |
|
// If the feature has zero length, fall back to arithmetic mean of point vectors. |
|
if (W1 < epsilon) x = X0, y = Y0, z = Z0; |
|
m = x * x + y * y + z * z; |
|
// If the feature still has an undefined ccentroid, then return. |
|
if (m < epsilon2) return [NaN, NaN]; |
|
} |
|
|
|
return [atan2(y, x) * degrees, asin(z / sqrt(m)) * degrees]; |
|
} |
|
|
|
function constant(x) { |
|
return function() { |
|
return x; |
|
}; |
|
} |
|
|
|
function compose(a, b) { |
|
|
|
function compose(x, y) { |
|
return x = a(x, y), b(x[0], x[1]); |
|
} |
|
|
|
if (a.invert && b.invert) compose.invert = function(x, y) { |
|
return x = b.invert(x, y), x && a.invert(x[0], x[1]); |
|
}; |
|
|
|
return compose; |
|
} |
|
|
|
function rotationIdentity(lambda, phi) { |
|
return [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi]; |
|
} |
|
|
|
rotationIdentity.invert = rotationIdentity; |
|
|
|
function rotateRadians(deltaLambda, deltaPhi, deltaGamma) { |
|
return (deltaLambda %= tau) ? (deltaPhi || deltaGamma ? compose(rotationLambda(deltaLambda), rotationPhiGamma(deltaPhi, deltaGamma)) |
|
: rotationLambda(deltaLambda)) |
|
: (deltaPhi || deltaGamma ? rotationPhiGamma(deltaPhi, deltaGamma) |
|
: rotationIdentity); |
|
} |
|
|
|
function forwardRotationLambda(deltaLambda) { |
|
return function(lambda, phi) { |
|
return lambda += deltaLambda, [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi]; |
|
}; |
|
} |
|
|
|
function rotationLambda(deltaLambda) { |
|
var rotation = forwardRotationLambda(deltaLambda); |
|
rotation.invert = forwardRotationLambda(-deltaLambda); |
|
return rotation; |
|
} |
|
|
|
function rotationPhiGamma(deltaPhi, deltaGamma) { |
|
var cosDeltaPhi = cos(deltaPhi), |
|
sinDeltaPhi = sin(deltaPhi), |
|
cosDeltaGamma = cos(deltaGamma), |
|
sinDeltaGamma = sin(deltaGamma); |
|
|
|
function rotation(lambda, phi) { |
|
var cosPhi = cos(phi), |
|
x = cos(lambda) * cosPhi, |
|
y = sin(lambda) * cosPhi, |
|
z = sin(phi), |
|
k = z * cosDeltaPhi + x * sinDeltaPhi; |
|
return [ |
|
atan2(y * cosDeltaGamma - k * sinDeltaGamma, x * cosDeltaPhi - z * sinDeltaPhi), |
|
asin(k * cosDeltaGamma + y * sinDeltaGamma) |
|
]; |
|
} |
|
|
|
rotation.invert = function(lambda, phi) { |
|
var cosPhi = cos(phi), |
|
x = cos(lambda) * cosPhi, |
|
y = sin(lambda) * cosPhi, |
|
z = sin(phi), |
|
k = z * cosDeltaGamma - y * sinDeltaGamma; |
|
return [ |
|
atan2(y * cosDeltaGamma + z * sinDeltaGamma, x * cosDeltaPhi + k * sinDeltaPhi), |
|
asin(k * cosDeltaPhi - x * sinDeltaPhi) |
|
]; |
|
}; |
|
|
|
return rotation; |
|
} |
|
|
|
function rotation(rotate) { |
|
rotate = rotateRadians(rotate[0] * radians, rotate[1] * radians, rotate.length > 2 ? rotate[2] * radians : 0); |
|
|
|
function forward(coordinates) { |
|
coordinates = rotate(coordinates[0] * radians, coordinates[1] * radians); |
|
return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates; |
|
} |
|
|
|
forward.invert = function(coordinates) { |
|
coordinates = rotate.invert(coordinates[0] * radians, coordinates[1] * radians); |
|
return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates; |
|
}; |
|
|
|
return forward; |
|
} |
|
|
|
// Generates a circle centered at [0°, 0°], with a given radius and precision. |
|
function circleStream(stream, radius, delta, direction, t0, t1) { |
|
if (!delta) return; |
|
var cosRadius = cos(radius), |
|
sinRadius = sin(radius), |
|
step = direction * delta; |
|
if (t0 == null) { |
|
t0 = radius + direction * tau; |
|
t1 = radius - step / 2; |
|
} else { |
|
t0 = circleRadius(cosRadius, t0); |
|
t1 = circleRadius(cosRadius, t1); |
|
if (direction > 0 ? t0 < t1 : t0 > t1) t0 += direction * tau; |
|
} |
|
for (var point, t = t0; direction > 0 ? t > t1 : t < t1; t -= step) { |
|
point = spherical([cosRadius, -sinRadius * cos(t), -sinRadius * sin(t)]); |
|
stream.point(point[0], point[1]); |
|
} |
|
} |
|
|
|
// Returns the signed angle of a cartesian point relative to [cosRadius, 0, 0]. |
|
function circleRadius(cosRadius, point) { |
|
point = cartesian(point), point[0] -= cosRadius; |
|
cartesianNormalizeInPlace(point); |
|
var radius = acos(-point[1]); |
|
return ((-point[2] < 0 ? -radius : radius) + tau - epsilon) % tau; |
|
} |
|
|
|
function circle() { |
|
var center = constant([0, 0]), |
|
radius = constant(90), |
|
precision = constant(6), |
|
ring, |
|
rotate, |
|
stream = {point: point}; |
|
|
|
function point(x, y) { |
|
ring.push(x = rotate(x, y)); |
|
x[0] *= degrees, x[1] *= degrees; |
|
} |
|
|
|
function circle() { |
|
var c = center.apply(this, arguments), |
|
r = radius.apply(this, arguments) * radians, |
|
p = precision.apply(this, arguments) * radians; |
|
ring = []; |
|
rotate = rotateRadians(-c[0] * radians, -c[1] * radians, 0).invert; |
|
circleStream(stream, r, p, 1); |
|
c = {type: "Polygon", coordinates: [ring]}; |
|
ring = rotate = null; |
|
return c; |
|
} |
|
|
|
circle.center = function(_) { |
|
return arguments.length ? (center = typeof _ === "function" ? _ : constant([+_[0], +_[1]]), circle) : center; |
|
}; |
|
|
|
circle.radius = function(_) { |
|
return arguments.length ? (radius = typeof _ === "function" ? _ : constant(+_), circle) : radius; |
|
}; |
|
|
|
circle.precision = function(_) { |
|
return arguments.length ? (precision = typeof _ === "function" ? _ : constant(+_), circle) : precision; |
|
}; |
|
|
|
return circle; |
|
} |
|
|
|
function clipBuffer() { |
|
var lines = [], |
|
line; |
|
return { |
|
point: function(x, y) { |
|
line.push([x, y]); |
|
}, |
|
lineStart: function() { |
|
lines.push(line = []); |
|
}, |
|
lineEnd: noop, |
|
rejoin: function() { |
|
if (lines.length > 1) lines.push(lines.pop().concat(lines.shift())); |
|
}, |
|
result: function() { |
|
var result = lines; |
|
lines = []; |
|
line = null; |
|
return result; |
|
} |
|
}; |
|
} |
|
|
|
function pointEqual(a, b) { |
|
return abs(a[0] - b[0]) < epsilon && abs(a[1] - b[1]) < epsilon; |
|
} |
|
|
|
function Intersection(point, points, other, entry) { |
|
this.x = point; |
|
this.z = points; |
|
this.o = other; // another intersection |
|
this.e = entry; // is an entry? |
|
this.v = false; // visited |
|
this.n = this.p = null; // next & previous |
|
} |
|
|
|
// A generalized polygon clipping algorithm: given a polygon that has been cut |
|
// into its visible line segments, and rejoins the segments by interpolating |
|
// along the clip edge. |
|
function clipRejoin(segments, compareIntersection, startInside, interpolate, stream) { |
|
var subject = [], |
|
clip = [], |
|
i, |
|
n; |
|
|
|
segments.forEach(function(segment) { |
|
if ((n = segment.length - 1) <= 0) return; |
|
var n, p0 = segment[0], p1 = segment[n], x; |
|
|
|
// If the first and last points of a segment are coincident, then treat as a |
|
// closed ring. TODO if all rings are closed, then the winding order of the |
|
// exterior ring should be checked. |
|
if (pointEqual(p0, p1)) { |
|
stream.lineStart(); |
|
for (i = 0; i < n; ++i) stream.point((p0 = segment[i])[0], p0[1]); |
|
stream.lineEnd(); |
|
return; |
|
} |
|
|
|
subject.push(x = new Intersection(p0, segment, null, true)); |
|
clip.push(x.o = new Intersection(p0, null, x, false)); |
|
subject.push(x = new Intersection(p1, segment, null, false)); |
|
clip.push(x.o = new Intersection(p1, null, x, true)); |
|
}); |
|
|
|
if (!subject.length) return; |
|
|
|
clip.sort(compareIntersection); |
|
link(subject); |
|
link(clip); |
|
|
|
for (i = 0, n = clip.length; i < n; ++i) { |
|
clip[i].e = startInside = !startInside; |
|
} |
|
|
|
var start = subject[0], |
|
points, |
|
point; |
|
|
|
while (1) { |
|
// Find first unvisited intersection. |
|
var current = start, |
|
isSubject = true; |
|
while (current.v) if ((current = current.n) === start) return; |
|
points = current.z; |
|
stream.lineStart(); |
|
do { |
|
current.v = current.o.v = true; |
|
if (current.e) { |
|
if (isSubject) { |
|
for (i = 0, n = points.length; i < n; ++i) stream.point((point = points[i])[0], point[1]); |
|
} else { |
|
interpolate(current.x, current.n.x, 1, stream); |
|
} |
|
current = current.n; |
|
} else { |
|
if (isSubject) { |
|
points = current.p.z; |
|
for (i = points.length - 1; i >= 0; --i) stream.point((point = points[i])[0], point[1]); |
|
} else { |
|
interpolate(current.x, current.p.x, -1, stream); |
|
} |
|
current = current.p; |
|
} |
|
current = current.o; |
|
points = current.z; |
|
isSubject = !isSubject; |
|
} while (!current.v); |
|
stream.lineEnd(); |
|
} |
|
} |
|
|
|
function link(array) { |
|
if (!(n = array.length)) return; |
|
var n, |
|
i = 0, |
|
a = array[0], |
|
b; |
|
while (++i < n) { |
|
a.n = b = array[i]; |
|
b.p = a; |
|
a = b; |
|
} |
|
a.n = b = array[0]; |
|
b.p = a; |
|
} |
|
|
|
var sum = adder(); |
|
|
|
function polygonContains(polygon, point) { |
|
var lambda = point[0], |
|
phi = point[1], |
|
sinPhi = sin(phi), |
|
normal = [sin(lambda), -cos(lambda), 0], |
|
angle = 0, |
|
winding = 0; |
|
|
|
sum.reset(); |
|
|
|
if (sinPhi === 1) phi = halfPi + epsilon; |
|
else if (sinPhi === -1) phi = -halfPi - epsilon; |
|
|
|
for (var i = 0, n = polygon.length; i < n; ++i) { |
|
if (!(m = (ring = polygon[i]).length)) continue; |
|
var ring, |
|
m, |
|
point0 = ring[m - 1], |
|
lambda0 = point0[0], |
|
phi0 = point0[1] / 2 + quarterPi, |
|
sinPhi0 = sin(phi0), |
|
cosPhi0 = cos(phi0); |
|
|
|
for (var j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) { |
|
var point1 = ring[j], |
|
lambda1 = point1[0], |
|
phi1 = point1[1] / 2 + quarterPi, |
|
sinPhi1 = sin(phi1), |
|
cosPhi1 = cos(phi1), |
|
delta = lambda1 - lambda0, |
|
sign$$1 = delta >= 0 ? 1 : -1, |
|
absDelta = sign$$1 * delta, |
|
antimeridian = absDelta > pi, |
|
k = sinPhi0 * sinPhi1; |
|
|
|
sum.add(atan2(k * sign$$1 * sin(absDelta), cosPhi0 * cosPhi1 + k * cos(absDelta))); |
|
angle += antimeridian ? delta + sign$$1 * tau : delta; |
|
|
|
// Are the longitudes either side of the point’s meridian (lambda), |
|
// and are the latitudes smaller than the parallel (phi)? |
|
if (antimeridian ^ lambda0 >= lambda ^ lambda1 >= lambda) { |
|
var arc = cartesianCross(cartesian(point0), cartesian(point1)); |
|
cartesianNormalizeInPlace(arc); |
|
var intersection = cartesianCross(normal, arc); |
|
cartesianNormalizeInPlace(intersection); |
|
var phiArc = (antimeridian ^ delta >= 0 ? -1 : 1) * asin(intersection[2]); |
|
if (phi > phiArc || phi === phiArc && (arc[0] || arc[1])) { |
|
winding += antimeridian ^ delta >= 0 ? 1 : -1; |
|
} |
|
} |
|
} |
|
} |
|
|
|
// First, determine whether the South pole is inside or outside: |
|
// |
|
// It is inside if: |
|
// * the polygon winds around it in a clockwise direction. |
|
// * the polygon does not (cumulatively) wind around it, but has a negative |
|
// (counter-clockwise) area. |
|
// |
|
// Second, count the (signed) number of times a segment crosses a lambda |
|
// from the point to the South pole. If it is zero, then the point is the |
|
// same side as the South pole. |
|
|
|
return (angle < -epsilon || angle < epsilon && sum < -epsilon) ^ (winding & 1); |
|
} |
|
|
|
function clip(pointVisible, clipLine, interpolate, start) { |
|
return function(sink) { |
|
var line = clipLine(sink), |
|
ringBuffer = clipBuffer(), |
|
ringSink = clipLine(ringBuffer), |
|
polygonStarted = false, |
|
polygon, |
|
segments, |
|
ring; |
|
|
|
var clip = { |
|
point: point, |
|
lineStart: lineStart, |
|
lineEnd: lineEnd, |
|
polygonStart: function() { |
|
clip.point = pointRing; |
|
clip.lineStart = ringStart; |
|
clip.lineEnd = ringEnd; |
|
segments = []; |
|
polygon = []; |
|
}, |
|
polygonEnd: function() { |
|
clip.point = point; |
|
clip.lineStart = lineStart; |
|
clip.lineEnd = lineEnd; |
|
segments = d3Array.merge(segments); |
|
var startInside = polygonContains(polygon, start); |
|
if (segments.length) { |
|
if (!polygonStarted) sink.polygonStart(), polygonStarted = true; |
|
clipRejoin(segments, compareIntersection, startInside, interpolate, sink); |
|
} else if (startInside) { |
|
if (!polygonStarted) sink.polygonStart(), polygonStarted = true; |
|
sink.lineStart(); |
|
interpolate(null, null, 1, sink); |
|
sink.lineEnd(); |
|
} |
|
if (polygonStarted) sink.polygonEnd(), polygonStarted = false; |
|
segments = polygon = null; |
|
}, |
|
sphere: function() { |
|
sink.polygonStart(); |
|
sink.lineStart(); |
|
interpolate(null, null, 1, sink); |
|
sink.lineEnd(); |
|
sink.polygonEnd(); |
|
} |
|
}; |
|
|
|
function point(lambda, phi) { |
|
if (pointVisible(lambda, phi)) sink.point(lambda, phi); |
|
} |
|
|
|
function pointLine(lambda, phi) { |
|
line.point(lambda, phi); |
|
} |
|
|
|
function lineStart() { |
|
clip.point = pointLine; |
|
line.lineStart(); |
|
} |
|
|
|
function lineEnd() { |
|
clip.point = point; |
|
line.lineEnd(); |
|
} |
|
|
|
function pointRing(lambda, phi) { |
|
ring.push([lambda, phi]); |
|
ringSink.point(lambda, phi); |
|
} |
|
|
|
function ringStart() { |
|
ringSink.lineStart(); |
|
ring = []; |
|
} |
|
|
|
function ringEnd() { |
|
pointRing(ring[0][0], ring[0][1]); |
|
ringSink.lineEnd(); |
|
|
|
var clean = ringSink.clean(), |
|
ringSegments = ringBuffer.result(), |
|
i, n = ringSegments.length, m, |
|
segment, |
|
point; |
|
|
|
ring.pop(); |
|
polygon.push(ring); |
|
ring = null; |
|
|
|
if (!n) return; |
|
|
|
// No intersections. |
|
if (clean & 1) { |
|
segment = ringSegments[0]; |
|
if ((m = segment.length - 1) > 0) { |
|
if (!polygonStarted) sink.polygonStart(), polygonStarted = true; |
|
sink.lineStart(); |
|
for (i = 0; i < m; ++i) sink.point((point = segment[i])[0], point[1]); |
|
sink.lineEnd(); |
|
} |
|
return; |
|
} |
|
|
|
// Rejoin connected segments. |
|
// TODO reuse ringBuffer.rejoin()? |
|
if (n > 1 && clean & 2) ringSegments.push(ringSegments.pop().concat(ringSegments.shift())); |
|
|
|
segments.push(ringSegments.filter(validSegment)); |
|
} |
|
|
|
return clip; |
|
}; |
|
} |
|
|
|
function validSegment(segment) { |
|
return segment.length > 1; |
|
} |
|
|
|
// Intersections are sorted along the clip edge. For both antimeridian cutting |
|
// and circle clipping, the same comparison is used. |
|
function compareIntersection(a, b) { |
|
return ((a = a.x)[0] < 0 ? a[1] - halfPi - epsilon : halfPi - a[1]) |
|
- ((b = b.x)[0] < 0 ? b[1] - halfPi - epsilon : halfPi - b[1]); |
|
} |
|
|
|
var clipAntimeridian = clip( |
|
function() { return true; }, |
|
clipAntimeridianLine, |
|
clipAntimeridianInterpolate, |
|
[-pi, -halfPi] |
|
); |
|
|
|
// Takes a line and cuts into visible segments. Return values: 0 - there were |
|
// intersections or the line was empty; 1 - no intersections; 2 - there were |
|
// intersections, and the first and last segments should be rejoined. |
|
function clipAntimeridianLine(stream) { |
|
var lambda0 = NaN, |
|
phi0 = NaN, |
|
sign0 = NaN, |
|
clean; // no intersections |
|
|
|
return { |
|
lineStart: function() { |
|
stream.lineStart(); |
|
clean = 1; |
|
}, |
|
point: function(lambda1, phi1) { |
|
var sign1 = lambda1 > 0 ? pi : -pi, |
|
delta = abs(lambda1 - lambda0); |
|
if (abs(delta - pi) < epsilon) { // line crosses a pole |
|
stream.point(lambda0, phi0 = (phi0 + phi1) / 2 > 0 ? halfPi : -halfPi); |
|
stream.point(sign0, phi0); |
|
stream.lineEnd(); |
|
stream.lineStart(); |
|
stream.point(sign1, phi0); |
|
stream.point(lambda1, phi0); |
|
clean = 0; |
|
} else if (sign0 !== sign1 && delta >= pi) { // line crosses antimeridian |
|
if (abs(lambda0 - sign0) < epsilon) lambda0 -= sign0 * epsilon; // handle degeneracies |
|
if (abs(lambda1 - sign1) < epsilon) lambda1 -= sign1 * epsilon; |
|
phi0 = clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1); |
|
stream.point(sign0, phi0); |
|
stream.lineEnd(); |
|
stream.lineStart(); |
|
stream.point(sign1, phi0); |
|
clean = 0; |
|
} |
|
stream.point(lambda0 = lambda1, phi0 = phi1); |
|
sign0 = sign1; |
|
}, |
|
lineEnd: function() { |
|
stream.lineEnd(); |
|
lambda0 = phi0 = NaN; |
|
}, |
|
clean: function() { |
|
return 2 - clean; // if intersections, rejoin first and last segments |
|
} |
|
}; |
|
} |
|
|
|
function clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1) { |
|
var cosPhi0, |
|
cosPhi1, |
|
sinLambda0Lambda1 = sin(lambda0 - lambda1); |
|
return abs(sinLambda0Lambda1) > epsilon |
|
? atan((sin(phi0) * (cosPhi1 = cos(phi1)) * sin(lambda1) |
|
- sin(phi1) * (cosPhi0 = cos(phi0)) * sin(lambda0)) |
|
/ (cosPhi0 * cosPhi1 * sinLambda0Lambda1)) |
|
: (phi0 + phi1) / 2; |
|
} |
|
|
|
function clipAntimeridianInterpolate(from, to, direction, stream) { |
|
var phi; |
|
if (from == null) { |
|
phi = direction * halfPi; |
|
stream.point(-pi, phi); |
|
stream.point(0, phi); |
|
stream.point(pi, phi); |
|
stream.point(pi, 0); |
|
stream.point(pi, -phi); |
|
stream.point(0, -phi); |
|
stream.point(-pi, -phi); |
|
stream.point(-pi, 0); |
|
stream.point(-pi, phi); |
|
} else if (abs(from[0] - to[0]) > epsilon) { |
|
var lambda = from[0] < to[0] ? pi : -pi; |
|
phi = direction * lambda / 2; |
|
stream.point(-lambda, phi); |
|
stream.point(0, phi); |
|
stream.point(lambda, phi); |
|
} else { |
|
stream.point(to[0], to[1]); |
|
} |
|
} |
|
|
|
function clipCircle(radius) { |
|
var cr = cos(radius), |
|
delta = 6 * radians, |
|
smallRadius = cr > 0, |
|
notHemisphere = abs(cr) > epsilon; // TODO optimise for this common case |
|
|
|
function interpolate(from, to, direction, stream) { |
|
circleStream(stream, radius, delta, direction, from, to); |
|
} |
|
|
|
function visible(lambda, phi) { |
|
return cos(lambda) * cos(phi) > cr; |
|
} |
|
|
|
// Takes a line and cuts into visible segments. Return values used for polygon |
|
// clipping: 0 - there were intersections or the line was empty; 1 - no |
|
// intersections 2 - there were intersections, and the first and last segments |
|
// should be rejoined. |
|
function clipLine(stream) { |
|
var point0, // previous point |
|
c0, // code for previous point |
|
v0, // visibility of previous point |
|
v00, // visibility of first point |
|
clean; // no intersections |
|
return { |
|
lineStart: function() { |
|
v00 = v0 = false; |
|
clean = 1; |
|
}, |
|
point: function(lambda, phi) { |
|
var point1 = [lambda, phi], |
|
point2, |
|
v = visible(lambda, phi), |
|
c = smallRadius |
|
? v ? 0 : code(lambda, phi) |
|
: v ? code(lambda + (lambda < 0 ? pi : -pi), phi) : 0; |
|
if (!point0 && (v00 = v0 = v)) stream.lineStart(); |
|
// Handle degeneracies. |
|
// TODO ignore if not clipping polygons. |
|
if (v !== v0) { |
|
point2 = intersect(point0, point1); |
|
if (!point2 || pointEqual(point0, point2) || pointEqual(point1, point2)) { |
|
point1[0] += epsilon; |
|
point1[1] += epsilon; |
|
v = visible(point1[0], point1[1]); |
|
} |
|
} |
|
if (v !== v0) { |
|
clean = 0; |
|
if (v) { |
|
// outside going in |
|
stream.lineStart(); |
|
point2 = intersect(point1, point0); |
|
stream.point(point2[0], point2[1]); |
|
} else { |
|
// inside going out |
|
point2 = intersect(point0, point1); |
|
stream.point(point2[0], point2[1]); |
|
stream.lineEnd(); |
|
} |
|
point0 = point2; |
|
} else if (notHemisphere && point0 && smallRadius ^ v) { |
|
var t; |
|
// If the codes for two points are different, or are both zero, |
|
// and there this segment intersects with the small circle. |
|
if (!(c & c0) && (t = intersect(point1, point0, true))) { |
|
clean = 0; |
|
if (smallRadius) { |
|
stream.lineStart(); |
|
stream.point(t[0][0], t[0][1]); |
|
stream.point(t[1][0], t[1][1]); |
|
stream.lineEnd(); |
|
} else { |
|
stream.point(t[1][0], t[1][1]); |
|
stream.lineEnd(); |
|
stream.lineStart(); |
|
stream.point(t[0][0], t[0][1]); |
|
} |
|
} |
|
} |
|
if (v && (!point0 || !pointEqual(point0, point1))) { |
|
stream.point(point1[0], point1[1]); |
|
} |
|
point0 = point1, v0 = v, c0 = c; |
|
}, |
|
lineEnd: function() { |
|
if (v0) stream.lineEnd(); |
|
point0 = null; |
|
}, |
|
// Rejoin first and last segments if there were intersections and the first |
|
// and last points were visible. |
|
clean: function() { |
|
return clean | ((v00 && v0) << 1); |
|
} |
|
}; |
|
} |
|
|
|
// Intersects the great circle between a and b with the clip circle. |
|
function intersect(a, b, two) { |
|
var pa = cartesian(a), |
|
pb = cartesian(b); |
|
|
|
// We have two planes, n1.p = d1 and n2.p = d2. |
|
// Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2). |
|
var n1 = [1, 0, 0], // normal |
|
n2 = cartesianCross(pa, pb), |
|
n2n2 = cartesianDot(n2, n2), |
|
n1n2 = n2[0], // cartesianDot(n1, n2), |
|
determinant = n2n2 - n1n2 * n1n2; |
|
|
|
// Two polar points. |
|
if (!determinant) return !two && a; |
|
|
|
var c1 = cr * n2n2 / determinant, |
|
c2 = -cr * n1n2 / determinant, |
|
n1xn2 = cartesianCross(n1, n2), |
|
A = cartesianScale(n1, c1), |
|
B = cartesianScale(n2, c2); |
|
cartesianAddInPlace(A, B); |
|
|
|
// Solve |p(t)|^2 = 1. |
|
var u = n1xn2, |
|
w = cartesianDot(A, u), |
|
uu = cartesianDot(u, u), |
|
t2 = w * w - uu * (cartesianDot(A, A) - 1); |
|
|
|
if (t2 < 0) return; |
|
|
|
var t = sqrt(t2), |
|
q = cartesianScale(u, (-w - t) / uu); |
|
cartesianAddInPlace(q, A); |
|
q = spherical(q); |
|
|
|
if (!two) return q; |
|
|
|
// Two intersection points. |
|
var lambda0 = a[0], |
|
lambda1 = b[0], |
|
phi0 = a[1], |
|
phi1 = b[1], |
|
z; |
|
|
|
if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z; |
|
|
|
var delta = lambda1 - lambda0, |
|
polar = abs(delta - pi) < epsilon, |
|
meridian = polar || delta < epsilon; |
|
|
|
if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z; |
|
|
|
// Check that the first point is between a and b. |
|
if (meridian |
|
? polar |
|
? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon ? phi0 : phi1) |
|
: phi0 <= q[1] && q[1] <= phi1 |
|
: delta > pi ^ (lambda0 <= q[0] && q[0] <= lambda1)) { |
|
var q1 = cartesianScale(u, (-w + t) / uu); |
|
cartesianAddInPlace(q1, A); |
|
return [q, spherical(q1)]; |
|
} |
|
} |
|
|
|
// Generates a 4-bit vector representing the location of a point relative to |
|
// the small circle's bounding box. |
|
function code(lambda, phi) { |
|
var r = smallRadius ? radius : pi - radius, |
|
code = 0; |
|
if (lambda < -r) code |= 1; // left |
|
else if (lambda > r) code |= 2; // right |
|
if (phi < -r) code |= 4; // below |
|
else if (phi > r) code |= 8; // above |
|
return code; |
|
} |
|
|
|
return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi, radius - pi]); |
|
} |
|
|
|
function clipLine(a, b, x0, y0, x1, y1) { |
|
var ax = a[0], |
|
ay = a[1], |
|
bx = b[0], |
|
by = b[1], |
|
t0 = 0, |
|
t1 = 1, |
|
dx = bx - ax, |
|
dy = by - ay, |
|
r; |
|
|
|
r = x0 - ax; |
|
if (!dx && r > 0) return; |
|
r /= dx; |
|
if (dx < 0) { |
|
if (r < t0) return; |
|
if (r < t1) t1 = r; |
|
} else if (dx > 0) { |
|
if (r > t1) return; |
|
if (r > t0) t0 = r; |
|
} |
|
|
|
r = x1 - ax; |
|
if (!dx && r < 0) return; |
|
r /= dx; |
|
if (dx < 0) { |
|
if (r > t1) return; |
|
if (r > t0) t0 = r; |
|
} else if (dx > 0) { |
|
if (r < t0) return; |
|
if (r < t1) t1 = r; |
|
} |
|
|
|
r = y0 - ay; |
|
if (!dy && r > 0) return; |
|
r /= dy; |
|
if (dy < 0) { |
|
if (r < t0) return; |
|
if (r < t1) t1 = r; |
|
} else if (dy > 0) { |
|
if (r > t1) return; |
|
if (r > t0) t0 = r; |
|
} |
|
|
|
r = y1 - ay; |
|
if (!dy && r < 0) return; |
|
r /= dy; |
|
if (dy < 0) { |
|
if (r > t1) return; |
|
if (r > t0) t0 = r; |
|
} else if (dy > 0) { |
|
if (r < t0) return; |
|
if (r < t1) t1 = r; |
|
} |
|
|
|
if (t0 > 0) a[0] = ax + t0 * dx, a[1] = ay + t0 * dy; |
|
if (t1 < 1) b[0] = ax + t1 * dx, b[1] = ay + t1 * dy; |
|
return true; |
|
} |
|
|
|
var clipMax = 1e9, clipMin = -clipMax; |
|
|
|
// TODO Use d3-polygon’s polygonContains here for the ring check? |
|
// TODO Eliminate duplicate buffering in clipBuffer and polygon.push? |
|
|
|
function clipRectangle(x0, y0, x1, y1) { |
|
|
|
function visible(x, y) { |
|
return x0 <= x && x <= x1 && y0 <= y && y <= y1; |
|
} |
|
|
|
function interpolate(from, to, direction, stream) { |
|
var a = 0, a1 = 0; |
|
if (from == null |
|
|| (a = corner(from, direction)) !== (a1 = corner(to, direction)) |
|
|| comparePoint(from, to) < 0 ^ direction > 0) { |
|
do stream.point(a === 0 || a === 3 ? x0 : x1, a > 1 ? y1 : y0); |
|
while ((a = (a + direction + 4) % 4) !== a1); |
|
} else { |
|
stream.point(to[0], to[1]); |
|
} |
|
} |
|
|
|
function corner(p, direction) { |
|
return abs(p[0] - x0) < epsilon ? direction > 0 ? 0 : 3 |
|
: abs(p[0] - x1) < epsilon ? direction > 0 ? 2 : 1 |
|
: abs(p[1] - y0) < epsilon ? direction > 0 ? 1 : 0 |
|
: direction > 0 ? 3 : 2; // abs(p[1] - y1) < epsilon |
|
} |
|
|
|
function compareIntersection(a, b) { |
|
return comparePoint(a.x, b.x); |
|
} |
|
|
|
function comparePoint(a, b) { |
|
var ca = corner(a, 1), |
|
cb = corner(b, 1); |
|
return ca !== cb ? ca - cb |
|
: ca === 0 ? b[1] - a[1] |
|
: ca === 1 ? a[0] - b[0] |
|
: ca === 2 ? a[1] - b[1] |
|
: b[0] - a[0]; |
|
} |
|
|
|
return function(stream) { |
|
var activeStream = stream, |
|
bufferStream = clipBuffer(), |
|
segments, |
|
polygon, |
|
ring, |
|
x__, y__, v__, // first point |
|
x_, y_, v_, // previous point |
|
first, |
|
clean; |
|
|
|
var clipStream = { |
|
point: point, |
|
lineStart: lineStart, |
|
lineEnd: lineEnd, |
|
polygonStart: polygonStart, |
|
polygonEnd: polygonEnd |
|
}; |
|
|
|
function point(x, y) { |
|
if (visible(x, y)) activeStream.point(x, y); |
|
} |
|
|
|
function polygonInside() { |
|
var winding = 0; |
|
|
|
for (var i = 0, n = polygon.length; i < n; ++i) { |
|
for (var ring = polygon[i], j = 1, m = ring.length, point = ring[0], a0, a1, b0 = point[0], b1 = point[1]; j < m; ++j) { |
|
a0 = b0, a1 = b1, point = ring[j], b0 = point[0], b1 = point[1]; |
|
if (a1 <= y1) { if (b1 > y1 && (b0 - a0) * (y1 - a1) > (b1 - a1) * (x0 - a0)) ++winding; } |
|
else { if (b1 <= y1 && (b0 - a0) * (y1 - a1) < (b1 - a1) * (x0 - a0)) --winding; } |
|
} |
|
} |
|
|
|
return winding; |
|
} |
|
|
|
// Buffer geometry within a polygon and then clip it en masse. |
|
function polygonStart() { |
|
activeStream = bufferStream, segments = [], polygon = [], clean = true; |
|
} |
|
|
|
function polygonEnd() { |
|
var startInside = polygonInside(), |
|
cleanInside = clean && startInside, |
|
visible = (segments = d3Array.merge(segments)).length; |
|
if (cleanInside || visible) { |
|
stream.polygonStart(); |
|
if (cleanInside) { |
|
stream.lineStart(); |
|
interpolate(null, null, 1, stream); |
|
stream.lineEnd(); |
|
} |
|
if (visible) { |
|
clipRejoin(segments, compareIntersection, startInside, interpolate, stream); |
|
} |
|
stream.polygonEnd(); |
|
} |
|
activeStream = stream, segments = polygon = ring = null; |
|
} |
|
|
|
function lineStart() { |
|
clipStream.point = linePoint; |
|
if (polygon) polygon.push(ring = []); |
|
first = true; |
|
v_ = false; |
|
x_ = y_ = NaN; |
|
} |
|
|
|
// TODO rather than special-case polygons, simply handle them separately. |
|
// Ideally, coincident intersection points should be jittered to avoid |
|
// clipping issues. |
|
function lineEnd() { |
|
if (segments) { |
|
linePoint(x__, y__); |
|
if (v__ && v_) bufferStream.rejoin(); |
|
segments.push(bufferStream.result()); |
|
} |
|
clipStream.point = point; |
|
if (v_) activeStream.lineEnd(); |
|
} |
|
|
|
function linePoint(x, y) { |
|
var v = visible(x, y); |
|
if (polygon) ring.push([x, y]); |
|
if (first) { |
|
x__ = x, y__ = y, v__ = v; |
|
first = false; |
|
if (v) { |
|
activeStream.lineStart(); |
|
activeStream.point(x, y); |
|
} |
|
} else { |
|
if (v && v_) activeStream.point(x, y); |
|
else { |
|
var a = [x_ = Math.max(clipMin, Math.min(clipMax, x_)), y_ = Math.max(clipMin, Math.min(clipMax, y_))], |
|
b = [x = Math.max(clipMin, Math.min(clipMax, x)), y = Math.max(clipMin, Math.min(clipMax, y))]; |
|
if (clipLine(a, b, x0, y0, x1, y1)) { |
|
if (!v_) { |
|
activeStream.lineStart(); |
|
activeStream.point(a[0], a[1]); |
|
} |
|
activeStream.point(b[0], b[1]); |
|
if (!v) activeStream.lineEnd(); |
|
clean = false; |
|
} else if (v) { |
|
activeStream.lineStart(); |
|
activeStream.point(x, y); |
|
clean = false; |
|
} |
|
} |
|
} |
|
x_ = x, y_ = y, v_ = v; |
|
} |
|
|
|
return clipStream; |
|
}; |
|
} |
|
|
|
function extent() { |
|
var x0 = 0, |
|
y0 = 0, |
|
x1 = 960, |
|
y1 = 500, |
|
cache, |
|
cacheStream, |
|
clip; |
|
|
|
return clip = { |
|
stream: function(stream) { |
|
return cache && cacheStream === stream ? cache : cache = clipRectangle(x0, y0, x1, y1)(cacheStream = stream); |
|
}, |
|
extent: function(_) { |
|
return arguments.length ? (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1], cache = cacheStream = null, clip) : [[x0, y0], [x1, y1]]; |
|
} |
|
}; |
|
} |
|
|
|
var lengthSum = adder(), |
|
lambda0$2, |
|
sinPhi0$1, |
|
cosPhi0$1; |
|
|
|
var lengthStream = { |
|
sphere: noop, |
|
point: noop, |
|
lineStart: lengthLineStart, |
|
lineEnd: noop, |
|
polygonStart: noop, |
|
polygonEnd: noop |
|
}; |
|
|
|
function lengthLineStart() { |
|
lengthStream.point = lengthPointFirst; |
|
lengthStream.lineEnd = lengthLineEnd; |
|
} |
|
|
|
function lengthLineEnd() { |
|
lengthStream.point = lengthStream.lineEnd = noop; |
|
} |
|
|
|
function lengthPointFirst(lambda, phi) { |
|
lambda *= radians, phi *= radians; |
|
lambda0$2 = lambda, sinPhi0$1 = sin(phi), cosPhi0$1 = cos(phi); |
|
lengthStream.point = lengthPoint; |
|
} |
|
|
|
function lengthPoint(lambda, phi) { |
|
lambda *= radians, phi *= radians; |
|
var sinPhi = sin(phi), |
|
cosPhi = cos(phi), |
|
delta = abs(lambda - lambda0$2), |
|
cosDelta = cos(delta), |
|
sinDelta = sin(delta), |
|
x = cosPhi * sinDelta, |
|
y = cosPhi0$1 * sinPhi - sinPhi0$1 * cosPhi * cosDelta, |
|
z = sinPhi0$1 * sinPhi + cosPhi0$1 * cosPhi * cosDelta; |
|
lengthSum.add(atan2(sqrt(x * x + y * y), z)); |
|
lambda0$2 = lambda, sinPhi0$1 = sinPhi, cosPhi0$1 = cosPhi; |
|
} |
|
|
|
function length(object) { |
|
lengthSum.reset(); |
|
geoStream(object, lengthStream); |
|
return +lengthSum; |
|
} |
|
|
|
var coordinates = [null, null], |
|
object = {type: "LineString", coordinates: coordinates}; |
|
|
|
function distance(a, b) { |
|
coordinates[0] = a; |
|
coordinates[1] = b; |
|
return length(object); |
|
} |
|
|
|
var containsObjectType = { |
|
Feature: function(object, point) { |
|
return containsGeometry(object.geometry, point); |
|
}, |
|
FeatureCollection: function(object, point) { |
|
var features = object.features, i = -1, n = features.length; |
|
while (++i < n) if (containsGeometry(features[i].geometry, point)) return true; |
|
return false; |
|
} |
|
}; |
|
|
|
var containsGeometryType = { |
|
Sphere: function() { |
|
return true; |
|
}, |
|
Point: function(object, point) { |
|
return containsPoint(object.coordinates, point); |
|
}, |
|
MultiPoint: function(object, point) { |
|
var coordinates = object.coordinates, i = -1, n = coordinates.length; |
|
while (++i < n) if (containsPoint(coordinates[i], point)) return true; |
|
return false; |
|
}, |
|
LineString: function(object, point) { |
|
return containsLine(object.coordinates, point); |
|
}, |
|
MultiLineString: function(object, point) { |
|
var coordinates = object.coordinates, i = -1, n = coordinates.length; |
|
while (++i < n) if (containsLine(coordinates[i], point)) return true; |
|
return false; |
|
}, |
|
Polygon: function(object, point) { |
|
return containsPolygon(object.coordinates, point); |
|
}, |
|
MultiPolygon: function(object, point) { |
|
var coordinates = object.coordinates, i = -1, n = coordinates.length; |
|
while (++i < n) if (containsPolygon(coordinates[i], point)) return true; |
|
return false; |
|
}, |
|
GeometryCollection: function(object, point) { |
|
var geometries = object.geometries, i = -1, n = geometries.length; |
|
while (++i < n) if (containsGeometry(geometries[i], point)) return true; |
|
return false; |
|
} |
|
}; |
|
|
|
function containsGeometry(geometry, point) { |
|
return geometry && containsGeometryType.hasOwnProperty(geometry.type) |
|
? containsGeometryType[geometry.type](geometry, point) |
|
: false; |
|
} |
|
|
|
function containsPoint(coordinates, point) { |
|
return distance(coordinates, point) === 0; |
|
} |
|
|
|
function containsLine(coordinates, point) { |
|
var ab = distance(coordinates[0], coordinates[1]), |
|
ao = distance(coordinates[0], point), |
|
ob = distance(point, coordinates[1]); |
|
return ao + ob <= ab + epsilon; |
|
} |
|
|
|
function containsPolygon(coordinates, point) { |
|
return !!polygonContains(coordinates.map(ringRadians), pointRadians(point)); |
|
} |
|
|
|
function ringRadians(ring) { |
|
return ring = ring.map(pointRadians), ring.pop(), ring; |
|
} |
|
|
|
function pointRadians(point) { |
|
return [point[0] * radians, point[1] * radians]; |
|
} |
|
|
|
function contains(object, point) { |
|
return (object && containsObjectType.hasOwnProperty(object.type) |
|
? containsObjectType[object.type] |
|
: containsGeometry)(object, point); |
|
} |
|
|
|
function graticuleX(y0, y1, dy) { |
|
var y = d3Array.range(y0, y1 - epsilon, dy).concat(y1); |
|
return function(x) { return y.map(function(y) { return [x, y]; }); }; |
|
} |
|
|
|
function graticuleY(x0, x1, dx) { |
|
var x = d3Array.range(x0, x1 - epsilon, dx).concat(x1); |
|
return function(y) { return x.map(function(x) { return [x, y]; }); }; |
|
} |
|
|
|
function graticule() { |
|
var x1, x0, X1, X0, |
|
y1, y0, Y1, Y0, |
|
dx = 10, dy = dx, DX = 90, DY = 360, |
|
x, y, X, Y, |
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precision = 2.5; |
|
|
|
function graticule() { |
|
return {type: "MultiLineString", coordinates: lines()}; |
|
} |
|
|
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function lines() { |
|
return d3Array.range(ceil(X0 / DX) * DX, X1, DX).map(X) |
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.concat(d3Array.range(ceil(Y0 / DY) * DY, Y1, DY).map(Y)) |
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.concat(d3Array.range(ceil(x0 / dx) * dx, x1, dx).filter(function(x) { return abs(x % DX) > epsilon; }).map(x)) |
|
.concat(d3Array.range(ceil(y0 / dy) * dy, y1, dy).filter(function(y) { return abs(y % DY) > epsilon; }).map(y)); |
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} |
|
|
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graticule.lines = function() { |
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return lines().map(function(coordinates) { return {type: "LineString", coordinates: coordinates}; }); |
|
}; |
|
|
|
graticule.outline = function() { |
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return { |
|
type: "Polygon", |
|
coordinates: [ |
|
X(X0).concat( |
|
Y(Y1).slice(1), |
|
X(X1).reverse().slice(1), |
|
Y(Y0).reverse().slice(1)) |
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] |
|
}; |
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}; |
|
|
|
graticule.extent = function(_) { |
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if (!arguments.length) return graticule.extentMinor(); |
|
return graticule.extentMajor(_).extentMinor(_); |
|
}; |
|
|
|
graticule.extentMajor = function(_) { |
|
if (!arguments.length) return [[X0, Y0], [X1, Y1]]; |
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X0 = +_[0][0], X1 = +_[1][0]; |
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Y0 = +_[0][1], Y1 = +_[1][1]; |
|
if (X0 > X1) _ = X0, X0 = X1, X1 = _; |
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if (Y0 > Y1) _ = Y0, Y0 = Y1, Y1 = _; |
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return graticule.precision(precision); |
|
}; |
|
|
|
graticule.extentMinor = function(_) { |
|
if (!arguments.length) return [[x0, y0], [x1, y1]]; |
|
x0 = +_[0][0], x1 = +_[1][0]; |
|
y0 = +_[0][1], y1 = +_[1][1]; |
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if (x0 > x1) _ = x0, x0 = x1, x1 = _; |
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if (y0 > y1) _ = y0, y0 = y1, y1 = _; |
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return graticule.precision(precision); |
|
}; |
|
|
|
graticule.step = function(_) { |
|
if (!arguments.length) return graticule.stepMinor(); |
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return graticule.stepMajor(_).stepMinor(_); |
|
}; |
|
|
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graticule.stepMajor = function(_) { |
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if (!arguments.length) return [DX, DY]; |
|
DX = +_[0], DY = +_[1]; |
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return graticule; |
|
}; |
|
|
|
graticule.stepMinor = function(_) { |
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if (!arguments.length) return [dx, dy]; |
|
dx = +_[0], dy = +_[1]; |
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return graticule; |
|
}; |
|
|
|
graticule.precision = function(_) { |
|
if (!arguments.length) return precision; |
|
precision = +_; |
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x = graticuleX(y0, y1, 90); |
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y = graticuleY(x0, x1, precision); |
|
X = graticuleX(Y0, Y1, 90); |
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Y = graticuleY(X0, X1, precision); |
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return graticule; |
|
}; |
|
|
|
return graticule |
|
.extentMajor([[-180, -90 + epsilon], [180, 90 - epsilon]]) |
|
.extentMinor([[-180, -80 - epsilon], [180, 80 + epsilon]]); |
|
} |
|
|
|
function graticule10() { |
|
return graticule()(); |
|
} |
|
|
|
function interpolate(a, b) { |
|
var x0 = a[0] * radians, |
|
y0 = a[1] * radians, |
|
x1 = b[0] * radians, |
|
y1 = b[1] * radians, |
|
cy0 = cos(y0), |
|
sy0 = sin(y0), |
|
cy1 = cos(y1), |
|
sy1 = sin(y1), |
|
kx0 = cy0 * cos(x0), |
|
ky0 = cy0 * sin(x0), |
|
kx1 = cy1 * cos(x1), |
|
ky1 = cy1 * sin(x1), |
|
d = 2 * asin(sqrt(haversin(y1 - y0) + cy0 * cy1 * haversin(x1 - x0))), |
|
k = sin(d); |
|
|
|
var interpolate = d ? function(t) { |
|
var B = sin(t *= d) / k, |
|
A = sin(d - t) / k, |
|
x = A * kx0 + B * kx1, |
|
y = A * ky0 + B * ky1, |
|
z = A * sy0 + B * sy1; |
|
return [ |
|
atan2(y, x) * degrees, |
|
atan2(z, sqrt(x * x + y * y)) * degrees |
|
]; |
|
} : function() { |
|
return [x0 * degrees, y0 * degrees]; |
|
}; |
|
|
|
interpolate.distance = d; |
|
|
|
return interpolate; |
|
} |
|
|
|
function identity(x) { |
|
return x; |
|
} |
|
|
|
var areaSum$1 = adder(), |
|
areaRingSum$1 = adder(), |
|
x00, |
|
y00, |
|
x0$1, |
|
y0$1; |
|
|
|
var areaStream$1 = { |
|
point: noop, |
|
lineStart: noop, |
|
lineEnd: noop, |
|
polygonStart: function() { |
|
areaStream$1.lineStart = areaRingStart$1; |
|
areaStream$1.lineEnd = areaRingEnd$1; |
|
}, |
|
polygonEnd: function() { |
|
areaStream$1.lineStart = areaStream$1.lineEnd = areaStream$1.point = noop; |
|
areaSum$1.add(abs(areaRingSum$1)); |
|
areaRingSum$1.reset(); |
|
}, |
|
result: function() { |
|
var area = areaSum$1 / 2; |
|
areaSum$1.reset(); |
|
return area; |
|
} |
|
}; |
|
|
|
function areaRingStart$1() { |
|
areaStream$1.point = areaPointFirst$1; |
|
} |
|
|
|
function areaPointFirst$1(x, y) { |
|
areaStream$1.point = areaPoint$1; |
|
x00 = x0$1 = x, y00 = y0$1 = y; |
|
} |
|
|
|
function areaPoint$1(x, y) { |
|
areaRingSum$1.add(y0$1 * x - x0$1 * y); |
|
x0$1 = x, y0$1 = y; |
|
} |
|
|
|
function areaRingEnd$1() { |
|
areaPoint$1(x00, y00); |
|
} |
|
|
|
var x0$2 = Infinity, |
|
y0$2 = x0$2, |
|
x1 = -x0$2, |
|
y1 = x1; |
|
|
|
var boundsStream$1 = { |
|
point: boundsPoint$1, |
|
lineStart: noop, |
|
lineEnd: noop, |
|
polygonStart: noop, |
|
polygonEnd: noop, |
|
result: function() { |
|
var bounds = [[x0$2, y0$2], [x1, y1]]; |
|
x1 = y1 = -(y0$2 = x0$2 = Infinity); |
|
return bounds; |
|
} |
|
}; |
|
|
|
function boundsPoint$1(x, y) { |
|
if (x < x0$2) x0$2 = x; |
|
if (x > x1) x1 = x; |
|
if (y < y0$2) y0$2 = y; |
|
if (y > y1) y1 = y; |
|
} |
|
|
|
// TODO Enforce positive area for exterior, negative area for interior? |
|
|
|
var X0$1 = 0, |
|
Y0$1 = 0, |
|
Z0$1 = 0, |
|
X1$1 = 0, |
|
Y1$1 = 0, |
|
Z1$1 = 0, |
|
X2$1 = 0, |
|
Y2$1 = 0, |
|
Z2$1 = 0, |
|
x00$1, |
|
y00$1, |
|
x0$3, |
|
y0$3; |
|
|
|
var centroidStream$1 = { |
|
point: centroidPoint$1, |
|
lineStart: centroidLineStart$1, |
|
lineEnd: centroidLineEnd$1, |
|
polygonStart: function() { |
|
centroidStream$1.lineStart = centroidRingStart$1; |
|
centroidStream$1.lineEnd = centroidRingEnd$1; |
|
}, |
|
polygonEnd: function() { |
|
centroidStream$1.point = centroidPoint$1; |
|
centroidStream$1.lineStart = centroidLineStart$1; |
|
centroidStream$1.lineEnd = centroidLineEnd$1; |
|
}, |
|
result: function() { |
|
var centroid = Z2$1 ? [X2$1 / Z2$1, Y2$1 / Z2$1] |
|
: Z1$1 ? [X1$1 / Z1$1, Y1$1 / Z1$1] |
|
: Z0$1 ? [X0$1 / Z0$1, Y0$1 / Z0$1] |
|
: [NaN, NaN]; |
|
X0$1 = Y0$1 = Z0$1 = |
|
X1$1 = Y1$1 = Z1$1 = |
|
X2$1 = Y2$1 = Z2$1 = 0; |
|
return centroid; |
|
} |
|
}; |
|
|
|
function centroidPoint$1(x, y) { |
|
X0$1 += x; |
|
Y0$1 += y; |
|
++Z0$1; |
|
} |
|
|
|
function centroidLineStart$1() { |
|
centroidStream$1.point = centroidPointFirstLine; |
|
} |
|
|
|
function centroidPointFirstLine(x, y) { |
|
centroidStream$1.point = centroidPointLine; |
|
centroidPoint$1(x0$3 = x, y0$3 = y); |
|
} |
|
|
|
function centroidPointLine(x, y) { |
|
var dx = x - x0$3, dy = y - y0$3, z = sqrt(dx * dx + dy * dy); |
|
X1$1 += z * (x0$3 + x) / 2; |
|
Y1$1 += z * (y0$3 + y) / 2; |
|
Z1$1 += z; |
|
centroidPoint$1(x0$3 = x, y0$3 = y); |
|
} |
|
|
|
function centroidLineEnd$1() { |
|
centroidStream$1.point = centroidPoint$1; |
|
} |
|
|
|
function centroidRingStart$1() { |
|
centroidStream$1.point = centroidPointFirstRing; |
|
} |
|
|
|
function centroidRingEnd$1() { |
|
centroidPointRing(x00$1, y00$1); |
|
} |
|
|
|
function centroidPointFirstRing(x, y) { |
|
centroidStream$1.point = centroidPointRing; |
|
centroidPoint$1(x00$1 = x0$3 = x, y00$1 = y0$3 = y); |
|
} |
|
|
|
function centroidPointRing(x, y) { |
|
var dx = x - x0$3, |
|
dy = y - y0$3, |
|
z = sqrt(dx * dx + dy * dy); |
|
|
|
X1$1 += z * (x0$3 + x) / 2; |
|
Y1$1 += z * (y0$3 + y) / 2; |
|
Z1$1 += z; |
|
|
|
z = y0$3 * x - x0$3 * y; |
|
X2$1 += z * (x0$3 + x); |
|
Y2$1 += z * (y0$3 + y); |
|
Z2$1 += z * 3; |
|
centroidPoint$1(x0$3 = x, y0$3 = y); |
|
} |
|
|
|
function PathContext(context) { |
|
this._context = context; |
|
} |
|
|
|
PathContext.prototype = { |
|
_radius: 4.5, |
|
pointRadius: function(_) { |
|
return this._radius = _, this; |
|
}, |
|
polygonStart: function() { |
|
this._line = 0; |
|
}, |
|
polygonEnd: function() { |
|
this._line = NaN; |
|
}, |
|
lineStart: function() { |
|
this._point = 0; |
|
}, |
|
lineEnd: function() { |
|
if (this._line === 0) this._context.closePath(); |
|
this._point = NaN; |
|
}, |
|
point: function(x, y) { |
|
switch (this._point) { |
|
case 0: { |
|
this._context.moveTo(x, y); |
|
this._point = 1; |
|
break; |
|
} |
|
case 1: { |
|
this._context.lineTo(x, y); |
|
break; |
|
} |
|
default: { |
|
this._context.moveTo(x + this._radius, y); |
|
this._context.arc(x, y, this._radius, 0, tau); |
|
break; |
|
} |
|
} |
|
}, |
|
result: noop |
|
}; |
|
|
|
var lengthSum$1 = adder(), |
|
lengthRing, |
|
x00$2, |
|
y00$2, |
|
x0$4, |
|
y0$4; |
|
|
|
var lengthStream$1 = { |
|
point: noop, |
|
lineStart: function() { |
|
lengthStream$1.point = lengthPointFirst$1; |
|
}, |
|
lineEnd: function() { |
|
if (lengthRing) lengthPoint$1(x00$2, y00$2); |
|
lengthStream$1.point = noop; |
|
}, |
|
polygonStart: function() { |
|
lengthRing = true; |
|
}, |
|
polygonEnd: function() { |
|
lengthRing = null; |
|
}, |
|
result: function() { |
|
var length = +lengthSum$1; |
|
lengthSum$1.reset(); |
|
return length; |
|
} |
|
}; |
|
|
|
function lengthPointFirst$1(x, y) { |
|
lengthStream$1.point = lengthPoint$1; |
|
x00$2 = x0$4 = x, y00$2 = y0$4 = y; |
|
} |
|
|
|
function lengthPoint$1(x, y) { |
|
x0$4 -= x, y0$4 -= y; |
|
lengthSum$1.add(sqrt(x0$4 * x0$4 + y0$4 * y0$4)); |
|
x0$4 = x, y0$4 = y; |
|
} |
|
|
|
function PathString() { |
|
this._string = []; |
|
} |
|
|
|
PathString.prototype = { |
|
_radius: 4.5, |
|
_circle: circle$1(4.5), |
|
pointRadius: function(_) { |
|
if ((_ = +_) !== this._radius) this._radius = _, this._circle = null; |
|
return this; |
|
}, |
|
polygonStart: function() { |
|
this._line = 0; |
|
}, |
|
polygonEnd: function() { |
|
this._line = NaN; |
|
}, |
|
lineStart: function() { |
|
this._point = 0; |
|
}, |
|
lineEnd: function() { |
|
if (this._line === 0) this._string.push("Z"); |
|
this._point = NaN; |
|
}, |
|
point: function(x, y) { |
|
switch (this._point) { |
|
case 0: { |
|
this._string.push("M", x, ",", y); |
|
this._point = 1; |
|
break; |
|
} |
|
case 1: { |
|
this._string.push("L", x, ",", y); |
|
break; |
|
} |
|
default: { |
|
if (this._circle == null) this._circle = circle$1(this._radius); |
|
this._string.push("M", x, ",", y, this._circle); |
|
break; |
|
} |
|
} |
|
}, |
|
result: function() { |
|
if (this._string.length) { |
|
var result = this._string.join(""); |
|
this._string = []; |
|
return result; |
|
} else { |
|
return null; |
|
} |
|
} |
|
}; |
|
|
|
function circle$1(radius) { |
|
return "m0," + radius |
|
+ "a" + radius + "," + radius + " 0 1,1 0," + -2 * radius |
|
+ "a" + radius + "," + radius + " 0 1,1 0," + 2 * radius |
|
+ "z"; |
|
} |
|
|
|
function index(projection, context) { |
|
var pointRadius = 4.5, |
|
projectionStream, |
|
contextStream; |
|
|
|
function path(object) { |
|
if (object) { |
|
if (typeof pointRadius === "function") contextStream.pointRadius(+pointRadius.apply(this, arguments)); |
|
geoStream(object, projectionStream(contextStream)); |
|
} |
|
return contextStream.result(); |
|
} |
|
|
|
path.area = function(object) { |
|
geoStream(object, projectionStream(areaStream$1)); |
|
return areaStream$1.result(); |
|
}; |
|
|
|
path.measure = function(object) { |
|
geoStream(object, projectionStream(lengthStream$1)); |
|
return lengthStream$1.result(); |
|
}; |
|
|
|
path.bounds = function(object) { |
|
geoStream(object, projectionStream(boundsStream$1)); |
|
return boundsStream$1.result(); |
|
}; |
|
|
|
path.centroid = function(object) { |
|
geoStream(object, projectionStream(centroidStream$1)); |
|
return centroidStream$1.result(); |
|
}; |
|
|
|
path.projection = function(_) { |
|
return arguments.length ? (projectionStream = _ == null ? (projection = null, identity) : (projection = _).stream, path) : projection; |
|
}; |
|
|
|
path.context = function(_) { |
|
if (!arguments.length) return context; |
|
contextStream = _ == null ? (context = null, new PathString) : new PathContext(context = _); |
|
if (typeof pointRadius !== "function") contextStream.pointRadius(pointRadius); |
|
return path; |
|
}; |
|
|
|
path.pointRadius = function(_) { |
|
if (!arguments.length) return pointRadius; |
|
pointRadius = typeof _ === "function" ? _ : (contextStream.pointRadius(+_), +_); |
|
return path; |
|
}; |
|
|
|
return path.projection(projection).context(context); |
|
} |
|
|
|
function transform(methods) { |
|
return { |
|
stream: transformer(methods) |
|
}; |
|
} |
|
|
|
function transformer(methods) { |
|
return function(stream) { |
|
var s = new TransformStream; |
|
for (var key in methods) s[key] = methods[key]; |
|
s.stream = stream; |
|
return s; |
|
}; |
|
} |
|
|
|
function TransformStream() {} |
|
|
|
TransformStream.prototype = { |
|
constructor: TransformStream, |
|
point: function(x, y) { this.stream.point(x, y); }, |
|
sphere: function() { this.stream.sphere(); }, |
|
lineStart: function() { this.stream.lineStart(); }, |
|
lineEnd: function() { this.stream.lineEnd(); }, |
|
polygonStart: function() { this.stream.polygonStart(); }, |
|
polygonEnd: function() { this.stream.polygonEnd(); } |
|
}; |
|
|
|
function fit(projection, fitBounds, object) { |
|
var clip = projection.clipExtent && projection.clipExtent(); |
|
projection.scale(150).translate([0, 0]); |
|
if (clip != null) projection.clipExtent(null); |
|
geoStream(object, projection.stream(boundsStream$1)); |
|
fitBounds(boundsStream$1.result()); |
|
if (clip != null) projection.clipExtent(clip); |
|
return projection; |
|
} |
|
|
|
function fitExtent(projection, extent, object) { |
|
return fit(projection, function(b) { |
|
var w = extent[1][0] - extent[0][0], |
|
h = extent[1][1] - extent[0][1], |
|
k = Math.min(w / (b[1][0] - b[0][0]), h / (b[1][1] - b[0][1])), |
|
x = +extent[0][0] + (w - k * (b[1][0] + b[0][0])) / 2, |
|
y = +extent[0][1] + (h - k * (b[1][1] + b[0][1])) / 2; |
|
projection.scale(150 * k).translate([x, y]); |
|
}, object); |
|
} |
|
|
|
function fitSize(projection, size, object) { |
|
return fitExtent(projection, [[0, 0], size], object); |
|
} |
|
|
|
function fitWidth(projection, width, object) { |
|
return fit(projection, function(b) { |
|
var w = +width, |
|
k = w / (b[1][0] - b[0][0]), |
|
x = (w - k * (b[1][0] + b[0][0])) / 2, |
|
y = -k * b[0][1]; |
|
projection.scale(150 * k).translate([x, y]); |
|
}, object); |
|
} |
|
|
|
function fitHeight(projection, height, object) { |
|
return fit(projection, function(b) { |
|
var h = +height, |
|
k = h / (b[1][1] - b[0][1]), |
|
x = -k * b[0][0], |
|
y = (h - k * (b[1][1] + b[0][1])) / 2; |
|
projection.scale(150 * k).translate([x, y]); |
|
}, object); |
|
} |
|
|
|
var maxDepth = 16, // maximum depth of subdivision |
|
cosMinDistance = cos(30 * radians); // cos(minimum angular distance) |
|
|
|
function resample(project, delta2) { |
|
return +delta2 ? resample$1(project, delta2) : resampleNone(project); |
|
} |
|
|
|
function resampleNone(project) { |
|
return transformer({ |
|
point: function(x, y) { |
|
x = project(x, y); |
|
this.stream.point(x[0], x[1]); |
|
} |
|
}); |
|
} |
|
|
|
function resample$1(project, delta2) { |
|
|
|
function resampleLineTo(x0, y0, lambda0, a0, b0, c0, x1, y1, lambda1, a1, b1, c1, depth, stream) { |
|
var dx = x1 - x0, |
|
dy = y1 - y0, |
|
d2 = dx * dx + dy * dy; |
|
if (d2 > 4 * delta2 && depth--) { |
|
var a = a0 + a1, |
|
b = b0 + b1, |
|
c = c0 + c1, |
|
m = sqrt(a * a + b * b + c * c), |
|
phi2 = asin(c /= m), |
|
lambda2 = abs(abs(c) - 1) < epsilon || abs(lambda0 - lambda1) < epsilon ? (lambda0 + lambda1) / 2 : atan2(b, a), |
|
p = project(lambda2, phi2), |
|
x2 = p[0], |
|
y2 = p[1], |
|
dx2 = x2 - x0, |
|
dy2 = y2 - y0, |
|
dz = dy * dx2 - dx * dy2; |
|
if (dz * dz / d2 > delta2 // perpendicular projected distance |
|
|| abs((dx * dx2 + dy * dy2) / d2 - 0.5) > 0.3 // midpoint close to an end |
|
|| a0 * a1 + b0 * b1 + c0 * c1 < cosMinDistance) { // angular distance |
|
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x2, y2, lambda2, a /= m, b /= m, c, depth, stream); |
|
stream.point(x2, y2); |
|
resampleLineTo(x2, y2, lambda2, a, b, c, x1, y1, lambda1, a1, b1, c1, depth, stream); |
|
} |
|
} |
|
} |
|
return function(stream) { |
|
var lambda00, x00, y00, a00, b00, c00, // first point |
|
lambda0, x0, y0, a0, b0, c0; // previous point |
|
|
|
var resampleStream = { |
|
point: point, |
|
lineStart: lineStart, |
|
lineEnd: lineEnd, |
|
polygonStart: function() { stream.polygonStart(); resampleStream.lineStart = ringStart; }, |
|
polygonEnd: function() { stream.polygonEnd(); resampleStream.lineStart = lineStart; } |
|
}; |
|
|
|
function point(x, y) { |
|
x = project(x, y); |
|
stream.point(x[0], x[1]); |
|
} |
|
|
|
function lineStart() { |
|
x0 = NaN; |
|
resampleStream.point = linePoint; |
|
stream.lineStart(); |
|
} |
|
|
|
function linePoint(lambda, phi) { |
|
var c = cartesian([lambda, phi]), p = project(lambda, phi); |
|
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x0 = p[0], y0 = p[1], lambda0 = lambda, a0 = c[0], b0 = c[1], c0 = c[2], maxDepth, stream); |
|
stream.point(x0, y0); |
|
} |
|
|
|
function lineEnd() { |
|
resampleStream.point = point; |
|
stream.lineEnd(); |
|
} |
|
|
|
function ringStart() { |
|
lineStart(); |
|
resampleStream.point = ringPoint; |
|
resampleStream.lineEnd = ringEnd; |
|
} |
|
|
|
function ringPoint(lambda, phi) { |
|
linePoint(lambda00 = lambda, phi), x00 = x0, y00 = y0, a00 = a0, b00 = b0, c00 = c0; |
|
resampleStream.point = linePoint; |
|
} |
|
|
|
function ringEnd() { |
|
resampleLineTo(x0, y0, lambda0, a0, b0, c0, x00, y00, lambda00, a00, b00, c00, maxDepth, stream); |
|
resampleStream.lineEnd = lineEnd; |
|
lineEnd(); |
|
} |
|
|
|
return resampleStream; |
|
}; |
|
} |
|
|
|
var transformRadians = transformer({ |
|
point: function(x, y) { |
|
this.stream.point(x * radians, y * radians); |
|
} |
|
}); |
|
|
|
function transformRotate(rotate) { |
|
return transformer({ |
|
point: function(x, y) { |
|
var r = rotate(x, y); |
|
return this.stream.point(r[0], r[1]); |
|
} |
|
}); |
|
} |
|
|
|
function scaleTranslate(k, dx, dy) { |
|
function transform$$1(x, y) { |
|
return [dx + k * x, dy - k * y]; |
|
} |
|
transform$$1.invert = function(x, y) { |
|
return [(x - dx) / k, (dy - y) / k]; |
|
}; |
|
return transform$$1; |
|
} |
|
|
|
function scaleTranslateRotate(k, dx, dy, alpha) { |
|
var cosAlpha = cos(alpha), |
|
sinAlpha = sin(alpha), |
|
a = cosAlpha * k, |
|
b = sinAlpha * k, |
|
ai = cosAlpha / k, |
|
bi = sinAlpha / k, |
|
ci = (sinAlpha * dy - cosAlpha * dx) / k, |
|
fi = (sinAlpha * dx + cosAlpha * dy) / k; |
|
function transform$$1(x, y) { |
|
return [a * x - b * y + dx, dy - b * x - a * y]; |
|
} |
|
transform$$1.invert = function(x, y) { |
|
return [ai * x - bi * y + ci, fi - bi * x - ai * y]; |
|
}; |
|
return transform$$1; |
|
} |
|
|
|
function projection(project) { |
|
return projectionMutator(function() { return project; })(); |
|
} |
|
|
|
function projectionMutator(projectAt) { |
|
var project, |
|
k = 150, // scale |
|
x = 480, y = 250, // translate |
|
lambda = 0, phi = 0, // center |
|
deltaLambda = 0, deltaPhi = 0, deltaGamma = 0, rotate, // pre-rotate |
|
alpha = 0, // post-rotate |
|
theta = null, preclip = clipAntimeridian, // pre-clip angle |
|
x0 = null, y0, x1, y1, postclip = identity, // post-clip extent |
|
delta2 = 0.5, // precision |
|
projectResample, |
|
projectTransform, |
|
projectRotateTransform, |
|
cache, |
|
cacheStream; |
|
|
|
function projection(point) { |
|
return projectRotateTransform(point[0] * radians, point[1] * radians); |
|
} |
|
|
|
function invert(point) { |
|
point = projectRotateTransform.invert(point[0], point[1]); |
|
return point && [point[0] * degrees, point[1] * degrees]; |
|
} |
|
|
|
projection.stream = function(stream) { |
|
return cache && cacheStream === stream ? cache : cache = transformRadians(transformRotate(rotate)(preclip(projectResample(postclip(cacheStream = stream))))); |
|
}; |
|
|
|
projection.preclip = function(_) { |
|
return arguments.length ? (preclip = _, theta = undefined, reset()) : preclip; |
|
}; |
|
|
|
projection.postclip = function(_) { |
|
return arguments.length ? (postclip = _, x0 = y0 = x1 = y1 = null, reset()) : postclip; |
|
}; |
|
|
|
projection.clipAngle = function(_) { |
|
return arguments.length ? (preclip = +_ ? clipCircle(theta = _ * radians) : (theta = null, clipAntimeridian), reset()) : theta * degrees; |
|
}; |
|
|
|
projection.clipExtent = function(_) { |
|
return arguments.length ? (postclip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipRectangle(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]]; |
|
}; |
|
|
|
projection.scale = function(_) { |
|
return arguments.length ? (k = +_, recenter()) : k; |
|
}; |
|
|
|
projection.translate = function(_) { |
|
return arguments.length ? (x = +_[0], y = +_[1], recenter()) : [x, y]; |
|
}; |
|
|
|
projection.center = function(_) { |
|
return arguments.length ? (lambda = _[0] % 360 * radians, phi = _[1] % 360 * radians, recenter()) : [lambda * degrees, phi * degrees]; |
|
}; |
|
|
|
projection.rotate = function(_) { |
|
return arguments.length ? (deltaLambda = _[0] % 360 * radians, deltaPhi = _[1] % 360 * radians, deltaGamma = _.length > 2 ? _[2] % 360 * radians : 0, recenter()) : [deltaLambda * degrees, deltaPhi * degrees, deltaGamma * degrees]; |
|
}; |
|
|
|
projection.angle = function(_) { |
|
return arguments.length ? (alpha = _ % 360 * radians, recenter()) : alpha * degrees; |
|
}; |
|
|
|
projection.precision = function(_) { |
|
return arguments.length ? (projectResample = resample(projectTransform, delta2 = _ * _), reset()) : sqrt(delta2); |
|
}; |
|
|
|
projection.fitExtent = function(extent, object) { |
|
return fitExtent(projection, extent, object); |
|
}; |
|
|
|
projection.fitSize = function(size, object) { |
|
return fitSize(projection, size, object); |
|
}; |
|
|
|
projection.fitWidth = function(width, object) { |
|
return fitWidth(projection, width, object); |
|
}; |
|
|
|
projection.fitHeight = function(height, object) { |
|
return fitHeight(projection, height, object); |
|
}; |
|
|
|
function recenter() { |
|
var center = scaleTranslateRotate(k, 0, 0, alpha).apply(null, project(lambda, phi)), |
|
transform$$1 = (alpha ? scaleTranslateRotate : scaleTranslate)(k, x - center[0], y - center[1], alpha); |
|
rotate = rotateRadians(deltaLambda, deltaPhi, deltaGamma); |
|
projectTransform = compose(project, transform$$1); |
|
projectRotateTransform = compose(rotate, projectTransform); |
|
projectResample = resample(projectTransform, delta2); |
|
return reset(); |
|
} |
|
|
|
function reset() { |
|
cache = cacheStream = null; |
|
return projection; |
|
} |
|
|
|
return function() { |
|
project = projectAt.apply(this, arguments); |
|
projection.invert = project.invert && invert; |
|
return recenter(); |
|
}; |
|
} |
|
|
|
function conicProjection(projectAt) { |
|
var phi0 = 0, |
|
phi1 = pi / 3, |
|
m = projectionMutator(projectAt), |
|
p = m(phi0, phi1); |
|
|
|
p.parallels = function(_) { |
|
return arguments.length ? m(phi0 = _[0] * radians, phi1 = _[1] * radians) : [phi0 * degrees, phi1 * degrees]; |
|
}; |
|
|
|
return p; |
|
} |
|
|
|
function cylindricalEqualAreaRaw(phi0) { |
|
var cosPhi0 = cos(phi0); |
|
|
|
function forward(lambda, phi) { |
|
return [lambda * cosPhi0, sin(phi) / cosPhi0]; |
|
} |
|
|
|
forward.invert = function(x, y) { |
|
return [x / cosPhi0, asin(y * cosPhi0)]; |
|
}; |
|
|
|
return forward; |
|
} |
|
|
|
function conicEqualAreaRaw(y0, y1) { |
|
var sy0 = sin(y0), n = (sy0 + sin(y1)) / 2; |
|
|
|
// Are the parallels symmetrical around the Equator? |
|
if (abs(n) < epsilon) return cylindricalEqualAreaRaw(y0); |
|
|
|
var c = 1 + sy0 * (2 * n - sy0), r0 = sqrt(c) / n; |
|
|
|
function project(x, y) { |
|
var r = sqrt(c - 2 * n * sin(y)) / n; |
|
return [r * sin(x *= n), r0 - r * cos(x)]; |
|
} |
|
|
|
project.invert = function(x, y) { |
|
var r0y = r0 - y; |
|
return [atan2(x, abs(r0y)) / n * sign(r0y), asin((c - (x * x + r0y * r0y) * n * n) / (2 * n))]; |
|
}; |
|
|
|
return project; |
|
} |
|
|
|
function conicEqualArea() { |
|
return conicProjection(conicEqualAreaRaw) |
|
.scale(155.424) |
|
.center([0, 33.6442]); |
|
} |
|
|
|
function albers() { |
|
return conicEqualArea() |
|
.parallels([29.5, 45.5]) |
|
.scale(1070) |
|
.translate([480, 250]) |
|
.rotate([96, 0]) |
|
.center([-0.6, 38.7]); |
|
} |
|
|
|
// The projections must have mutually exclusive clip regions on the sphere, |
|
// as this will avoid emitting interleaving lines and polygons. |
|
function multiplex(streams) { |
|
var n = streams.length; |
|
return { |
|
point: function(x, y) { var i = -1; while (++i < n) streams[i].point(x, y); }, |
|
sphere: function() { var i = -1; while (++i < n) streams[i].sphere(); }, |
|
lineStart: function() { var i = -1; while (++i < n) streams[i].lineStart(); }, |
|
lineEnd: function() { var i = -1; while (++i < n) streams[i].lineEnd(); }, |
|
polygonStart: function() { var i = -1; while (++i < n) streams[i].polygonStart(); }, |
|
polygonEnd: function() { var i = -1; while (++i < n) streams[i].polygonEnd(); } |
|
}; |
|
} |
|
|
|
// A composite projection for the United States, configured by default for |
|
// 960×500. The projection also works quite well at 960×600 if you change the |
|
// scale to 1285 and adjust the translate accordingly. The set of standard |
|
// parallels for each region comes from USGS, which is published here: |
|
// http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers |
|
function albersUsa() { |
|
var cache, |
|
cacheStream, |
|
lower48 = albers(), lower48Point, |
|
alaska = conicEqualArea().rotate([154, 0]).center([-2, 58.5]).parallels([55, 65]), alaskaPoint, // EPSG:3338 |
|
hawaii = conicEqualArea().rotate([157, 0]).center([-3, 19.9]).parallels([8, 18]), hawaiiPoint, // ESRI:102007 |
|
point, pointStream = {point: function(x, y) { point = [x, y]; }}; |
|
|
|
function albersUsa(coordinates) { |
|
var x = coordinates[0], y = coordinates[1]; |
|
return point = null, |
|
(lower48Point.point(x, y), point) |
|
|| (alaskaPoint.point(x, y), point) |
|
|| (hawaiiPoint.point(x, y), point); |
|
} |
|
|
|
albersUsa.invert = function(coordinates) { |
|
var k = lower48.scale(), |
|
t = lower48.translate(), |
|
x = (coordinates[0] - t[0]) / k, |
|
y = (coordinates[1] - t[1]) / k; |
|
return (y >= 0.120 && y < 0.234 && x >= -0.425 && x < -0.214 ? alaska |
|
: y >= 0.166 && y < 0.234 && x >= -0.214 && x < -0.115 ? hawaii |
|
: lower48).invert(coordinates); |
|
}; |
|
|
|
albersUsa.stream = function(stream) { |
|
return cache && cacheStream === stream ? cache : cache = multiplex([lower48.stream(cacheStream = stream), alaska.stream(stream), hawaii.stream(stream)]); |
|
}; |
|
|
|
albersUsa.precision = function(_) { |
|
if (!arguments.length) return lower48.precision(); |
|
lower48.precision(_), alaska.precision(_), hawaii.precision(_); |
|
return reset(); |
|
}; |
|
|
|
albersUsa.scale = function(_) { |
|
if (!arguments.length) return lower48.scale(); |
|
lower48.scale(_), alaska.scale(_ * 0.35), hawaii.scale(_); |
|
return albersUsa.translate(lower48.translate()); |
|
}; |
|
|
|
albersUsa.translate = function(_) { |
|
if (!arguments.length) return lower48.translate(); |
|
var k = lower48.scale(), x = +_[0], y = +_[1]; |
|
|
|
lower48Point = lower48 |
|
.translate(_) |
|
.clipExtent([[x - 0.455 * k, y - 0.238 * k], [x + 0.455 * k, y + 0.238 * k]]) |
|
.stream(pointStream); |
|
|
|
alaskaPoint = alaska |
|
.translate([x - 0.307 * k, y + 0.201 * k]) |
|
.clipExtent([[x - 0.425 * k + epsilon, y + 0.120 * k + epsilon], [x - 0.214 * k - epsilon, y + 0.234 * k - epsilon]]) |
|
.stream(pointStream); |
|
|
|
hawaiiPoint = hawaii |
|
.translate([x - 0.205 * k, y + 0.212 * k]) |
|
.clipExtent([[x - 0.214 * k + epsilon, y + 0.166 * k + epsilon], [x - 0.115 * k - epsilon, y + 0.234 * k - epsilon]]) |
|
.stream(pointStream); |
|
|
|
return reset(); |
|
}; |
|
|
|
albersUsa.fitExtent = function(extent, object) { |
|
return fitExtent(albersUsa, extent, object); |
|
}; |
|
|
|
albersUsa.fitSize = function(size, object) { |
|
return fitSize(albersUsa, size, object); |
|
}; |
|
|
|
albersUsa.fitWidth = function(width, object) { |
|
return fitWidth(albersUsa, width, object); |
|
}; |
|
|
|
albersUsa.fitHeight = function(height, object) { |
|
return fitHeight(albersUsa, height, object); |
|
}; |
|
|
|
function reset() { |
|
cache = cacheStream = null; |
|
return albersUsa; |
|
} |
|
|
|
return albersUsa.scale(1070); |
|
} |
|
|
|
function azimuthalRaw(scale) { |
|
return function(x, y) { |
|
var cx = cos(x), |
|
cy = cos(y), |
|
k = scale(cx * cy); |
|
return [ |
|
k * cy * sin(x), |
|
k * sin(y) |
|
]; |
|
} |
|
} |
|
|
|
function azimuthalInvert(angle) { |
|
return function(x, y) { |
|
var z = sqrt(x * x + y * y), |
|
c = angle(z), |
|
sc = sin(c), |
|
cc = cos(c); |
|
return [ |
|
atan2(x * sc, z * cc), |
|
asin(z && y * sc / z) |
|
]; |
|
} |
|
} |
|
|
|
var azimuthalEqualAreaRaw = azimuthalRaw(function(cxcy) { |
|
return sqrt(2 / (1 + cxcy)); |
|
}); |
|
|
|
azimuthalEqualAreaRaw.invert = azimuthalInvert(function(z) { |
|
return 2 * asin(z / 2); |
|
}); |
|
|
|
function azimuthalEqualArea() { |
|
return projection(azimuthalEqualAreaRaw) |
|
.scale(124.75) |
|
.clipAngle(180 - 1e-3); |
|
} |
|
|
|
var azimuthalEquidistantRaw = azimuthalRaw(function(c) { |
|
return (c = acos(c)) && c / sin(c); |
|
}); |
|
|
|
azimuthalEquidistantRaw.invert = azimuthalInvert(function(z) { |
|
return z; |
|
}); |
|
|
|
function azimuthalEquidistant() { |
|
return projection(azimuthalEquidistantRaw) |
|
.scale(79.4188) |
|
.clipAngle(180 - 1e-3); |
|
} |
|
|
|
function mercatorRaw(lambda, phi) { |
|
return [lambda, log(tan((halfPi + phi) / 2))]; |
|
} |
|
|
|
mercatorRaw.invert = function(x, y) { |
|
return [x, 2 * atan(exp(y)) - halfPi]; |
|
}; |
|
|
|
function mercator() { |
|
return mercatorProjection(mercatorRaw) |
|
.scale(961 / tau); |
|
} |
|
|
|
function mercatorProjection(project) { |
|
var m = projection(project), |
|
center = m.center, |
|
scale = m.scale, |
|
translate = m.translate, |
|
clipExtent = m.clipExtent, |
|
x0 = null, y0, x1, y1; // clip extent |
|
|
|
m.scale = function(_) { |
|
return arguments.length ? (scale(_), reclip()) : scale(); |
|
}; |
|
|
|
m.translate = function(_) { |
|
return arguments.length ? (translate(_), reclip()) : translate(); |
|
}; |
|
|
|
m.center = function(_) { |
|
return arguments.length ? (center(_), reclip()) : center(); |
|
}; |
|
|
|
m.clipExtent = function(_) { |
|
return arguments.length ? ((_ == null ? x0 = y0 = x1 = y1 = null : (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1])), reclip()) : x0 == null ? null : [[x0, y0], [x1, y1]]; |
|
}; |
|
|
|
function reclip() { |
|
var k = pi * scale(), |
|
t = m(rotation(m.rotate()).invert([0, 0])); |
|
return clipExtent(x0 == null |
|
? [[t[0] - k, t[1] - k], [t[0] + k, t[1] + k]] : project === mercatorRaw |
|
? [[Math.max(t[0] - k, x0), y0], [Math.min(t[0] + k, x1), y1]] |
|
: [[x0, Math.max(t[1] - k, y0)], [x1, Math.min(t[1] + k, y1)]]); |
|
} |
|
|
|
return reclip(); |
|
} |
|
|
|
function tany(y) { |
|
return tan((halfPi + y) / 2); |
|
} |
|
|
|
function conicConformalRaw(y0, y1) { |
|
var cy0 = cos(y0), |
|
n = y0 === y1 ? sin(y0) : log(cy0 / cos(y1)) / log(tany(y1) / tany(y0)), |
|
f = cy0 * pow(tany(y0), n) / n; |
|
|
|
if (!n) return mercatorRaw; |
|
|
|
function project(x, y) { |
|
if (f > 0) { if (y < -halfPi + epsilon) y = -halfPi + epsilon; } |
|
else { if (y > halfPi - epsilon) y = halfPi - epsilon; } |
|
var r = f / pow(tany(y), n); |
|
return [r * sin(n * x), f - r * cos(n * x)]; |
|
} |
|
|
|
project.invert = function(x, y) { |
|
var fy = f - y, r = sign(n) * sqrt(x * x + fy * fy); |
|
return [atan2(x, abs(fy)) / n * sign(fy), 2 * atan(pow(f / r, 1 / n)) - halfPi]; |
|
}; |
|
|
|
return project; |
|
} |
|
|
|
function conicConformal() { |
|
return conicProjection(conicConformalRaw) |
|
.scale(109.5) |
|
.parallels([30, 30]); |
|
} |
|
|
|
function equirectangularRaw(lambda, phi) { |
|
return [lambda, phi]; |
|
} |
|
|
|
equirectangularRaw.invert = equirectangularRaw; |
|
|
|
function equirectangular() { |
|
return projection(equirectangularRaw) |
|
.scale(152.63); |
|
} |
|
|
|
function conicEquidistantRaw(y0, y1) { |
|
var cy0 = cos(y0), |
|
n = y0 === y1 ? sin(y0) : (cy0 - cos(y1)) / (y1 - y0), |
|
g = cy0 / n + y0; |
|
|
|
if (abs(n) < epsilon) return equirectangularRaw; |
|
|
|
function project(x, y) { |
|
var gy = g - y, nx = n * x; |
|
return [gy * sin(nx), g - gy * cos(nx)]; |
|
} |
|
|
|
project.invert = function(x, y) { |
|
var gy = g - y; |
|
return [atan2(x, abs(gy)) / n * sign(gy), g - sign(n) * sqrt(x * x + gy * gy)]; |
|
}; |
|
|
|
return project; |
|
} |
|
|
|
function conicEquidistant() { |
|
return conicProjection(conicEquidistantRaw) |
|
.scale(131.154) |
|
.center([0, 13.9389]); |
|
} |
|
|
|
var A1 = 1.340264, |
|
A2 = -0.081106, |
|
A3 = 0.000893, |
|
A4 = 0.003796, |
|
M = sqrt(3) / 2, |
|
iterations = 12; |
|
|
|
function equalEarthRaw(lambda, phi) { |
|
var l = asin(M * sin(phi)), l2 = l * l, l6 = l2 * l2 * l2; |
|
return [ |
|
lambda * cos(l) / (M * (A1 + 3 * A2 * l2 + l6 * (7 * A3 + 9 * A4 * l2))), |
|
l * (A1 + A2 * l2 + l6 * (A3 + A4 * l2)) |
|
]; |
|
} |
|
|
|
equalEarthRaw.invert = function(x, y) { |
|
var l = y, l2 = l * l, l6 = l2 * l2 * l2; |
|
for (var i = 0, delta, fy, fpy; i < iterations; ++i) { |
|
fy = l * (A1 + A2 * l2 + l6 * (A3 + A4 * l2)) - y; |
|
fpy = A1 + 3 * A2 * l2 + l6 * (7 * A3 + 9 * A4 * l2); |
|
l -= delta = fy / fpy, l2 = l * l, l6 = l2 * l2 * l2; |
|
if (abs(delta) < epsilon2) break; |
|
} |
|
return [ |
|
M * x * (A1 + 3 * A2 * l2 + l6 * (7 * A3 + 9 * A4 * l2)) / cos(l), |
|
asin(sin(l) / M) |
|
]; |
|
}; |
|
|
|
function equalEarth() { |
|
return projection(equalEarthRaw) |
|
.scale(177.158); |
|
} |
|
|
|
function gnomonicRaw(x, y) { |
|
var cy = cos(y), k = cos(x) * cy; |
|
return [cy * sin(x) / k, sin(y) / k]; |
|
} |
|
|
|
gnomonicRaw.invert = azimuthalInvert(atan); |
|
|
|
function gnomonic() { |
|
return projection(gnomonicRaw) |
|
.scale(144.049) |
|
.clipAngle(60); |
|
} |
|
|
|
function scaleTranslate$1(kx, ky, tx, ty) { |
|
return kx === 1 && ky === 1 && tx === 0 && ty === 0 ? identity : transformer({ |
|
point: function(x, y) { |
|
this.stream.point(x * kx + tx, y * ky + ty); |
|
} |
|
}); |
|
} |
|
|
|
function identity$1() { |
|
var k = 1, tx = 0, ty = 0, sx = 1, sy = 1, transform$$1 = identity, // scale, translate and reflect |
|
x0 = null, y0, x1, y1, // clip extent |
|
postclip = identity, |
|
cache, |
|
cacheStream, |
|
projection; |
|
|
|
function reset() { |
|
cache = cacheStream = null; |
|
return projection; |
|
} |
|
|
|
return projection = { |
|
stream: function(stream) { |
|
return cache && cacheStream === stream ? cache : cache = transform$$1(postclip(cacheStream = stream)); |
|
}, |
|
postclip: function(_) { |
|
return arguments.length ? (postclip = _, x0 = y0 = x1 = y1 = null, reset()) : postclip; |
|
}, |
|
clipExtent: function(_) { |
|
return arguments.length ? (postclip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipRectangle(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]]; |
|
}, |
|
scale: function(_) { |
|
return arguments.length ? (transform$$1 = scaleTranslate$1((k = +_) * sx, k * sy, tx, ty), reset()) : k; |
|
}, |
|
translate: function(_) { |
|
return arguments.length ? (transform$$1 = scaleTranslate$1(k * sx, k * sy, tx = +_[0], ty = +_[1]), reset()) : [tx, ty]; |
|
}, |
|
reflectX: function(_) { |
|
return arguments.length ? (transform$$1 = scaleTranslate$1(k * (sx = _ ? -1 : 1), k * sy, tx, ty), reset()) : sx < 0; |
|
}, |
|
reflectY: function(_) { |
|
return arguments.length ? (transform$$1 = scaleTranslate$1(k * sx, k * (sy = _ ? -1 : 1), tx, ty), reset()) : sy < 0; |
|
}, |
|
fitExtent: function(extent, object) { |
|
return fitExtent(projection, extent, object); |
|
}, |
|
fitSize: function(size, object) { |
|
return fitSize(projection, size, object); |
|
}, |
|
fitWidth: function(width, object) { |
|
return fitWidth(projection, width, object); |
|
}, |
|
fitHeight: function(height, object) { |
|
return fitHeight(projection, height, object); |
|
} |
|
}; |
|
} |
|
|
|
function naturalEarth1Raw(lambda, phi) { |
|
var phi2 = phi * phi, phi4 = phi2 * phi2; |
|
return [ |
|
lambda * (0.8707 - 0.131979 * phi2 + phi4 * (-0.013791 + phi4 * (0.003971 * phi2 - 0.001529 * phi4))), |
|
phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) |
|
]; |
|
} |
|
|
|
naturalEarth1Raw.invert = function(x, y) { |
|
var phi = y, i = 25, delta; |
|
do { |
|
var phi2 = phi * phi, phi4 = phi2 * phi2; |
|
phi -= delta = (phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) - y) / |
|
(1.007226 + phi2 * (0.015085 * 3 + phi4 * (-0.044475 * 7 + 0.028874 * 9 * phi2 - 0.005916 * 11 * phi4))); |
|
} while (abs(delta) > epsilon && --i > 0); |
|
return [ |
|
x / (0.8707 + (phi2 = phi * phi) * (-0.131979 + phi2 * (-0.013791 + phi2 * phi2 * phi2 * (0.003971 - 0.001529 * phi2)))), |
|
phi |
|
]; |
|
}; |
|
|
|
function naturalEarth1() { |
|
return projection(naturalEarth1Raw) |
|
.scale(175.295); |
|
} |
|
|
|
function orthographicRaw(x, y) { |
|
return [cos(y) * sin(x), sin(y)]; |
|
} |
|
|
|
orthographicRaw.invert = azimuthalInvert(asin); |
|
|
|
function orthographic() { |
|
return projection(orthographicRaw) |
|
.scale(249.5) |
|
.clipAngle(90 + epsilon); |
|
} |
|
|
|
function stereographicRaw(x, y) { |
|
var cy = cos(y), k = 1 + cos(x) * cy; |
|
return [cy * sin(x) / k, sin(y) / k]; |
|
} |
|
|
|
stereographicRaw.invert = azimuthalInvert(function(z) { |
|
return 2 * atan(z); |
|
}); |
|
|
|
function stereographic() { |
|
return projection(stereographicRaw) |
|
.scale(250) |
|
.clipAngle(142); |
|
} |
|
|
|
function transverseMercatorRaw(lambda, phi) { |
|
return [log(tan((halfPi + phi) / 2)), -lambda]; |
|
} |
|
|
|
transverseMercatorRaw.invert = function(x, y) { |
|
return [-y, 2 * atan(exp(x)) - halfPi]; |
|
}; |
|
|
|
function transverseMercator() { |
|
var m = mercatorProjection(transverseMercatorRaw), |
|
center = m.center, |
|
rotate = m.rotate; |
|
|
|
m.center = function(_) { |
|
return arguments.length ? center([-_[1], _[0]]) : (_ = center(), [_[1], -_[0]]); |
|
}; |
|
|
|
m.rotate = function(_) { |
|
return arguments.length ? rotate([_[0], _[1], _.length > 2 ? _[2] + 90 : 90]) : (_ = rotate(), [_[0], _[1], _[2] - 90]); |
|
}; |
|
|
|
return rotate([0, 0, 90]) |
|
.scale(159.155); |
|
} |
|
|
|
exports.geoArea = area; |
|
exports.geoBounds = bounds; |
|
exports.geoCentroid = centroid; |
|
exports.geoCircle = circle; |
|
exports.geoClipAntimeridian = clipAntimeridian; |
|
exports.geoClipCircle = clipCircle; |
|
exports.geoClipExtent = extent; |
|
exports.geoClipRectangle = clipRectangle; |
|
exports.geoContains = contains; |
|
exports.geoDistance = distance; |
|
exports.geoGraticule = graticule; |
|
exports.geoGraticule10 = graticule10; |
|
exports.geoInterpolate = interpolate; |
|
exports.geoLength = length; |
|
exports.geoPath = index; |
|
exports.geoAlbers = albers; |
|
exports.geoAlbersUsa = albersUsa; |
|
exports.geoAzimuthalEqualArea = azimuthalEqualArea; |
|
exports.geoAzimuthalEqualAreaRaw = azimuthalEqualAreaRaw; |
|
exports.geoAzimuthalEquidistant = azimuthalEquidistant; |
|
exports.geoAzimuthalEquidistantRaw = azimuthalEquidistantRaw; |
|
exports.geoConicConformal = conicConformal; |
|
exports.geoConicConformalRaw = conicConformalRaw; |
|
exports.geoConicEqualArea = conicEqualArea; |
|
exports.geoConicEqualAreaRaw = conicEqualAreaRaw; |
|
exports.geoConicEquidistant = conicEquidistant; |
|
exports.geoConicEquidistantRaw = conicEquidistantRaw; |
|
exports.geoEqualEarth = equalEarth; |
|
exports.geoEqualEarthRaw = equalEarthRaw; |
|
exports.geoEquirectangular = equirectangular; |
|
exports.geoEquirectangularRaw = equirectangularRaw; |
|
exports.geoGnomonic = gnomonic; |
|
exports.geoGnomonicRaw = gnomonicRaw; |
|
exports.geoIdentity = identity$1; |
|
exports.geoProjection = projection; |
|
exports.geoProjectionMutator = projectionMutator; |
|
exports.geoMercator = mercator; |
|
exports.geoMercatorRaw = mercatorRaw; |
|
exports.geoNaturalEarth1 = naturalEarth1; |
|
exports.geoNaturalEarth1Raw = naturalEarth1Raw; |
|
exports.geoOrthographic = orthographic; |
|
exports.geoOrthographicRaw = orthographicRaw; |
|
exports.geoStereographic = stereographic; |
|
exports.geoStereographicRaw = stereographicRaw; |
|
exports.geoTransverseMercator = transverseMercator; |
|
exports.geoTransverseMercatorRaw = transverseMercatorRaw; |
|
exports.geoRotation = rotation; |
|
exports.geoStream = geoStream; |
|
exports.geoTransform = transform; |
|
|
|
Object.defineProperty(exports, '__esModule', { value: true }); |
|
|
|
})));
|
|
|