cheap-ruler
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A collection of fast approximations to common geographic measurements.
489 lines (429 loc) • 16.5 kB
JavaScript
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
typeof define === 'function' && define.amd ? define(factory) :
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.CheapRuler = factory());
})(this, (function () { 'use strict';
const factors = {
kilometers: 1,
miles: 1000 / 1609.344,
nauticalmiles: 1000 / 1852,
meters: 1000,
metres: 1000,
yards: 1000 / 0.9144,
feet: 1000 / 0.3048,
inches: 1000 / 0.0254
};
// Values that define WGS84 ellipsoid model of the Earth
const RE = 6378.137; // equatorial radius
const FE = 1 / 298.257223563; // flattening
const E2 = FE * (2 - FE);
const RAD = Math.PI / 180;
/**
* A collection of very fast approximations to common geodesic measurements. Useful for performance-sensitive code that measures things on a city scale.
*/
class CheapRuler {
/**
* Creates a ruler object from tile coordinates (y and z).
*
* @param {number} y
* @param {number} z
* @param {keyof typeof factors} [units='kilometers']
* @returns {CheapRuler}
* @example
* const ruler = cheapRuler.fromTile(1567, 12);
* //=ruler
*/
static fromTile(y, z, units) {
const n = Math.PI * (1 - 2 * (y + 0.5) / Math.pow(2, z));
const lat = Math.atan(0.5 * (Math.exp(n) - Math.exp(-n))) / RAD;
return new CheapRuler(lat, units);
}
/**
* Multipliers for converting between units.
*
* @example
* // convert 50 meters to yards
* 50 * CheapRuler.units.yards / CheapRuler.units.meters;
*/
static get units() {
return factors;
}
/**
* Creates a ruler instance for very fast approximations to common geodesic measurements around a certain latitude.
*
* @param {number} lat latitude
* @param {keyof typeof factors} [units='kilometers']
* @example
* const ruler = cheapRuler(35.05, 'miles');
* //=ruler
*/
constructor(lat, units) {
if (lat === undefined) throw new Error('No latitude given.');
if (units && !factors[units]) throw new Error(`Unknown unit ${ units }. Use one of: ${ Object.keys(factors).join(', ')}`);
// Curvature formulas from https://en.wikipedia.org/wiki/Earth_radius#Meridional
const m = RAD * RE * (units ? factors[units] : 1);
const coslat = Math.cos(lat * RAD);
const w2 = 1 / (1 - E2 * (1 - coslat * coslat));
const w = Math.sqrt(w2);
// multipliers for converting longitude and latitude degrees into distance
this.kx = m * w * coslat; // based on normal radius of curvature
this.ky = m * w * w2 * (1 - E2); // based on meridonal radius of curvature
}
/**
* Given two points of the form [longitude, latitude], returns the distance.
*
* @param {[number, number]} a point [longitude, latitude]
* @param {[number, number]} b point [longitude, latitude]
* @returns {number} distance
* @example
* const distance = ruler.distance([30.5, 50.5], [30.51, 50.49]);
* //=distance
*/
distance(a, b) {
const dx = wrap(a[0] - b[0]) * this.kx;
const dy = (a[1] - b[1]) * this.ky;
return Math.sqrt(dx * dx + dy * dy);
}
/**
* Returns the bearing between two points in angles.
*
* @param {[number, number]} a point [longitude, latitude]
* @param {[number, number]} b point [longitude, latitude]
* @returns {number} bearing
* @example
* const bearing = ruler.bearing([30.5, 50.5], [30.51, 50.49]);
* //=bearing
*/
bearing(a, b) {
const dx = wrap(b[0] - a[0]) * this.kx;
const dy = (b[1] - a[1]) * this.ky;
return Math.atan2(dx, dy) / RAD;
}
/**
* Returns a new point given distance and bearing from the starting point.
*
* @param {[number, number]} p point [longitude, latitude]
* @param {number} dist distance
* @param {number} bearing
* @returns {[number, number]} point [longitude, latitude]
* @example
* const point = ruler.destination([30.5, 50.5], 0.1, 90);
* //=point
*/
destination(p, dist, bearing) {
const a = bearing * RAD;
return this.offset(p,
Math.sin(a) * dist,
Math.cos(a) * dist);
}
/**
* Returns a new point given easting and northing offsets (in ruler units) from the starting point.
*
* @param {[number, number]} p point [longitude, latitude]
* @param {number} dx easting
* @param {number} dy northing
* @returns {[number, number]} point [longitude, latitude]
* @example
* const point = ruler.offset([30.5, 50.5], 10, 10);
* //=point
*/
offset(p, dx, dy) {
return [
p[0] + dx / this.kx,
p[1] + dy / this.ky
];
}
/**
* Given a line (an array of points), returns the total line distance.
*
* @param {[number, number][]} points [longitude, latitude]
* @returns {number} total line distance
* @example
* const length = ruler.lineDistance([
* [-67.031, 50.458], [-67.031, 50.534],
* [-66.929, 50.534], [-66.929, 50.458]
* ]);
* //=length
*/
lineDistance(points) {
let total = 0;
for (let i = 0; i < points.length - 1; i++) {
total += this.distance(points[i], points[i + 1]);
}
return total;
}
/**
* Given a polygon (an array of rings, where each ring is an array of points), returns the area.
*
* @param {[number, number][][]} polygon
* @returns {number} area value in the specified units (square kilometers by default)
* @example
* const area = ruler.area([[
* [-67.031, 50.458], [-67.031, 50.534], [-66.929, 50.534],
* [-66.929, 50.458], [-67.031, 50.458]
* ]]);
* //=area
*/
area(polygon) {
let sum = 0;
for (let i = 0; i < polygon.length; i++) {
const ring = polygon[i];
for (let j = 0, len = ring.length, k = len - 1; j < len; k = j++) {
sum += wrap(ring[j][0] - ring[k][0]) * (ring[j][1] + ring[k][1]) * (i ? -1 : 1);
}
}
return (Math.abs(sum) / 2) * this.kx * this.ky;
}
/**
* Returns the point at a specified distance along the line.
*
* @param {[number, number][]} line
* @param {number} dist distance
* @returns {[number, number]} point [longitude, latitude]
* @example
* const point = ruler.along(line, 2.5);
* //=point
*/
along(line, dist) {
let sum = 0;
if (dist <= 0) return line[0];
for (let i = 0; i < line.length - 1; i++) {
const p0 = line[i];
const p1 = line[i + 1];
const d = this.distance(p0, p1);
sum += d;
if (sum > dist) return interpolate(p0, p1, (dist - (sum - d)) / d);
}
return line[line.length - 1];
}
/**
* Returns the distance from a point `p` to a line segment `a` to `b`.
*
* @pointToSegmentDistance
* @param {[number, number]} p point [longitude, latitude]
* @param {[number, number]} a segment point 1 [longitude, latitude]
* @param {[number, number]} b segment point 2 [longitude, latitude]
* @returns {number} distance
* @example
* const distance = ruler.pointToSegmentDistance([-67.04, 50.5], [-67.05, 50.57], [-67.03, 50.54]);
* //=distance
*/
pointToSegmentDistance(p, a, b) {
let [x, y] = a;
let dx = wrap(b[0] - x) * this.kx;
let dy = (b[1] - y) * this.ky;
if (dx !== 0 || dy !== 0) {
const t = (wrap(p[0] - x) * this.kx * dx + (p[1] - y) * this.ky * dy) / (dx * dx + dy * dy);
if (t > 1) {
x = b[0];
y = b[1];
} else if (t > 0) {
x += (dx / this.kx) * t;
y += (dy / this.ky) * t;
}
}
dx = wrap(p[0] - x) * this.kx;
dy = (p[1] - y) * this.ky;
return Math.sqrt(dx * dx + dy * dy);
}
/**
* Returns an object of the form {point, index, t}, where point is closest point on the line
* from the given point, index is the start index of the segment with the closest point,
* and t is a parameter from 0 to 1 that indicates where the closest point is on that segment.
*
* @param {[number, number][]} line
* @param {[number, number]} p point [longitude, latitude]
* @returns {{point: [number, number], index: number, t: number}} {point, index, t}
* @example
* const point = ruler.pointOnLine(line, [-67.04, 50.5]).point;
* //=point
*/
pointOnLine(line, p) {
let minDist = Infinity;
let minX = line[0][0];
let minY = line[0][1];
let minI = 0;
let minT = 0;
for (let i = 0; i < line.length - 1; i++) {
let x = line[i][0];
let y = line[i][1];
let dx = wrap(line[i + 1][0] - x) * this.kx;
let dy = (line[i + 1][1] - y) * this.ky;
let t = 0;
if (dx !== 0 || dy !== 0) {
t = (wrap(p[0] - x) * this.kx * dx + (p[1] - y) * this.ky * dy) / (dx * dx + dy * dy);
if (t > 1) {
x = line[i + 1][0];
y = line[i + 1][1];
} else if (t > 0) {
x += (dx / this.kx) * t;
y += (dy / this.ky) * t;
}
}
dx = wrap(p[0] - x) * this.kx;
dy = (p[1] - y) * this.ky;
const sqDist = dx * dx + dy * dy;
if (sqDist < minDist) {
minDist = sqDist;
minX = x;
minY = y;
minI = i;
minT = t;
}
}
return {
point: [minX, minY],
index: minI,
t: Math.max(0, Math.min(1, minT))
};
}
/**
* Returns a part of the given line between the start and the stop points (or their closest points on the line).
*
* @param {[number, number]} start point [longitude, latitude]
* @param {[number, number]} stop point [longitude, latitude]
* @param {[number, number][]} line
* @returns {[number, number][]} line part of a line
* @example
* const line2 = ruler.lineSlice([-67.04, 50.5], [-67.05, 50.56], line1);
* //=line2
*/
lineSlice(start, stop, line) {
let p1 = this.pointOnLine(line, start);
let p2 = this.pointOnLine(line, stop);
if (p1.index > p2.index || (p1.index === p2.index && p1.t > p2.t)) {
const tmp = p1;
p1 = p2;
p2 = tmp;
}
const slice = [p1.point];
const l = p1.index + 1;
const r = p2.index;
if (!equals(line[l], slice[0]) && l <= r)
slice.push(line[l]);
for (let i = l + 1; i <= r; i++) {
slice.push(line[i]);
}
if (!equals(line[r], p2.point))
slice.push(p2.point);
return slice;
}
/**
* Returns a part of the given line between the start and the stop points indicated by distance along the line.
*
* @param {number} start start distance
* @param {number} stop stop distance
* @param {[number, number][]} line
* @returns {[number, number][]} part of a line
* @example
* const line2 = ruler.lineSliceAlong(10, 20, line1);
* //=line2
*/
lineSliceAlong(start, stop, line) {
let sum = 0;
const slice = [];
for (let i = 0; i < line.length - 1; i++) {
const p0 = line[i];
const p1 = line[i + 1];
const d = this.distance(p0, p1);
sum += d;
if (sum > start && slice.length === 0) {
slice.push(interpolate(p0, p1, (start - (sum - d)) / d));
}
if (sum >= stop) {
slice.push(interpolate(p0, p1, (stop - (sum - d)) / d));
return slice;
}
if (sum > start) slice.push(p1);
}
return slice;
}
/**
* Given a point, returns a bounding box object ([w, s, e, n]) created from the given point buffered by a given distance.
*
* @param {[number, number]} p point [longitude, latitude]
* @param {number} buffer
* @returns {[number, number, number, number]} bbox ([w, s, e, n])
* @example
* const bbox = ruler.bufferPoint([30.5, 50.5], 0.01);
* //=bbox
*/
bufferPoint(p, buffer) {
const v = buffer / this.ky;
const h = buffer / this.kx;
return [
p[0] - h,
p[1] - v,
p[0] + h,
p[1] + v
];
}
/**
* Given a bounding box, returns the box buffered by a given distance.
*
* @param {[number, number, number, number]} bbox ([w, s, e, n])
* @param {number} buffer
* @returns {[number, number, number, number]} bbox ([w, s, e, n])
* @example
* const bbox = ruler.bufferBBox([30.5, 50.5, 31, 51], 0.2);
* //=bbox
*/
bufferBBox(bbox, buffer) {
const v = buffer / this.ky;
const h = buffer / this.kx;
return [
bbox[0] - h,
bbox[1] - v,
bbox[2] + h,
bbox[3] + v
];
}
/**
* Returns true if the given point is inside in the given bounding box, otherwise false.
*
* @param {[number, number]} p point [longitude, latitude]
* @param {[number, number, number, number]} bbox ([w, s, e, n])
* @returns {boolean}
* @example
* const inside = ruler.insideBBox([30.5, 50.5], [30, 50, 31, 51]);
* //=inside
*/
insideBBox(p, bbox) { // eslint-disable-line
return wrap(p[0] - bbox[0]) >= 0 &&
wrap(p[0] - bbox[2]) <= 0 &&
p[1] >= bbox[1] &&
p[1] <= bbox[3];
}
}
/**
* @param {[number, number]} a
* @param {[number, number]} b
*/
function equals(a, b) {
return a[0] === b[0] && a[1] === b[1];
}
/**
* @param {[number, number]} a
* @param {[number, number]} b
* @param {number} t
* @returns {[number, number]}
*/
function interpolate(a, b, t) {
const dx = wrap(b[0] - a[0]);
const dy = b[1] - a[1];
return [
a[0] + dx * t,
a[1] + dy * t
];
}
/**
* normalize a degree value into [-180..180] range
* @param {number} deg
*/
function wrap(deg) {
while (deg < -180) deg += 360;
while (deg > 180) deg -= 360;
return deg;
}
return CheapRuler;
}));