gis-tools-ts
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A collection of geospatial tools primarily designed for WGS84, Web Mercator, and S2.
198 lines • 6.38 kB
JavaScript
import { ProjectionBase } from './base.js';
import { EPSLN, HALF_PI, QUART_PI } from '../constants/index.js';
import { adjustLon, msfnz, phi2z, tsfnz } from '../common.js';
/**
* # Mercator Projection
*
* The Mercator projection is a cylindrical map projection originating from the 16th century.
* It is widely recognized as the first regularly used map projection. It is a conformal projection
* where the equator projects to a straight line at constant scale. A rhumb line, or course of
* constant heading, projects to a straight line, making it suitable for navigational purposes.
*
* **Classification**: Conformal cylindrical
*
* **Available forms**: Forward and Inverse, spherical and ellipsoidal
*
* **Defined area**: Global, but best used near the equator
*
* **Alias**: `merc`
*
* **Domain**: 2D
*
* **Input type**: Geodetic coordinates
*
* **Output type**: Projected coordinates
*
* ## Projection String
* ```ini
* +proj=merc
* ```
*
* ## Usage
* The Mercator projection is often used for equatorial regions and navigational charts. It is not
* suitable for world maps due to significant area distortions. For example, Greenland appears
* larger than South America in the projection, despite Greenland's actual area being approximately
* one-eighth of South America's.
*
* **Examples:**
*
* - Using latitude of true scale:
* ```bash
* $ echo 56.35 12.32 | proj +proj=merc +lat_ts=56.5
* 3470306.37 759599.90
* ```
* - Using scaling factor:
* ```bash
* $ echo 56.35 12.32 | proj +proj=merc +k_0=2
* 12545706.61 2746073.80
* ```
*
* **Note**: `+lat_ts` and `+k_0` are mutually exclusive. If both are used, `+lat_ts` takes
* precedence over `+k_0`.
*
* ## Parameters
* - `lat_ts`: Latitude of true scale
* - `k_0`: Scaling factor
* - `lon_0`: Longitude of origin
* - `x_0`: False easting
* - `y_0`: False northing
* - `ellps`: Ellipsoid
* - `R`: Radius of the sphere
*
* ## Mathematical Definition
*
* **Spherical Form**
* - **Forward Projection**:
* $$x = k_0 \cdot R \cdot \lambda$$
* $$y = k_0 \cdot R \cdot \psi$$
* where
* $$\psi = \ln\left(\tan\left(\frac{\pi}{4} + \frac{\phi}{2}\right)\right)$$
* - **Inverse Projection**:
* $$\lambda = x / (k_0 \cdot R)$$
* $$\psi = y / (k_0 \cdot R)$$
* $$\phi = \frac{\pi}{2} - 2 \cdot \arctan\left(\exp(-\psi)\right)$$
*
* **Ellipsoidal Form**
* - **Forward Projection**:
* $$x = k_0 \cdot a \cdot \lambda$$
* $$y = k_0 \cdot a \cdot \psi$$
* where
* $$\psi = \ln\left(\tan\left(\frac{\pi}{4} + \frac{\phi}{2}\right)\right) - 0.5 \cdot e \cdot \ln\left(\frac{1 + e \cdot \sin(\phi)}{1 - e \cdot \sin(\phi)}\right)$$
* - **Inverse Projection**:
* $$\lambda = x / (k_0 \cdot a)$$
* $$\psi = y / (k_0 \cdot a)$$
* $$\phi = \arctan(\tau)$$
* where
* $$\tau = \tan(\phi)$$
*
* ## Further Reading
* - [Wikipedia: Mercator Projection](https://en.wikipedia.org/wiki/Mercator_projection)
* - [Wolfram Mathworld: Mercator Projection](http://mathworld.wolfram.com/MercatorProjection.html)
*
* 
*/
export class Mercator extends ProjectionBase {
name = 'Mercator';
static names = [
'Mercator',
'Popular Visualisation Pseudo Mercator',
'Mercator_1SP',
'Mercator_Auxiliary_Sphere',
'merc',
];
/**
* Preps an Mercator projection
* @param params - projection specific parameters
*/
constructor(params) {
const { sin, cos, sqrt } = Math;
super(params);
const con = this.b / this.a;
this.es = 1 - con * con;
this.e = sqrt(this.es);
if (this.latTs !== undefined) {
if (this.sphere) {
this.k0 = cos(this.latTs);
}
else {
this.k0 = msfnz(this.e, sin(this.latTs), cos(this.latTs));
}
}
else {
if (this.k0 === undefined) {
if (this.k !== undefined) {
this.k0 = this.k;
}
else {
this.k0 = 1;
}
}
}
}
/**
* Mercator forward equations--mapping lon-lat to x-y
* @param p - lon-lat WGS84 point
*/
forward(p) {
const { abs, sin, log, tan } = Math;
const { x: lon, y: lat } = p;
// convert to radians
// if (lat * R2D > 90 && lat * R2D < -90 && lon * R2D > 180 && lon * R2D < -180) {
// return;
// }
let x, y;
if (abs(abs(lat) - HALF_PI) <= EPSLN) {
throw new Error('cass:pj_init_merc: lat == +/-90');
}
else {
if (this.sphere) {
x = this.x0 + this.a * this.k0 * adjustLon(lon - this.long0);
y = this.y0 + this.a * this.k0 * log(tan(QUART_PI + 0.5 * lat));
}
else {
const sinphi = sin(lat);
const ts = tsfnz(this.e, lat, sinphi);
x = this.x0 + this.a * this.k0 * adjustLon(lon - this.long0);
y = this.y0 - this.a * this.k0 * log(ts);
}
p.x = x;
p.y = y;
}
}
/**
* Mercator inverse equations--mapping x-y to lon-lat
* @param p - Mercator point
*/
inverse(p) {
const { atan, exp } = Math;
const x = p.x - this.x0;
const y = p.y - this.y0;
let lat;
if (this.sphere) {
lat = HALF_PI - 2 * atan(exp(-y / (this.a * this.k0)));
}
else {
const ts = exp(-y / (this.a * this.k0));
lat = phi2z(this.e, ts);
if (lat === -9999)
throw new Error('cass:pj_init_merc: lat == +/-90');
}
const lon = adjustLon(this.long0 + x / (this.a * this.k0));
p.x = lon;
p.y = lat;
}
}
/** WebMercator Projection */
export class WebMercator extends Mercator {
name = 'WebMercator';
static names = ['WebMercator', 'WGS 84 / Pseudo-Mercator', 'webmerc'];
/**
* Preps a WebMercator projection
* @param params - projection specific parameters
*/
constructor(params) {
super(params);
this.sphere = true;
}
}
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