s2-tools/dist/proj4/projections/merc.d.ts

A collection of geospatial tools primarily designed for WGS84, Web Mercator, and S2.

import { ProjectionBase } from './base';
import type { VectorPoint } from '../../geometry';
import type { ProjectionParams, ProjectionTransform } from '.';
/**
 * # 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
 * ```
 * +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 * R * λ
 *   y = k_0 * R * ψ
 *   ```
 *   where
 *   ```
 *   ψ = ln(tan(π/4 + φ/2))
 *   ```
 * - **Inverse Projection**:
 *   ```
 *   λ = x / (k_0 * R)
 *   ψ = y / (k_0 * R)
 *   φ = π/2 - 2 * atan(exp(-ψ))
 *   ```
 *
 * **Ellipsoidal Form**
 * - **Forward Projection**:
 *   ```
 *   x = k_0 * a * λ
 *   y = k_0 * a * ψ
 *   ```
 *   where
 *   ```
 *   ψ = ln(tan(π/4 + φ/2)) - 0.5 * e * ln((1 + e * sin(φ)) / (1 - e * sin(φ)))
 *   ```
 * - **Inverse Projection**:
 *   ```
 *   λ = x / (k_0 * a)
 *   ψ = y / (k_0 * a)
 *   φ = tan^-1(τ)
 *   ```
 *   where
 *   ```
 *   τ = tan(φ)
 *   ```
 *
 * ## Further Reading
 * - [Wikipedia: Mercator Projection](https://en.wikipedia.org/wiki/Mercator_projection)
 * - [Wolfram Mathworld: Mercator Projection](http://mathworld.wolfram.com/MercatorProjection.html)
 *
 * ![Mercator Projection](https://github.com/Open-S2/s2-tools/blob/master/assets/proj4/projections/images/merc.png?raw=true)
 */
export declare class Mercator extends ProjectionBase implements ProjectionTransform {
    name: string;
    static names: string[];
    /**
     * Preps an Mercator projection
     * @param params - projection specific parameters
     */
    constructor(params?: ProjectionParams);
    /**
     * Mercator forward equations--mapping lon-lat to x-y
     * @param p - lon-lat WGS84 point
     */
    forward(p: VectorPoint): void;
    /**
     * Mercator inverse equations--mapping x-y to lon-lat
     * @param p - Mercator point
     */
    inverse(p: VectorPoint): void;
}
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