SphericalCoordinates

This documentation is incomplete and may be incorrect

class SphericalCoordinates

See also Wikipedia, Wolfram MathWorld.

  • The poles (phi) are at the positive and negative y axis.
  • The equator starts at positive z.

Conversion from spherical to Cartesian (rectilinear) coordinates:

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
  <mtr><mrow><mi>x</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
  <mtr><mrow><mi>y</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
  <mtr><mrow><mi>z</mi><mo>=</mo><mn>ρ</mn><mi>cos</mi><mn>θφ</mn></mrow></mtr>
</mtable>
</mfenced>
</math>

Conversion from Cartesian (rectilinear) to spherical coordinates:

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
  <mtr><mrow><mi>r</mi><mo>=</mo><msqrt>
    <msup><mi>x</mi><mn>2</mn></msup><mo>+</mo>
    <msup><mi>y</mi><mn>2</mn></msup><mo>+</mo>
    <msup><mi>z</mi><mn>2</mn></msup>
  </msqrt></mrow></mtr>
  <mtr><mrow><mi>θ</mi><mo>=</mo><mo>arccos</mo><mfrac><mi>z</mi><mi>r</mi></mfrac></mrow></mtr>
  <mtr><mrow><mi>φ</mi><mo>=</mo><mo>arctan</mo><mfrac><mi>y</mi><mi>x</mi></mfrac></mrow></mtr>
</mtable>
</mfenced>
</math>

Ranges

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mfenced open="{" close="">
<mtable columnalign="left">
  <mtr><mrow><mi>r</mi><mo>≥<mn>0</mn></mtr>
  <mtr><mrow><mi>θ</mi><mo>≥<mn>0</mn></mtr>
  <mtr><mrow><mi>φ</mi><mo>≥<mn>0</mn></mtr>
</mtable>
</mfenced>
</math>

Usage

import {SphericalCoordinates} from '@math.gl/core';

Creating a SphericalCoordinates object

const spherical = new SphericalCoordinates({phi: 0, theta: 0});
const spherical = new SphericalCoordinates({pitch: 0, bearing: 0});
const spherical = new SphericalCoordinates({longitude: 0, latitude: 0});

Converting to a direction Vector3

const direction = new SphericalCoordinates().toVector3();

Manipulating spherical coordinates;

spherical.bearing += 3; // Add three degrees to bearing
spherical.theta -= Math.PI / 4; // Subtract PI/4 radians from theta.

Members

// Standard spherical coordinates

phi

theta

radius

altitude

// lnglatZ coordinates

lng

lat

z

Methods

constructor

SphericalCoordinates({phi = 0, theta = 0, radius = 1.0})
SphericalCoordinates({bearing = 0, pitch = 0, altitude = 1.0})
SphericalCoordinates({longitude = 0, latitude = 0, z = 1.0})
  • phi=0 - rotation around X (latitude)
  • theta=0 - rotation around Y (longitude)
  • radius=1 - Distance from center

set

set(radius, phi, theta)

clone

clone()

copy

copy(other)

fromLngLatZ

fromLngLatZ([lng, lat, z])

fromVector3

fromVector3(v)

makeSafe

makeSafe()

// restrict phi to be betwee EPS and PI-EPS

toVector3

toVector3(center = [0, 0, 0])

// TODO - add parameter for orientation of sphere? up vector etc?

check

Remarks

  • Inspired by THREE.js THREE.Spherical class