Documentation / @interstellar-tools/equations / isOnTriaxialEllipsoidSurface

Function: isOnTriaxialEllipsoidSurface()

function isOnTriaxialEllipsoidSurface(
  x: number,
  y: number,
  z: number,
  a: number,
  b: number,
  c: number,
  eps?: number
): boolean;

Defined in: cartography/is-on-triaxial-ellipsoid-surface.ts:53

Test whether a 3D point lies on the surface of a triaxial ellipsoid (within a tolerance).

A triaxial ellipsoid centered at the origin with semi-axes ($a$), ($b$), ($c$) aligned to the ($x$), ($y$), ($z$) axes is defined by the implicit surface:

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$

This function evaluates the left-hand side and checks whether it is within eps of 1.

Notes:

• This is a pure geometric surface membership test; it does not compute the closest point on the ellipsoid or any geodetic latitude/longitude.
• For ellipsoids of revolution (oblate/prolate), you typically have ($a=b$), but this supports the general triaxial case.

Parameters

Parameter	Type	Default value	Description
x	number	undefined	X coordinate (finite).
y	number	undefined	Y coordinate (finite).
z	number	undefined	Z coordinate (finite).
a	number	undefined	Semi-axis length along x (finite, > 0).
b	number	undefined	Semi-axis length along y (finite, > 0).
c	number	undefined	Semi-axis length along z (finite, > 0).
eps	number	1e-12	Allowed absolute tolerance on the implicit value (finite, >= 0). Defaults to 1e-12.

Returns

boolean

true if the point satisfies the ellipsoid equation within eps, otherwise false.

Throws

If any input is not a finite number.

Throws

If a <= 0, b <= 0, c <= 0, or eps < 0.

Examples

// Ellipsoid with semi-axes a=3, b=2, c=1
// Point on +X axis should be on the surface: (x,y,z) = (a,0,0)
const onSurface = isOnTriaxialEllipsoidSurface(3, 0, 0, 3, 2, 1);
// onSurface === true

// Slightly off the surface (use a looser eps if needed)
const onSurface = isOnTriaxialEllipsoidSurface(3.0000001, 0, 0, 3, 2, 1, 1e-6);
// onSurface === true

See

• https://en.wikipedia.org/wiki/Ellipsoid Ellipsoid (general definition and implicit equation)
• https://mathworld.wolfram.com/Ellipsoid.html Wolfram MathWorld — Ellipsoid (properties and equations)
• https://en.wikipedia.org/wiki/Triaxial_ellipsoid Triaxial ellipsoid (special case discussion)