@web-engine-dev/math

---

@web-engine-dev/math / Sphere

Class: Sphere

A bounding sphere defined by a center point and radius. Immutable by design — all operations return new instances.

Bounding spheres are the fastest primitive for broad-phase culling:

• Frustum-sphere test is 6 dot products
• Sphere-sphere test is 1 distance comparison
• Rotation-invariant (no need to recompute on rotation)

Example

const sphere = new Sphere(new Vec3(0, 5, 0), 2);
if (sphere.containsPoint(point)) { ... }
if (sphere.intersectsSphere(otherSphere)) { ... }

Constructors

Constructor

new Sphere(center?, radius?): Sphere

Parameters

center?

Vec3 = ...

radius?

number = 0

Returns

Sphere

Properties

center

readonly center: Vec3

---

radius

readonly radius: number

Accessors

diameter

Get Signature

get diameter(): number

Diameter: 2r

Returns

number

---

surfaceArea

Get Signature

get surfaceArea(): number

Surface area: 4πr²

Returns

number

---

volume

Get Signature

get volume(): number

Volume: 4/3 πr³

Returns

number

Methods

closestPoint()

closestPoint(point): Vec3

Returns the closest point on the sphere surface to a given point.

Parameters

point

Vec3

Returns

Vec3

---

containsPoint()

containsPoint(point): boolean

Checks if a point is inside the sphere.

Parameters

point

Vec3

Returns

boolean

---

containsSphere()

containsSphere(sphere): boolean

Checks if the sphere fully contains another sphere.

Parameters

sphere

Sphere

Returns

boolean

---

distanceToPoint()

distanceToPoint(point): number

Returns the distance from a point to the sphere surface (negative if inside).

Parameters

point

Vec3

Returns

number

---

equals()

equals(sphere, epsilon?): boolean

Parameters

sphere

Sphere

epsilon?

number = 0

Returns

boolean

---

expand()

expand(amount): Sphere

Returns a sphere expanded by the given amount.

Parameters

amount

number

Returns

Sphere

---

expandByPoint()

expandByPoint(point): Sphere

Returns a sphere that encloses this sphere and a point.

Parameters

point

Vec3

Returns

Sphere

---

intersectsAABB()

intersectsAABB(box): boolean

Checks if the sphere intersects an AABB.

Parameters

box

AABB

Returns

boolean

---

intersectsPlane()

intersectsPlane(plane): -1 | 0 | 1

Checks which side of a plane the sphere is on.

Parameters

plane

Plane

Returns

-1 | 0 | 1

1 = entirely on positive side, -1 = entirely on negative side, 0 = intersecting.

---

intersectsSphere()

intersectsSphere(sphere): boolean

Checks if the sphere intersects another sphere.

Parameters

sphere

Sphere

Returns

boolean

---

merge()

merge(other): Sphere

Returns a sphere that encloses both this sphere and another.

Parameters

other

Sphere

Returns

Sphere

---

toAABB()

toAABB(): AABB

Returns the AABB that encloses this sphere.

Returns

AABB

---

toString()

toString(): string

Returns

string

---

transform()

transform(matrix): Sphere

Transforms the sphere by a matrix. The radius is scaled by the maximum axis scale.

Parameters

matrix

Mat4

Returns

Sphere

---

translate()

translate(offset): Sphere

Returns a sphere translated by a vector.

Parameters

offset

Vec3

Returns

Sphere

---

from()

static from(center, radius): Sphere

Creates a sphere from center and radius.

Parameters

center

Vec3

radius

number

Returns

Sphere

---

fromAABB()

static fromAABB(box): Sphere

Creates a bounding sphere that encloses an AABB.

Parameters

box

AABB

Returns

Sphere

---

fromPoints()

static fromPoints(points): Sphere

Computes a bounding sphere from an array of points using Ritter's algorithm. Not guaranteed to be optimal but runs in O(n) and produces tight bounds.

Parameters

points

Vec3[]

Returns

Sphere