Bounding volume collision detection with THREE.js

This article shows how to implement collision detection between bounding boxes and spheres using the Three.js library. It is assumed that before reading this you have read our 3D collision detection introductory article first, and have basic knowledge about Three.js.

Using Box3 and Sphere

Three.js has objects that represent mathematical volumes and shapes — for 3D AABB and bounding spheres we can use the Box3 and Sphere objects. Once instantiated, they have methods available to do intersection tests against other volumes.

Instantiating boxes

To create a Box3 instance, we need to provide the lower and upper boundaries of the box. Usually we will want this AABB to be "linked" to an object in our 3D world (like a character.) In Three.js, Geometry instances have a boundingBox property with min and max boundaries for the object. Keep in mind that in order for this property to be defined, you need to manually call Geometry.computeBoundingBox beforehand.

var knot = new THREE.Mesh(
  new THREE.TorusKnotGeometry(0.5, 0.1),
  new MeshNormalMaterial({}));
knot.geometry.computeBoundingBox();
var knotBBox = new Box3(
  knot.geometry.boundingBox.min,
  knot.geometry.boundingBox.max);

A more simple alternative that fixes the previous issue is to set those boundaries later on with Box3.setFromObject, which will compute the dimensions taking into account a 3D entity's transformations and any child meshes as well.

var knot = new THREE.Mesh(
  new THREE.TorusKnotGeometry(0.5, 0.1),
  new MeshNormalMaterial({}));
var knotBBox = new Box3(new THREE.Vector3(), new THREE.Vector3());
knotBBox.setFromObject(knot);

Instantiating spheres

Instantiating Sphere objects is similar. We need to provide the sphere's center and radius, which can be added to the boundingSphere property available in Geometry.

var knot = new THREE.Mesh(
  new THREE.TorusKnotGeometry(0.5, 0.1),
  new MeshNormalMaterial({}));
var knotBSphere = new Sphere(
  knot.position,
  knot.geometry.boundingSphere.radius);

Unfortunately, there is no equivalent of Box3.setFromObject for Sphere instances. So if we apply transformations or change the position of the Mesh, we need to manually update the bounding sphere. For instance:

knot.scale.set(2, 2, 2);
knotBSphere.radius = knot.geometry.radius * 2;

Intersection tests

Point versus Box3 / Sphere

Both Box3 and Sphere have a containsPoint method to do this test.

var point = new THREE.Vector3(2, 4, 7);
knotBBox.containsPoint(point);

Box3 versus Box3

The Box3.isIntersectionBox method is available for performing this test.

knotBbox.isIntersectionBox(otherBox);

Sphere versus Sphere

In a similar fashion as before, there is a Sphere.intersectsSphere method to perform this test.

knotBSphere.intersectsSphere(otherSphere);

Sphere versus Box3

Unfortunately this test is not implemented in Three.js, but we can patch Sphere to implement a Sphere versus AABB intersection algorithm.

// expand THREE.js Sphere to support collision tests vs Box3
// we are creating a vector outside the method scope to
// avoid spawning a new instance of Vector3 on every check
THREE.Sphere.__closest = new THREE.Vector3();
THREE.Sphere.prototype.intersectsBox = function (box) {
    // get box closest point to sphere center by clamping
    THREE.Sphere.__closest.set(this.center.x, this.center.y, this.center.z);
    THREE.Sphere.__closest.clamp(box.min, box.max);
    var distance =  this.center.distanceToSquared(THREE.Sphere.__closest);
    return distance < (this.radius * this.radius);
};

Demos

We have prepared some live demos to demonstrate these techniques, with source code to examine.

• Point versus Box and Sphere
• Box versus Box and Sphere
• Sphere versus Box and Sphere

Using BoundingBoxHelper

As an alternative to using raw Box3 and Sphere objects, Three.js has a useful object to make handling bounding boxes easier: BoundingBoxHelper. This helper takes a Mesh and calculates a bounding box volume for it (including its child meshes.) This results in a new box Mesh representing the bounding box and a Box3 object, which is the actual bounding box.

The advantages of using this helper are:

• It has an update() method that will resize the bounding box if the linked Mesh rotates or changes its dimensions, and update its position.
• It takes into account the child meshes when computing the size of the bounding box, so the original mesh and all its children are wrapped.
• We can easily debug collisions by rendering the Meshes that BoundingBoxHelper creates. By default they are created with a wireframe material.

The main disadvantage is that it only creates box bounding volumes, so if you need spheres vs AABB tests you need to create your own Sphere objects.

To use it, we need to create a new BoundingBoxHelper instance and supply the geometry and — optionally — a color that will be used for the wireframe material.

var knot = new THREE.Mesh(
  new THREE.TorusKnotGeometry(0.5, 0.1),
  new THREE.MeshNormalMaterial({})
);
var knotBBox = new THREE.BoundingBoxHelper(knot, 0x00ff00);

If we change the Mesh position, rotation, scale, etc. we need to call the update() method so the BoundingBoxHelper instance matches its linked Mesh.

knot.position.set(-3, 2, 1);
knot.rotation.x = -Math.PI / 4;
// update the bounding box so it stills wraps the knot
knotBBox.update(); 

Performing collision tests is done in the same way as explained in the above section — a BoundingBoxHelper contains a Box3 instance in its box property, whihc is ideal for performing the test.

// box vs box
knotBBox.box.isIntersectionBox(otherBBox.box);
// box vs point
knotBBox.box.containsPoint(point.position);

Demos

There are two demos you can take a look at on our live demos page. The first one showcases point versus box collisions using BoundingBoxHelper. The second one performs box versus box tests.