three.js/src/math/Box3.js

import { Vector3 } from './Vector3.js';

class Box3 {

	constructor( min, max ) {

		Object.defineProperty( this, 'isBox3', { value: true } );

		this.min = ( min !== undefined ) ? min : new Vector3( + Infinity, + Infinity, + Infinity );
		this.max = ( max !== undefined ) ? max : new Vector3( - Infinity, - Infinity, - Infinity );

	}

	set( min, max ) {

		this.min.copy( min );
		this.max.copy( max );

		return this;

	}

	setFromArray( array ) {

		let minX = + Infinity;
		let minY = + Infinity;
		let minZ = + Infinity;

		let maxX = - Infinity;
		let maxY = - Infinity;
		let maxZ = - Infinity;

		for ( let i = 0, l = array.length; i < l; i += 3 ) {

			const x = array[ i ];
			const y = array[ i + 1 ];
			const z = array[ i + 2 ];

			if ( x < minX ) minX = x;
			if ( y < minY ) minY = y;
			if ( z < minZ ) minZ = z;

			if ( x > maxX ) maxX = x;
			if ( y > maxY ) maxY = y;
			if ( z > maxZ ) maxZ = z;

		}

		this.min.set( minX, minY, minZ );
		this.max.set( maxX, maxY, maxZ );

		return this;

	}

	setFromBufferAttribute( attribute ) {

		let minX = + Infinity;
		let minY = + Infinity;
		let minZ = + Infinity;

		let maxX = - Infinity;
		let maxY = - Infinity;
		let maxZ = - Infinity;

		for ( let i = 0, l = attribute.count; i < l; i ++ ) {

			const x = attribute.getX( i );
			const y = attribute.getY( i );
			const z = attribute.getZ( i );

			if ( x < minX ) minX = x;
			if ( y < minY ) minY = y;
			if ( z < minZ ) minZ = z;

			if ( x > maxX ) maxX = x;
			if ( y > maxY ) maxY = y;
			if ( z > maxZ ) maxZ = z;

		}

		this.min.set( minX, minY, minZ );
		this.max.set( maxX, maxY, maxZ );

		return this;

	}

	setFromPoints( points ) {

		this.makeEmpty();

		for ( let i = 0, il = points.length; i < il; i ++ ) {

			this.expandByPoint( points[ i ] );

		}

		return this;

	}

	setFromCenterAndSize( center, size ) {

		const halfSize = _vector.copy( size ).multiplyScalar( 0.5 );

		this.min.copy( center ).sub( halfSize );
		this.max.copy( center ).add( halfSize );

		return this;

	}

	setFromObject( object ) {

		this.makeEmpty();

		return this.expandByObject( object );

	}

	clone() {

		return new this.constructor().copy( this );

	}

	copy( box ) {

		this.min.copy( box.min );
		this.max.copy( box.max );

		return this;

	}

	makeEmpty() {

		this.min.x = this.min.y = this.min.z = + Infinity;
		this.max.x = this.max.y = this.max.z = - Infinity;

		return this;

	}

	isEmpty() {

		// this is a more robust check for empty than ( volume <= 0 ) because volume can get positive with two negative axes

		return ( this.max.x < this.min.x ) || ( this.max.y < this.min.y ) || ( this.max.z < this.min.z );

	}

	getCenter( target ) {

		if ( target === undefined ) {

			console.warn( 'THREE.Box3: .getCenter() target is now required' );
			target = new Vector3();

		}

		return this.isEmpty() ? target.set( 0, 0, 0 ) : target.addVectors( this.min, this.max ).multiplyScalar( 0.5 );

	}

	getSize( target ) {

		if ( target === undefined ) {

			console.warn( 'THREE.Box3: .getSize() target is now required' );
			target = new Vector3();

		}

		return this.isEmpty() ? target.set( 0, 0, 0 ) : target.subVectors( this.max, this.min );

	}

	expandByPoint( point ) {

		this.min.min( point );
		this.max.max( point );

		return this;

	}

	expandByVector( vector ) {

		this.min.sub( vector );
		this.max.add( vector );

		return this;

	}

	expandByScalar( scalar ) {

		this.min.addScalar( - scalar );
		this.max.addScalar( scalar );

		return this;

	}

	expandByObject( object ) {

		// Computes the world-axis-aligned bounding box of an object (including its children),
		// accounting for both the object's, and children's, world transforms

		object.updateWorldMatrix( false, false );

		const geometry = object.geometry;

		if ( geometry !== undefined ) {

			if ( geometry.boundingBox === null ) {

				geometry.computeBoundingBox();

			}

			_box.copy( geometry.boundingBox );
			_box.applyMatrix4( object.matrixWorld );

			this.union( _box );

		}

		const children = object.children;

		for ( let i = 0, l = children.length; i < l; i ++ ) {

			this.expandByObject( children[ i ] );

		}

		return this;

	}

	containsPoint( point ) {

		return point.x < this.min.x || point.x > this.max.x ||
			point.y < this.min.y || point.y > this.max.y ||
			point.z < this.min.z || point.z > this.max.z ? false : true;

	}

	containsBox( box ) {

		return this.min.x <= box.min.x && box.max.x <= this.max.x &&
			this.min.y <= box.min.y && box.max.y <= this.max.y &&
			this.min.z <= box.min.z && box.max.z <= this.max.z;

	}

	getParameter( point, target ) {

		// This can potentially have a divide by zero if the box
		// has a size dimension of 0.

		if ( target === undefined ) {

			console.warn( 'THREE.Box3: .getParameter() target is now required' );
			target = new Vector3();

		}

		return target.set(
			( point.x - this.min.x ) / ( this.max.x - this.min.x ),
			( point.y - this.min.y ) / ( this.max.y - this.min.y ),
			( point.z - this.min.z ) / ( this.max.z - this.min.z )
		);

	}

	intersectsBox( box ) {

		// using 6 splitting planes to rule out intersections.
		return box.max.x < this.min.x || box.min.x > this.max.x ||
			box.max.y < this.min.y || box.min.y > this.max.y ||
			box.max.z < this.min.z || box.min.z > this.max.z ? false : true;

	}

	intersectsSphere( sphere ) {

		// Find the point on the AABB closest to the sphere center.
		this.clampPoint( sphere.center, _vector );

		// If that point is inside the sphere, the AABB and sphere intersect.
		return _vector.distanceToSquared( sphere.center ) <= ( sphere.radius * sphere.radius );

	}

	intersectsPlane( plane ) {

		// We compute the minimum and maximum dot product values. If those values
		// are on the same side (back or front) of the plane, then there is no intersection.

		let min, max;

		if ( plane.normal.x > 0 ) {

			min = plane.normal.x * this.min.x;
			max = plane.normal.x * this.max.x;

		} else {

			min = plane.normal.x * this.max.x;
			max = plane.normal.x * this.min.x;

		}

		if ( plane.normal.y > 0 ) {

			min += plane.normal.y * this.min.y;
			max += plane.normal.y * this.max.y;

		} else {

			min += plane.normal.y * this.max.y;
			max += plane.normal.y * this.min.y;

		}

		if ( plane.normal.z > 0 ) {

			min += plane.normal.z * this.min.z;
			max += plane.normal.z * this.max.z;

		} else {

			min += plane.normal.z * this.max.z;
			max += plane.normal.z * this.min.z;

		}

		return ( min <= - plane.constant && max >= - plane.constant );

	}

	intersectsTriangle( triangle ) {

		if ( this.isEmpty() ) {

			return false;

		}

		// compute box center and extents
		this.getCenter( _center );
		_extents.subVectors( this.max, _center );

		// translate triangle to aabb origin
		_v0.subVectors( triangle.a, _center );
		_v1.subVectors( triangle.b, _center );
		_v2.subVectors( triangle.c, _center );

		// compute edge vectors for triangle
		_f0.subVectors( _v1, _v0 );
		_f1.subVectors( _v2, _v1 );
		_f2.subVectors( _v0, _v2 );

		// test against axes that are given by cross product combinations of the edges of the triangle and the edges of the aabb
		// make an axis testing of each of the 3 sides of the aabb against each of the 3 sides of the triangle = 9 axis of separation
		// axis_ij = u_i x f_j (u0, u1, u2 = face normals of aabb = x,y,z axes vectors since aabb is axis aligned)
		let axes = [
			0, - _f0.z, _f0.y, 0, - _f1.z, _f1.y, 0, - _f2.z, _f2.y,
			_f0.z, 0, - _f0.x, _f1.z, 0, - _f1.x, _f2.z, 0, - _f2.x,
			- _f0.y, _f0.x, 0, - _f1.y, _f1.x, 0, - _f2.y, _f2.x, 0
		];
		if ( ! satForAxes( axes, _v0, _v1, _v2, _extents ) ) {

			return false;

		}

		// test 3 face normals from the aabb
		axes = [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ];
		if ( ! satForAxes( axes, _v0, _v1, _v2, _extents ) ) {

			return false;

		}

		// finally testing the face normal of the triangle
		// use already existing triangle edge vectors here
		_triangleNormal.crossVectors( _f0, _f1 );
		axes = [ _triangleNormal.x, _triangleNormal.y, _triangleNormal.z ];

		return satForAxes( axes, _v0, _v1, _v2, _extents );

	}

	clampPoint( point, target ) {

		if ( target === undefined ) {

			console.warn( 'THREE.Box3: .clampPoint() target is now required' );
			target = new Vector3();

		}

		return target.copy( point ).clamp( this.min, this.max );

	}

	distanceToPoint( point ) {

		const clampedPoint = _vector.copy( point ).clamp( this.min, this.max );

		return clampedPoint.sub( point ).length();

	}

	getBoundingSphere( target ) {

		if ( target === undefined ) {

			console.error( 'THREE.Box3: .getBoundingSphere() target is now required' );
			//target = new Sphere(); // removed to avoid cyclic dependency

		}

		this.getCenter( target.center );

		target.radius = this.getSize( _vector ).length() * 0.5;

		return target;

	}

	intersect( box ) {

		this.min.max( box.min );
		this.max.min( box.max );

		// ensure that if there is no overlap, the result is fully empty, not slightly empty with non-inf/+inf values that will cause subsequence intersects to erroneously return valid values.
		if ( this.isEmpty() ) this.makeEmpty();

		return this;

	}

	union( box ) {

		this.min.min( box.min );
		this.max.max( box.max );

		return this;

	}

	applyMatrix4( matrix ) {

		// transform of empty box is an empty box.
		if ( this.isEmpty() ) return this;

		// NOTE: I am using a binary pattern to specify all 2^3 combinations below
		_points[ 0 ].set( this.min.x, this.min.y, this.min.z ).applyMatrix4( matrix ); // 000
		_points[ 1 ].set( this.min.x, this.min.y, this.max.z ).applyMatrix4( matrix ); // 001
		_points[ 2 ].set( this.min.x, this.max.y, this.min.z ).applyMatrix4( matrix ); // 010
		_points[ 3 ].set( this.min.x, this.max.y, this.max.z ).applyMatrix4( matrix ); // 011
		_points[ 4 ].set( this.max.x, this.min.y, this.min.z ).applyMatrix4( matrix ); // 100
		_points[ 5 ].set( this.max.x, this.min.y, this.max.z ).applyMatrix4( matrix ); // 101
		_points[ 6 ].set( this.max.x, this.max.y, this.min.z ).applyMatrix4( matrix ); // 110
		_points[ 7 ].set( this.max.x, this.max.y, this.max.z ).applyMatrix4( matrix ); // 111

		this.setFromPoints( _points );

		return this;

	}

	translate( offset ) {

		this.min.add( offset );
		this.max.add( offset );

		return this;

	}

	equals( box ) {

		return box.min.equals( this.min ) && box.max.equals( this.max );

	}

}

function satForAxes( axes, v0, v1, v2, extents ) {

	for ( let i = 0, j = axes.length - 3; i <= j; i += 3 ) {

		_testAxis.fromArray( axes, i );
		// project the aabb onto the seperating axis
		const r = extents.x * Math.abs( _testAxis.x ) + extents.y * Math.abs( _testAxis.y ) + extents.z * Math.abs( _testAxis.z );
		// project all 3 vertices of the triangle onto the seperating axis
		const p0 = v0.dot( _testAxis );
		const p1 = v1.dot( _testAxis );
		const p2 = v2.dot( _testAxis );
		// actual test, basically see if either of the most extreme of the triangle points intersects r
		if ( Math.max( - Math.max( p0, p1, p2 ), Math.min( p0, p1, p2 ) ) > r ) {

			// points of the projected triangle are outside the projected half-length of the aabb
			// the axis is seperating and we can exit
			return false;

		}

	}

	return true;

}

const _points = [
	new Vector3(),
	new Vector3(),
	new Vector3(),
	new Vector3(),
	new Vector3(),
	new Vector3(),
	new Vector3(),
	new Vector3()
];

const _vector = new Vector3();

const _box = new Box3();

// triangle centered vertices

const _v0 = new Vector3();
const _v1 = new Vector3();
const _v2 = new Vector3();

// triangle edge vectors

const _f0 = new Vector3();
const _f1 = new Vector3();
const _f2 = new Vector3();

const _center = new Vector3();
const _extents = new Vector3();
const _triangleNormal = new Vector3();
const _testAxis = new Vector3();


export { Box3 };