three.js/src/math/Plane.js

/**
 * @author bhouston / http://exocortex.com
 */

THREE.Plane = function ( normal, constant ) {

	this.normal = normal !== undefined ? normal.clone() : new THREE.Vector3( 1, 0, 0 );
	this.constant = constant !== undefined ? constant : 0;

};

THREE.Plane.prototype = {

	constructor: THREE.Plane,

	set: function ( normal, constant ) {

		this.normal.copy( normal );
		this.constant = constant;

		return this;

	},

	setComponents: function ( x, y, z, w ) {

		this.normal.set( x, y, z );
		this.constant = w;

		return this;

	},

	setFromNormalAndCoplanarPoint: function ( normal, point ) {

		this.normal.copy( normal ).normalize();
		this.constant = - point.dot( this.normal );	// must be this.normal, not normal, as this.normal is normalized

		return this;

	},

	setFromCoplanarPoints: function ( a, b, c ) {

		var normal = THREE.Plane.__v1.sub( c, b ).crossSelf(
					 THREE.Plane.__v2.sub( a, b ) ).normalize();

		// Q: should an error be thrown if normal is zero (e.g. degenerate plane)?

		this.setFromNormalAndCoplanarPoint( normal, a );

		return this;

	},

	copy: function ( plane ) {

		this.normal.copy( plane.normal );
		this.constant = plane.constant;

		return this;

	},

	normalize: function () {

		// Note: will lead to a divide by zero if the plane is invalid.

		var inverseNormalLength = 1.0 / this.normal.length();
		this.normal.multiplyScalar( inverseNormalLength );
		this.constant *= inverseNormalLength;

		return this;

	},

	distanceToPoint: function ( point ) {

		return this.normal.dot( point ) + this.constant;

	},

	distanceToSphere: function ( sphere ) {

		return this.distanceToPoint( sphere.center ) - sphere.radius;

	},

	projectPoint: function ( point, optionalTarget ) {

		return this.orthoPoint( point, optionalTarget ).subSelf( point ).negate();

	},

	orthoPoint: function ( point, optionalTarget ) {

		var perpendicularMagnitude = this.distanceToPoint( point );

		var result = optionalTarget || new THREE.Vector3();
		return result.copy( this.normal ).multiplyScalar( perpendicularMagnitude );

	},

	isIntersectionLine: function ( startPoint, endPoint ) {

		// Note: this tests if a line intersects the plane, not whether it (or its end-points) are coplanar with it.

		var startSign = this.distanceToPoint( startPoint );
		var endSign = this.distanceToPoint( endPoint );

		return ( startSign < 0 && endSign > 0 ) || ( endSign < 0 && startSign > 0 );

	},

	coplanarPoint: function ( optionalTarget ) {

		var result = optionalTarget || new THREE.Vector3();
		return result.copy( this.normal ).multiplyScalar( - this.constant );

	},

	transform: function( matrix, optionalNormalMatrix ) {

		var newNormal = THREE.Plane.__v1, newCoplanarPoint = THREE.Plane.__v2;

		// compute new normal based on theory here:
		// http://www.songho.ca/opengl/gl_normaltransform.html
		optionalNormalMatrix = optionalNormalMatrix || new THREE.Matrix3().getInverse( matrix ).transpose();
		newNormal = optionalNormalMatrix.multiplyVector3( newNormal.copy( this.normal ) );

		newCoplanarPoint = this.coplanarPoint( newCoplanarPoint );
		newCoplanarPoint = matrix.multiplyVector3( newCoplanarPoint );

		this.setFromNormalAndCoplanarPoint( newNormal, newCoplanarPoint );

		return this;
		
	},

	translate: function ( offset ) {

		this.constant = this.constant - offset.dot( this.normal );

		return this;

	},

	equals: function ( plane ) {

		return plane.normal.equals( this.normal ) && ( plane.constant == this.constant );

	},

	clone: function () {

		return new THREE.Plane().copy( this );

	}

};

THREE.Plane.__vZero = new THREE.Vector3( 0, 0, 0 );
THREE.Plane.__v1 = new THREE.Vector3();
THREE.Plane.__v2 = new THREE.Vector3();