three.js/src/extras/curves/CubicBezierCurve.js

/**************************************************************
 *	Cubic Bezier curve
 **************************************************************/

THREE.CubicBezierCurve = function ( v0, v1, v2, v3 ) {

	this.v0 = v0;
	this.v1 = v1;
	this.v2 = v2;
	this.v3 = v3;

};

THREE.CubicBezierCurve.prototype = Object.create( THREE.Curve.prototype );

THREE.CubicBezierCurve.prototype.getPoint = function ( t ) {

	var tx, ty;

	tx = THREE.Shape.Utils.b3( t, this.v0.x, this.v1.x, this.v2.x, this.v3.x );
	ty = THREE.Shape.Utils.b3( t, this.v0.y, this.v1.y, this.v2.y, this.v3.y );

	return new THREE.Vector2( tx, ty );

};

THREE.CubicBezierCurve.prototype.getTangent = function( t ) {

	var tx, ty;

	tx = THREE.Curve.Utils.tangentCubicBezier( t, this.v0.x, this.v1.x, this.v2.x, this.v3.x );
	ty = THREE.Curve.Utils.tangentCubicBezier( t, this.v0.y, this.v1.y, this.v2.y, this.v3.y );

	var tangent = new THREE.Vector2( tx, ty );
	tangent.normalize();

	return tangent;

};