/**
 * @author zz85 / http://www.lab4games.net/zz85/blog
 */

THREE.CurveUtils = {

	tangentQuadraticBezier: function ( t, p0, p1, p2 ) {

		return 2 * ( 1 - t ) * ( p1 - p0 ) + 2 * t * ( p2 - p1 );

	},

	// Puay Bing, thanks for helping with this derivative!

	tangentCubicBezier: function ( t, p0, p1, p2, p3 ) {

		return - 3 * p0 * ( 1 - t ) * ( 1 - t )  +
			3 * p1 * ( 1 - t ) * ( 1 - t ) - 6 * t * p1 * ( 1 - t ) +
			6 * t *  p2 * ( 1 - t ) - 3 * t * t * p2 +
			3 * t * t * p3;

	},

	tangentSpline: function ( t, p0, p1, p2, p3 ) {

		// To check if my formulas are correct

		var h00 = 6 * t * t - 6 * t; 	// derived from 2t^3 − 3t^2 + 1
		var h10 = 3 * t * t - 4 * t + 1; // t^3 − 2t^2 + t
		var h01 = - 6 * t * t + 6 * t; 	// − 2t3 + 3t2
		var h11 = 3 * t * t - 2 * t;	// t3 − t2

		return h00 + h10 + h01 + h11;

	},

	// Catmull-Rom

	interpolate: function( p0, p1, p2, p3, t ) {

		var v0 = ( p2 - p0 ) * 0.5;
		var v1 = ( p3 - p1 ) * 0.5;
		var t2 = t * t;
		var t3 = t * t2;
		return ( 2 * p1 - 2 * p2 + v0 + v1 ) * t3 + ( - 3 * p1 + 3 * p2 - 2 * v0 - v1 ) * t2 + v0 * t + p1;

	}

};