<!-- AVATAR-FORGE · part 195 -->
pedia.org/wiki/B%C3%A9zier_curve
 */

function CatmullRom( t, p0, p1, p2, p3 ) {

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

}

//

function QuadraticBezierP0( t, p ) {

	const k = 1 - t;
	return k * k * p;

}

function QuadraticBezierP1( t, p ) {

	return 2 * ( 1 - t ) * t * p;

}

function QuadraticBezierP2( t, p ) {

	return t * t * p;

}

function QuadraticBezier( t, p0, p1, p2 ) {

	return QuadraticBezierP0( t, p0 ) + QuadraticBezierP1( t, p1 ) +
		QuadraticBezierP2( t, p2 );

}

//

function CubicBezierP0( t, p ) {

	const k = 1 - t;
	return k * k * k * p;

}

function CubicBezierP1( t, p ) {

	const k = 1 - t;
	return 3 * k * k * t * p;

}

function CubicBezierP2( t, p ) {

	return 3 * ( 1 - t ) * t * t * p;

}

function CubicBezierP3( t, p ) {

	return t * t * t * p;

}

function CubicBezier( t, p0, p1, p2, p3 ) {

	return CubicBezierP0( t, p0 ) + CubicBezierP1( t, p1 ) + CubicBezierP2( t, p2 ) +
		CubicBezierP3( t, p3 );

}

class CubicBezierCurve extends Curve {

	constructor( v0 = new Vector2(), v1 = new Vector2(), v2 = new Vector2(), v3 = new Vector2() ) {

		super();

		this.isCubicBezierCurve = true;

		this.type = 'CubicBezierCurve';

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

	}

	getPoint( t, optionalTarget = new Vector2() ) {

		const point = optionalTarget;

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

		point.set(
			CubicBezier( t, v0.x, v1.x, v2.x, v3.x ),
			CubicBezier( t, v0.y, v1.y, v2.y, v3.y )
		);

		return point;

	}

	copy( source ) {

		super.copy( source );

		this.v0.copy( source.v0 );
		this.v1.copy( source.v1 );
		this.v2.copy( source.v2 );
		this.v3.copy( source.v3 );

		return this;

	}

	toJSON() {

		const data = super.toJSON();

		data.v0 = this.v0.toArray();
		data.v1 = this.v1.toArray();
		data.v2 = this.v2.toArray();
		data.v3 = this.v3.toArray();

		return data;

	}

	fromJSON( json ) {

		super.fromJSON( json );

		this.v0.fromArray( json.v0 );
		this.v1.fromArray( json.v1 );
		this.v2.fromArray( json.v2 );
		this.v3.fromArray( json.v3 );

		return this;

	}

}

class CubicBezierCurve3 extends Curve {

	constructor( v0 = new Vector3(), v1 = new Vector3(), v2 = new Vector3(), v3 = new Vector3() ) {

		super();

		this.isCubicBezierCurve3 = true;

		this.type = 'CubicBezierCurve3';

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

	}

	getPoint( t, optionalTarget = new Vector3() ) {

		const point = optionalTarget;

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

		point.set(
			CubicBezier( t, v0.x, v1.x, v2.x, v3.x ),
			CubicBezier( t, v0.y, v1.y, v2.y, v3.y ),
			CubicBezier( t, v0.z, v1.z, v2.z, v3.z )
		);

		return point;

	}

	copy( source ) {

		super.copy( source );

		this.v0.copy( source.v0 );
		this.v1.copy( source.v1 );
		this.v2.copy( source.v2 );
		this.v3.copy( source.v3 );

		return this;

	}

	toJSON() {

		const data = super.toJSON();

		data.v0 = this.v0.toArray();
		data.v1 = this.v1.toArray();
		data.v2 = this.v2.toArray();
		data.v3 = this.v3.toArray();

		return data;

	}

	fromJSON( json ) {

		super.fromJSON( json );

		this.v0.fromArray( json.v0 );
		this.v1.fromArray( json.v1 );
		this.v2.fromArray( json.v2 );
		this.v3.fromArray( json.v3 );

		return this;

	}

}

class LineCurve extends Curve {

	constructor( v1 = new Vector2(), v2 = new Vector2() ) {

		super();

		this.isLineCurve = true;

		this.type = 'LineCurve';

		this.v1 = v1;
		this.v2 = v2;

	}

	getPoint( t, optionalTarget = new Vector2() ) {

		const point = optionalTarget;

		if ( t === 1 ) {

			point.copy( this.v2 );

		} else {

			point.copy( this.v2 ).sub( this.v1 );
			point.multiplyScalar( t ).add( this.v1 );

		}

		return point;

	}

	// Line curve is linear, so we can overwrite default getPointAt
	getPointAt( u, optionalTarget ) {

		return this.getPoint( u, optionalTarget );

	}

	getTangent( t, optionalTarget = new Vector2() ) {

		return optionalTarget.subVectors( this.v2, this.v1 ).normalize();

	}

	getTangentAt( u, optionalTarget ) {

		return this.getTangent( u, optionalTarget );

	}

	copy( source ) {

		super.copy( source );

		this.v1.copy( source.v1 );
		this.v2.copy( source.v2 );

		return this;

	}

	toJSON() {

		const data = super.toJSON();

		data.v1 = this.v1.toArray();
		data.v2 = this.v2.toArray();

		return data;

	}

	fromJSON( json ) {

		super.fromJSON( json );

		this.v1.fromArray( json.v1 );
		this.v2.fromArray( json.v2 );

		return this;

	}

}

class LineCurve3 extends Curve {

	constructor( v1 = new Vector3(), v2 = new Vector3() ) {

		super();

		this.isLineCurve3 = true;

		this.type = 'LineCurve3';

		this.v1 = v1;
		this.v2 = v2;

	}

	getPoint( t, optionalTarget = new Vector3() ) {

		const point = optionalTarget;

		if ( t === 1 ) {

			point.copy( this.v2 );