class QuadBezierLine {
	constructor(_p0, _p1, _p2, _step, _uniformSpeedMode) {
		this.step=_step;
		this.points=[];
		this.uniformSpeedMode=_uniformSpeedMode;
		this.updatePoints(_p0, _p1, _p2);
	}
	
	//Speed(t_) = Sqrt[A*t*t+B*t+C]
	speed(t) {
		return Math.sqrt(this.A * t * t + this.B * t + this.C);
	}
	
	//Length(t) = Integrate[Speed[t], t]
	//Length(t_) = ((2*Sqrt[A]*((2*A*t + B)*Sqrt[A*t^2 + B*t + C] - B*Sqrt[C]) +
	//	(B^2 - 4*A*C)*(Log[B + 2*Sqrt[A]*Sqrt[C]] - 
	//	Log[B + 2*A*t + 2*Sqrt[A]*Sqrt[A*t^2 + B*t + C]]))/(8*A^(3/2)))
	length(t) {
		let temp1 = Math.sqrt(this.C + t * (this.B + this.A * t));
		let temp2 = (2 * this.A * t * temp1 + this.B * (temp1 - Math.sqrt(this.C)));
		let temp3 = Math.log(this.B + 2 * Math.sqrt(this.A) * Math.sqrt(this.C));
		let temp4 = Math.log(this.B + 2 * this.A * t + 2 * Math.sqrt(this.A) * temp1);
		let temp5 = 2 * Math.sqrt(this.A) * temp2;
		let temp6 = (this.B * this.B - 4 * this.A * this.C) * (temp3 - temp4);
		return (temp5 + temp6) / (8 * Math.pow(this.A, 1.5));
	}
	
	//u'=u-(Length(u)-len)/Speed(u)
	invertLength(u0, len) {
		let u1 = u0, u2;
		do {
			u2 = u1 - (this.length(u1) - len) / this.speed(u1);
			if (Math.abs(u1 - u2) < 0.000001)
				break;
			u1 = u2;
		} while (true);
		return u2;
	}
	
	updatePoints(_p0, _p1, _p2) {
		this.p0=_p0;
		this.p1=_p1;
		this.p2=_p2;
		
		let ax = this.p0.x - 2 * this.p1.x + this.p2.x;
		let ay = this.p0.y - 2 * this.p1.y + this.p2.y;
		let bx = 2 * this.p1.x - 2 * this.p0.x;
		let by = 2 * this.p1.y - 2 * this.p0.y;

		this.A = 4 * (ax * ax + ay *ay);
		this.B = 4 * (ax * bx + ay *by);
		this.C = bx * bx + by * by;
		
		this.points.length = 0;
		let totalLength = this.length(1);
		
		for (let index = 1; index < this.step; index++) {  
			let t = index / this.step;
			
			if(this.uniformSpeedMode) {
				t = this.invertLength(t, totalLength*t);
			}
			
			let x = (1-t)*(1-t)*this.p0.x+2*(1-t)*t*this.p1.x+t*t*this.p2.x;
			let y = (1-t)*(1-t)*this.p0.y+2*(1-t)*t*this.p1.y+t*t*this.p2.y;
			
			this.points.push({x:x, y:y});
		}
	}
	
	draw() {
		this.points.forEach(pt => {
			fill('green');
			ellipse(pt.x, pt.y, 5, 5);
		});
	}
}