Draw a bezier curve and shoot a projectile in same direction

Questions & Answers
1

Hello!

I’m actually trying to make a similar control like Angry Bird. I want to make a bezier’s curve renderer in real time acording to input touch. And when input ends I want to shoot an arrow exactly in the same direction. Which it’s best way to make this? I’ve already have this mechanism almost working with a Line Renderer and Vector3.Lerp but I want to change it to a curve.

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2

This code gives you a point on a bezier curve, given the 4 control points and a value between 0 and 1 (0 being the start of the curve, 1 the end).

public class Bezier {
    public static Vector2 interpolate(Vector2 start, Vector2 end, Vector2 A, Vector2 B, float f) {
    	Vector2 a = Vector2.Lerp(start, A, f);
    	Vector2 b = Vector2.Lerp(A, B, f);
    	Vector2 c = Vector2.Lerp(B, end, f);
    
    	Vector2 d = Vector2.Lerp(a, b, f);
    	Vector2 e = Vector2.Lerp(b, c, f);
    
    	return Vector2.Lerp(d, e, f);
    }
}

But for this, a bezier curve is not really applicable, since you only have two control points (the start position and a vector based of the start velocity). For this I would use a basic euler integration:

Vector2 startPos, startVel;              //these would be set via your touch input
Vector2 gravity = new Vector2(0, -1);    //change as needed
int steps = 10;                          //how many points
float distance = 10;                     //how far

Vector2[] curvePoints = new Vector2[steps];

curvePoints[0] = startPos;
Vector2 tmpVel = startVel;

float h = distance/steps;

for (int i = 1; i < steps; ++i) {
    curvePoints _= curvePoints[i-1] + h * tmpVel;_

tmpVel += h * gravity;
}
The curvePoints array now holds the points that can be drawn either via a LineRenderer or any other way of visualisation.

3

I Like to use a method like this, having it possible to poll on any part of the curve.
Its based on y = gt^2/2 + vit.

	float gravity=-.91f;
	Vector2 PolCurve(Vector2 position,Vector2 speed,float time)
	{ 
		return (new Vector2(position.x + speed.x*time,position.y + gravity * (Mathf.Pow(time,2f))/2f + speed.y * time));
	}

That way you can also have them moving along the line like some games have by using an offset on the time.