点在圆内碰撞响应：如何将点保持在圆内？

Question

I have given a diagram of my current small problem that I need help with. My main purpose is to keep the point from going outside the circle. Nothing else.

The center of the circle is positioned at (x, y).

I only solved a little bit of the problem, and that is the collision detection part of my problem, as given below:

public void bound(Point p, Circle c){
    double distance = Math.hypot(p.x - c.x, p.y - c.y);
    if (distance >= c.radius){
        //Clueless from here on out.
    }
}

The part where I left a comment is the spot I couldn't figure anything out. I did tried to set the point's velocityX and velocityY to 0, but I realized the point will just stay put whenever it touches the circle.

So, I'm sort of stuck.

Answer 1

I have resolved this issue.

public void reflect(Hole h){
    //R = -2*(V dot N)*N + V
    //N is normalized.
    double nx = (this.position[0]+this.diameter/2) - (h.x+16);
    double ny = (this.position[1]+this.diameter/2) - (h.y+16);
    double nd = Math.hypot(nx, ny);
    if (nd == 0)
        nd = 1;
    nx /= nd;
    ny /= nd;
    double dotProduct = this.speed[0]*nx+this.speed[1]*ny;
    this.speed[0] += (float)(-2*dotProduct*nx);
    this.speed[1] += (float)(-2*dotProduct*ny);
}

public void reflectResponse() {
    for (int i = 0; i <= 1; i++) {
        position[i] -= speed[i];
        speed[i] *= 0.992f;
    }
}

I tried Oli Charlesworth's method from the comments, but it made things more... "complicated" than I expected. Someone else mentioned I used a completely 100%, vector-based algorithm, since I'm relying a lot on vector-based movements.

TIPS TO THOSE WHO DO READ THIS:

1. If you're working on object movements and collisions with vectors, seek vector-based algorithms.
2. If you're working with angles (either degrees or radians), use Oli Charlesworth's method.