Java detect collision for fast moving objects

Question

I have problem, that balls that move too fast can fly through wall (walls are 4 pixels wide, and speed of ball occasionally is more than 400 pixels per second (which is more than 4 pixels per update assuming fps is 60)). I researched it on StackOverflow, but the solution for others is not suitable for me, as they are using rectangles, and i am using pixel collision. Here is method which returns if ball intersects with wall (method is in Ball class):

public boolean intersects(Wall w) {

    BufferedImage im1 = new BufferedImage (size, size, BufferedImage.TYPE_INT_ARGB);        // size is diameter of the ball
    BufferedImage im2 = new BufferedImage (size, size, BufferedImage.TYPE_INT_ARGB);
    Graphics2D g1 = im1.createGraphics();
    Graphics2D g2 = im2.createGraphics();
    g1.translate(-x + size/2, -y + size/2);         
    g2.translate(-x + size/2, -y + size/2);
    render(g1);
    w.render(g2);
    g1.dispose();
    g2.dispose();

    for (int x = 0; x < im1.getWidth(); x++){
        for (int y = 0; y < im1.getHeight(); y++){
            Color c1 = new Color(im1.getRGB(x, y), true);
            Color c2 = new Color(im2.getRGB(x, y), true);
            if (c1.getAlpha() != 0 && c2.getAlpha() != 0){
                return true;
            }
        }
    }

    return false;

}

Here is how ball is drawn:

public void render(Graphics2D g) {
    color = new Color (Color.HSBtoRGB(hue, 0.5f, 0.5f));
    g.setColor (color);
    g.fillOval((int)(x-size/2), (int) (y-size/2), size, size);
}

The wall is simply defined as 2 points, and here is how wall is drawn:

public void render(Graphics2D g2) {
    g2.setColor(new Color(r, g, b));
    g2.setStroke(new BasicStroke(width));     //width = 4
    g2.draw(new Line2D.Float(p1.x, p1.y, p2.x, p2.y));
}

Answer 1

I have a couple of quick ideas that you might want to attempt.

Why not check the endpoints against the dimensions of the wall (some simple algebra and I think what you might already be trying to do). If you need help with the algebra involved I'll include a link below. Basically just record the starting point of the ball (prior to moving), and on update check the old location versus the estimated location, and run a function to see if a collision occurs. This will become tricky however if you want realistic physics.

https://gamedev.stackexchange.com/questions/26004/how-to-detect-2d-line-on-line-collision

In the above link, just assume your walls are one line, and the previous coordinates and the expected next coordinates of the ball form the other line. This method works very well if you only have the ball moving in straight lines.

Your only alternative might be to have two simultaneous models running (basically a visual space which you have in showing the ball and walls, and a virtual setup checking the physics behind what you are showing.