Question

I’m trying to write a spraypaint type program but I have forgotten all my maths.

I need some sort of probability equation to pick pixels near where the user clicks. So the probability should be high near the center and then decrease as the distance from the center gets higher and once you reach a certain distance the probability should be zero.
Also the probability at the center should be a smooth curve (if you know what I mean)

Answer 1

I’m not sure which language you’re coding in, so here’s some pseudo-code. I will assume you know the corresponding syntax in the language you’re coding in.

// Parameters:
// Radius is the radius of the brush in pixels
// Strength is a double ranging 0.0 to 1.0 and multiplies the probability of a pixel being painted
function spraypaint(int radius, double strength) {
    strength = (strength * 2) - 1; //Change strength from 0.0->1.0 to -1.0->1.0 for logical application

    // For each pixel within the square...
    for(int x = -radius; x < radius; x++) {
        for(int y = -radius; y < radius; y++) {
            double distance = sqrt(x*x + y*y); // Get distance from center pixel
            double angle = 90*(distance/radius); // Get angle of "bell curve"
            double probability = sine(angle); // Determine probability of filling in this pixel

            // Apply additional probability based on strength parameter
            if(strength >= 0.0)
                probability += ((1-probability) * strength);
            else
                probability += probability * strength;

            if(distance > radius) {
                continue;   // Skip this pixel if it's out of the circle's radius
            }

            if(random(0.0 to 1.0) < probability) { // If we random a decimal lower than our probability
                setPixel(mouse.x + x, mouse.y + y, "Black"); // Draw this pixel
            }
        }
    }
}

The basic idea is:

Iterate through each pixel and...

1. Find its distance from the center pixel (The clicked pixel).
2. Get distance/radius (0.0 to 1.0) and find the corresponding sine, creating a
   smooth probability curve.
3. Apply the supplied strength to the probability.
4. Pull a random double 0.0 to 1.0 and draw the pixel if it's within our probability.