Shader patterns

float frequency = .5;
float trianglewave = abs(2 * frac(x * frequency) - 1); // repeating triangle wave /\/\/\...
float squarewave = round(abs(2 * frac(x * frequency + .25) - 1)); // repeating square wave

float FilteredStep(float edge, float x, float fw)
{
    return saturate((x + fw / 2 - edge) / fw);
}

// Euclid length because built-in does abs(ddx(x)) + abs(ddy(y))
float widthU = fwidth(u);
float widthV = fwidth(v);
float combinedWidth = length(vec2(widthU, widthV));

float aaStep(float compValue, float gradient)
{
        float halfChange = fwidth(gradient) / 2;
        // base the range of the inverse lerp on the change over one pixel
        float lowerEdge = compValue - halfChange;
        float upperEdge = compValue + halfChange;
        // inverse lerp
        float stepped = (gradient - lowerEdge) / (upperEdge - lowerEdge);
        stepped = saturate(stepped);
        return stepped;
}