How to draw a circle on a plane with OSL (Open Shading Language)?

Question

This is my very first day of learning Open Shading Language. I have watched few videos in Youtube and learned a little.

Right now, for learning purpose only, I want to know what OSL codes can draw one black circle against the white ground of plane, but I can't find any tutorial to teach me that.

Next, I want to know how to do a circle grid like this below.

And this too.

Answer 1

These scripts will create two nodes. The first one is for the grid and the second one for the circle. By changing the size of the grid, you will have more or less circles. By changing the radius, you will have bigger or smaller circles.

shader Tiles2D(
    point Vector = P,
    float Size = 1,
    float Offset = 0,
    output vector Tiles = vector(0,0,0)
)
{
   Tiles = Vector * Size;
   Tiles[2] = 0;
   Tiles[0] += step(1,mod(Tiles[1],2)) * Offset;
   Tiles -= floor(Tiles);

}

shader Circle(
            point Vector = P,
            float Radius = 0.5,
            output float Fac = 0)
{
    vector st = Vector;
    vector dist = st - vector(0.5,0.5,0);
    Fac = smoothstep(Radius*0.99, Radius * 1.01,dot(dist,dist)*4);
}