如何在netpbm图像中绘制平滑像素？

Question

I just wrote a small netpbm parser and I am having fun with it, drawing mostly parametric equations. They look OK for a first time thing, but how can I expand upon this and have something that looks legit? This picture is how my method recreated the Arctic Monkeys logo which was just

0.5[cos(19t) - cos(21t)] (I was trying to plot both cosines first before superpositioning them)

It obviously looks very "crispy" and sharp. I used as small of a step size as I could without it taking forever to finish. (0.0005, takes < 5 sec)

The only idea I had was that when drawing a white pixel, I should also draw its immediate neighbors with some slightly lighter gray. And then draw the neighbors of THOSE pixels with even lighter gray. Almost like the white color is "dissolving" or "dissipating".

I didn't try to implement this because it felt like a really bad way to do it and I am not even sure it'd produce anything near the desirable effect so I thought I'd ask first.

EDIT: here's a sample code that draws just a small spiral

the draw loop:

for (int t = 0; t < 6 * M_PI; t += 0.0005)
    {
        double r = t;
        new_x = 10 * r * cosf(0.1 * M_PI * t);
        new_y = -10 * r * sinf(0.1 * M_PI * t);
        img.SetPixel(new_x + img.img_width / 2, new_y + img.img_height / 2, 255);
    }

//img is a PPM image with magic number P5 (binary grayscale)

SetPixel:

void PPMimage::SetPixel(const uint16_t x, const uint16_t y, const uint16_t pixelVal)
{
    assert(pixelVal >= 0 && pixelVal <= max_greys && "pixelVal larger than image's maximum max_grey\n%d");
    assert(x >= 0 && x < img_width && "X value larger than image width\n");
    assert(y >= 0 && y < img_height && "Y value larger than image height\n");


    img_raster[y * img_width + x] = pixelVal;
}

This is what this code produces

Answer 1

A very basic form of antialiasing for a scatter plot (made of points rather than lines) can be achieved by applying something like stochastic rounding: consider the brush to be a pixel-sized square (but note the severe limitations of this model), centered at the non-integer coordinates of the plotted point, and compute its overlap with the four pixels that share the corner closest to that point. Treat that overlap fraction as a grayscale fraction and set each pixel to the largest value for a large number of points approximating a line, or do alpha blending for a small number of discrete points.