How to Draw a Circle with OpenGL and GLSL

How to Draw a Circle with OpenGL

If you've completed part 1 and 2 of this series, you should already be familiar with length and step. length will allow us to determine the distance of a fragment, relative to a pre-defined radius. And step will allow us to shade that pixel white if it falls within the radius' bounds, producing a white circle. We'll begin by writing some shader code, using functions you already know from the last chapter.

Filename: circle.frag

#ifdef GL_ES
precision lowp float;
#endif

uniform vec2 u_resolution;

float draw_circle(vec2 position, float radius) {
    return step(length(position), radius);
}

void main() {
    vec2 position = gl_FragCoord.xy / u_resolution;
    float circle = draw_circle(position, 0.3);
    vec3 color = vec3(circle);

    gl_FragColor = vec4(color, 1.0);
}

We will now explain each line of code, except for lines we've already explained in past chapters.

Line 7-9: We define a draw_circle function that accepts a position and a radius. We then pass those parameters into step. If the radius is less than the length of the vec2 position, this function will return a 0.0. In other words, if the length of the position is greater than the radius (outside the radius), return a 0.0. Otherwise, it is within the radius and should return a 1.0.

Line 12: We get the normalized position of the fragment/pixel that main() is currently processing. This calculation will run on every single fragment, so we will be dealing with millions of positions.

Line 13: We pass the position and a radius of 0.3 into our draw_cirle function. This will return a 1.0 for all pixels within the radius 0.3 from the bottom left corner of the screen, which we store into the vec3 color.

Line 15: We then assign color and an alpha of 1.0 to gl_FragColor, which will shade the pixel the appropriate color.

Run this shader on Linux with the glslViewer circle.frag command. Or within VisualStudio on Windows 10 and macOS.

You can attempt the calculations, yourself, to get a better understanding of how each pixel is shaded. Try it with a fragment at position (58,38):

1. With a screen 800px wide by 600px tall, (58,38) would get normalized to (0.0725,0.06333).
2. When passed into the length function, the square root of (0.0725² + 0.06333²) is 0.0962.
3. Because 0.0962 is less than (within) the radius of 0.3, that lower left positioned pixel gets shaded a solid white color.

If you were to calculate each pixel, manually, you would end up with the same image above. So while these calculations are all correct, we still have a part of a circle in the bottom left corner. To center the circle, we just need to offset the position by 0.5.

Filename: circle.frag

#ifdef GL_ES
precision lowp float;
#endif

uniform vec2 u_resolution;

float draw_circle(vec2 position, float radius) {
    return step(length(position), radius);
}

void main() {
    vec2 position = gl_FragCoord.xy / u_resolution;
    vec2 offset = vec2(0.5, 0.5);
    float circle = draw_circle(position - offset, 0.3);
    vec3 color = vec3(circle);

    gl_FragColor = vec4(color, 1.0);
}

Now with the same exercise as before:

1. With a screen 800px wide by 600px tall, (58, 38) would get normalized to (0.0725, 0.06333).
2. Line 14: We then offset the position (0.0725, 0.06333) - (0.5, 0.5) which results in (-0.4275, -0.43667).
3. When passed into the length function, the square root of (-0.4275² + -0.43667²) is 0.4388.
4. Because 0.4388 is greater than (outside) the radius of 0.3, that lower left positioned pixel that's outside the radius of the circle gets shaded a solid black color, this time.

And with a fragment positioned at the center of the screen:

1. With a screen 800px wide by 600px tall, (400, 300) would get normalized to (0.5, 0.5).
2. Line 14: We then offset the position (0.5,0.5) - (0.5, 0.5) which results in (0, 0).
3. When passed into the length function, the square root of (0.0² + 0.0²) is 0.0.
4. Because 0.0 is less than the radius of 0.3, that center positioned pixel that's within the radius of the circle gets shaded a solid white color.

Run this shader on Linux with the glslViewer circle.frag command and you should see the following image: