I want to draw 2d circle using line list, which will look something like that, but without empty spaces to look like the solid border:

And also I want to draw filled circle usign triangle list or strip.

Does anyone could help me with algorithms for that?

Well, I know about cos and sin, but I also wish to know how to shift points smoothly that there was no gaps between them? Because even if I rotate points only on 1 degree, It will still have gaps and circle will not looks solid if I want to draw it with horizontal lines like in the screenshot above.

That alternating line texturing is, well: Texturing. So why not use a texture ? A 1x2 would suffice (wrapped). Make sure texcoords are aligned and scaled to screen pixels (if that's what you're after). Or do it procedurally in the pixel shader grabbing the screen coord, as suggested.

Now draw a triangulated ring with e.g. a tri-strip. Alternatively mask with another ring shaped texture (can be done procedurally, too).

Edit: Ignore the above, I was fixated on the alternatiing line pattern. Here's some code for triangulating a ring.

I found an algorithm to draw filled and empty circles:

Here is one for filled circle:

void DrawFilledCircle(Vector3 startPoint, Vector2 radius, Color color)
      {
         List<VertexPositionTextureColor> circle = new List<VertexPositionTextureColor>();
         //Center of the circle
         float xPos = startPoint.X;
         float yPos = startPoint.Y;
         
         float x1 = xPos;
         float y1 = yPos;

         for (int i = 0; i <= 363; i += 3)
         {
            float angle = (i / 57.3f);
            float x2 = xPos + (radius.X * (float)Math.Sin(angle));
            float y2 = yPos + (radius.Y * (float)Math.Cos(angle));
            circle.Add(new VertexPositionTextureColor(new Vector3(xPos, yPos, 0), Vector2.Zero,  color));
            circle.Add(new VertexPositionTextureColor(new Vector3(x1, y1, 0), Vector2.Zero, color));
            circle.Add(new VertexPositionTextureColor(new Vector3(x2, y2, 0), Vector2.Zero, color));
            
            y1 = y2;
            x1 = x2;
         }

         for (int i = 0; i < circle.Count; i++)
         {
            var vertex = circle[i];
            vertex.TextureCoordinate = new Vector2(0.5f + (vertex.Position.X - startPoint.X) / (2 * radius.X),
                             0.5f + (vertex.Position.Y - startPoint.Y) / (2 * radius.Y));
            circle[i] = vertex;
         }

         circle2Dfilled = Buffer.Vertex.New(GraphicsDevice, circle.ToArray());
      }

And here is an algorithm for empty circle:

void DrawEmptyCircle(Vector3 startPoint, Vector2 radius, Color color)
      {
         List<VertexPositionColor> circle = new List<VertexPositionColor>();
         float X, Y;

         var stepDegree = 0.3f;
         for (float angle = 0; angle <= 360; angle += stepDegree)
         {
            X = startPoint.X + radius.X * (float)Math.Cos((angle));
            Y = startPoint.Y + radius.Y * (float)Math.Sin((angle));
            Vector3 point = new Vector3(X, Y, 0);
            circle.Add(new VertexPositionColor(point, color));
         }
         circle2D = Buffer.Vertex.New(GraphicsDevice, circle.ToArray());
      }

The only thing here is that I dont know how to control thickness of the circle border. It depends from stepDegree value. If it bigger, the border also bigger, but dependency is not so obvious. For ex, value 0.1 will give me at least 2-3 pixels width for the circle border. So, I have no idea how to correctly control border thickness with this.

If anyone have idea, you are welcome.

Forgot to mention that filled circle I draw with TriangleStrip and empty circle - with LineStrip.

float4 RingShortPS(float2 tex: TEXCOORD) : SV_Target
{
    float inner = 0.8;             // relative inner radius. Could be from a constant buffer.
    float r = length(2*tex-1);     // sign-normalize tex-coords (could be done in VS)
    return min(r < 1, r > inner);  // difference of the two circle disks
}

Looks cool, but I want to create the same in my code.

I tried to do it with triangles, but fail. Maybe you can prompt me an algorithm for that?

Yeah, please ignore, this was just for fun.

Look at the code I linked to, it's HLSL but consider it pseudo-code. That's the algorithm. It's a triangle-strip, alternating inner and outer side of the ring. tristream is your list of vertices. It's basically two circles at once, with different radii.

I tried to make something similar, but end up with this:

float thickness = 10;
         for (int i = 0; i <= 363; i++)
         {
            float x = startPoint.X + (radius.X * (float)Math.Cos(MathUtil.DegreesToRadians(i)));
            float y = startPoint.Y + (radius.Y * (float)Math.Sin(MathUtil.DegreesToRadians(i)));
            circle.Add(new VertexPositionColor(new Vector3(x, y, 0), color));
            x += thickness;
            circle.Add(new VertexPositionColor(new Vector3(x, y, 0), color));
            x = startPoint.X + (radius.X * (float)Math.Cos(MathUtil.DegreesToRadians(i)));
            y = startPoint.Y + (radius.Y * (float)Math.Sin(MathUtil.DegreesToRadians(i)));
            circle.Add(new VertexPositionColor(new Vector3(x, y+ thickness, 0), color));

         }