GDI+ Line Drawing Algorithm

Question

I cannot understand the way GDI+ is drawing line on a surface, may be it has some algorithm to do it.

For ex. lets take a surface 10x10 px.

  Bitmap img = new Bitmap(10, 10);

Now lets draw a line on this surface, with width 5px and top offset 5px.

  using (var g = Graphics.FromImage(img))
     {
        g.Clear(Color.White);
        var pen = new Pen(Color.Brown);
        pen.Width = 5;
        g.DrawLine(pen, 0F, 5F, 10F,  5F);
     }

We will get:

The drawing didn't begin at pixel #5, it began from pixel #4. It is obvious, that the start point is calculated separately. But how?

I've tried to get a regularity, and got this:

  y = offset + width/2 - 1

where y is real start point y, offset is selected start point y.

But in some cases this doesn't work. For example, lets take width=6, selected top offset = 0, we will get y=2, and it will be drawn this way:

It must show 6 pixels but it didn't.

So there must be more general algorythm for selecting the start point, but I really have no idea aboit what it can be. Any help appreciated.

Answer 1

There is no offset in the line drawing. The co-ordinates you specify in the DrawLine method define the centre of the line. The top pixel is y - width / 2 and the bottom is y - width / 2 + width - 1. That second formula takes into account the fact that width / 2 is rounded down. Also, the top line is y = 0 and the bottom line is y = 9. So, for you first line:

top = 5 - (5 / 2) = 3
bottom = 5 - (5 / 2) + 5 - 1 = 7

and the second line:

top = 2 - (6 / 2) = -1
bottom = 2 - (6 / 2) + 6 - 1 = 4

The top edge is clipped to the edge of the bitmap so the line width is reduced.

Answer 2

In the first example, it looks like a line with a width of 5 pixels, centered on row 5 (counting starts at 0, not 1). This seems like a reasonable outcome.

In the second example, it looks like a line of width 6, centered between rows 1 and 2, where the top row is cut off, because it extends beyond the borders of the image.