GraphicsPath - Why does order of AddLine methods matter

Question

I am drawing a triangle with the following code

int x = x coordinate for center;
int ax = x coordinate for left;
int bx = x coordinate for right;
int top = y coordinate for top;
int bottom = y coordinate for bottom;

//           (x, top)
//(ax, bottom)      (bx, bottom) 

GraphicsPath path = new GraphicsPath();
// _
path.AddLine(ax, bottom, bx, bottom);
// /
path.AddLine(ax, bottom, x, top);
// \
path.AddLine(bx, bottom, x, top);
// order of drawing is _ / \ (bottom line, left side, right side)

When I call DrawPath, it always draws my lines, no matter the order. But when I call FillPath, it does nothing. Only when my order is / _ \ or \ _ / does my triangle actually fill. Why is this?

Answer 1

It turns out that the answer I posted originally didn't really solve the problem and that it worked on my machine because of an additional change I introduced, which is to change the FillMode:

GraphicsPath path = new GraphicsPath(FillMode.Winding);

When you use the Winding mode, the algorithm will detect a closed path even if you didn't add the lines in order.