OpenGL Polygons...

I'm drawing a polygon using OpenGL:

Code:

---

glBegin(GL_POLYGON);
for (theta = 0; theta < 2 * pi; theta += 0.5)
{
  point = Centre + Vector(theta, 50);
  WindowToGlCoords(MakeWindowCoords(point)).glVertex3d();
}
glEnd();

---

Centre is of type Vector which is a class that deals with mathematical vectors. For example, centre could lie somewhere near the centre of the screen. The constructor of Vector that takes two coordinates takes an angle and a magnitude. But basically, you don't have to worry too much about that bit because I know the coordinates are coming out right.

The problem is, If I have GL_POLYGON_SMOOTH enabled I end up with faint lines from the first vertex of the polygon to each other polygon, presumably where its been split up into tris for drawing.

Does anybody know how this problem can occur, and how to fix it? (or any other information / places i should look!!)

Thanks all!

-jEFF