Thick Line Drawing

I’m making a program that draws lines by coloring in each pixel one at a time to form the line (using Bresenhan’s algorithm) and the line can have thickness from 1 to 15. My problem is when I connect two thick lines together (thickness > 1) sometimes there are gaps at the connecting points of the line and I do not have a smooth edge. How would I overcome this problem?

I guess it depends on how you fill in the lines, I don’t think you have any problem with OpenGL but with your algorithm.