I read this topic and immediately the figure 0.375 popped into my head. Reading
appendix H of the Red book has revealed why:
If exact two-dimensional rasterization is desired, you must carefully specify both the orthographic projection and the vertices of primitives that are to be rasterized. The orthographic projection should be specified with integer coordinates, as shown in the following example:
gluOrtho2D(0, width, 0, height);
where width and height are the dimensions of the viewport. Given this projection matrix, polygon vertices and pixel image positions should be placed at integer coordinates to rasterize predictably. For example, glRecti(0, 0, 1, 1) reliably fills the lower left pixel of the viewport, and glRasterPos2i(0, 0) reliably positions an unzoomed image at the lower left of the viewport. Point vertices, line vertices, and bitmap positions should be placed at half-integer locations, however. For example, a line drawn from (x1, 0.5) to (x2, 0.5) will be reliably rendered along the bottom row of pixels int the viewport, and a point drawn at (0.5, 0.5) will reliably fill the same pixel as glRecti(0, 0, 1, 1).
An optimum compromise that allows all primitives to be specified at integer positions, while still ensuring predictable rasterization, is to translate x and y by 0.375, as shown in the following code fragment. Such a translation keeps polygon and pixel image edges safely away from the centers of pixels, while moving line vertices close enough to the pixel centers.
glViewport(0, 0, width, height);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(0, width, 0, height);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.375, 0.375, 0.0);
/* render all primitives at integer positions */
Does this help in your situation?