Opengl pixel perfect 2D drawing - opengl

Question

I'm working on a 2d engine. It already works quite good, but I keep getting pixel-errors.
For example, my window is 960x540 pixels, I draw a line from (0, 0) to (959, 0). I would expect that every pixel on scan-line 0 will be set to a color, but no: the right-most pixel is not drawn. Same problem when I draw vertically to pixel 539. I really need to draw to (960, 0) or (0, 540) to have it drawn.
As I was born in the pixel-era, I am convinced that this is not the correct result. When my screen was 320x200 pixels big, I could draw from 0 to 319 and from 0 to 199, and my screen would be full. Now I end up with a screen with a right/bottom pixel not drawn.
This can be due to different things:
where I expect the opengl line primitive is drawn from a pixel to a pixel inclusive, that last pixel just is actually exclusive? Is that it?
my projection matrix is incorrect?
I am under a false assumption that when I have a backbuffer of 960x540, that is actually has one pixel more?
Something else?
Can someone please help me? I have been looking into this problem for a long time now, and every time when I thought it was ok, I saw after a while that it actually wasn't.
Here is some of my code, I tried to strip it down as much as possible. When I call my line-function, every coordinate is added with 0.375, 0.375 to make it correct on both ATI and nvidia adapters.
int width = resX();
int height = resY();
for (int i = 0; i < height; i += 2)
rm->line(0, i, width - 1, i, vec4f(1, 0, 0, 1));
for (int i = 1; i < height; i += 2)
rm->line(0, i, width - 1, i, vec4f(0, 1, 0, 1));
// when I do this, one pixel to the right remains undrawn
void rendermachine::line(int x1, int y1, int x2, int y2, const vec4f &color)
{
... some code to decide what std::vector the coordinates should be pushed into
// m_z is a z-coordinate, I use z-buffering to preserve correct drawing orders
// vec2f(0, 0) is a texture-coordinate, the line is drawn without texturing
target->push_back(vertex(vec3f((float)x1 + 0.375f, (float)y1 + 0.375f, m_z), color, vec2f(0, 0)));
target->push_back(vertex(vec3f((float)x2 + 0.375f, (float)y2 + 0.375f, m_z), color, vec2f(0, 0)));
}
void rendermachine::update(...)
{
... render target object is queried for width and height, in my test it is just the back buffer so the window client resolution is returned
mat4f mP;
mP.setOrthographic(0, (float)width, (float)height, 0, 0, 8000000);
... all vertices are copied to video memory
... drawing
if (there are lines to draw)
glDrawArrays(GL_LINES, (int)offset, (int)lines.size());
...
}
// And the (very simple) shader to draw these lines
// Vertex shader
#version 120
attribute vec3 aVertexPosition;
attribute vec4 aVertexColor;
uniform mat4 mP;
varying vec4 vColor;
void main(void) {
gl_Position = mP * vec4(aVertexPosition, 1.0);
vColor = aVertexColor;
}
// Fragment shader
#version 120
#ifdef GL_ES
precision highp float;
#endif
varying vec4 vColor;
void main(void) {
gl_FragColor = vColor.rgb;
}

Answer 1

In OpenGL, lines are rasterized using the "Diamond Exit" rule. This is almost the same as saying that the end coordinate is exclusive, but not quite...
This is what the OpenGL spec has to say:
http://www.opengl.org/documentation/specs/version1.1/glspec1.1/node47.html
Also have a look at the OpenGL FAQ, http://www.opengl.org/archives/resources/faq/technical/rasterization.htm, item "14.090 How do I obtain exact pixelization of lines?". It says "The OpenGL specification allows for a wide range of line rendering hardware, so exact pixelization may not be possible at all."
Many will argue that you should not use lines in OpenGL at all. Their behaviour is based on how ancient SGI hardware worked, not on what makes sense. (And lines with widths >1 are nearly impossible to use in a way that looks good!)

Answer 2

Note that OpenGL coordinate space has no notion of integers, everything is a float and the "centre" of an OpenGL pixel is really at the 0.5,0.5 instead of its top-left corner. Therefore, if you want a 1px wide line from 0,0 to 10,10 inclusive, you really had to draw a line from 0.5,0.5 to 10.5,10.5.
This will be especially apparent if you turn on anti-aliasing, if you have anti-aliasing and you try to draw from 50,0 to 50,100 you may see a blurry 2px wide line because the line fell in-between two pixels.