Orthographic unit translation mismatch on grid (e.g. 64 pixels translates incorrectly)

I am looking for some insight into a small problem with unit translations on a grid.

Update and Solved

I solved my own issue. See below for details. Everything in this part of the post turned out to be correct. If anything it can act as a miniature tutorial / example / help for the next person.

Setup

• FBO, VAO, VBO
• 512x448 window
• 64x64 grid
• gl_Position = projection * world * position;
• projection is defined by ortho(-w/2.0f, w/2.0f, -h/2.0f, h/2.0f); This is a textbook orthogonal projection function.
• world is defined by a fixed camera position at (0, 0)
• position is defined by the sprite's position.

Problem

In the screenshot below (1:1 scaling) the grid spacing is 64x64 and I am drawing the unit at (64, 64), however the unit draws roughly ~10px in the wrong position. I've tried uniform window dimensions to prevent any distortion on the pixel size, but now I am a bit lost in the proper way in providing a 1:1 pixel-to-world-unit projection. Anyhow, here are some quick images to aide in the problem.

I decided to super-impose a bunch of the sprites at what the engine believes is 64x offsets.

When this seemed off place, I went about and did the base case of 1 unit. Which seemed to line up as expected. The yellow shows a 1px difference in the movement.

What I Want

Ideally moving in any direction 64-units would output the following (super-imposed units):

Vertices

It would appear that the vertices going into the vertex shader are correct. For example, in reference to the first image the data looks like this in the VBO:

 x y x y ---------------------------- tl | 0.0 24.0 64.0 24.0 bl | 0.0 0.0 -> 64.0 0.0 tr | 16.0 0.0 80.0 0.0 br | 16.0 24.0 80.0 24.0 

For sake of completeness here is the actual array corresponding to the above movements:

 x y z w r g b a s t ------------------------------------------------------------- tl | 0.0 23.0 0.0 1.0 0.0 0.0 0.0 1.0 0.14210527 0.62650603 bl | 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.14210527 0.76506025 tr | 16.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.2263158 0.76506025 br | 16.0 23.0 0.0 1.0 0.0 0.0 0.0 1.0 0.2263158 0.62650603 ------------------------------------------------------------- ------------------------------------------------------------- tl | 64.0 24.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.21084337 bl | 64.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.3554217 tr | 80.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.08421053 0.3554217 br | 80.0 24.0 0.0 1.0 0.0 0.0 0.0 1.0 0.08421053 0.21084337 // side bar: I know that I have unnecessary data with having a z-axis. // The engine flips between perspective and orthogonal and I // haven't selectively started pruning data. 

Projection Matrix

The projection matrix for the 512x448 window looks like this:

0.00390625 0.0 0.0 0.0 0.0 0.004464286 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 1.0 

and is constructed with a textbook orthogonal projection function:

ortho(-w/2.0f, w/2.0f, -h/2.0f, h/2.0f); // explicitly: ortho(-512/2.0f, 512/2.0f, -448/2.0f, 448.0f ortho(float left, float right, float bottom, float top) { projection.setIdentity(); projection.m00 = 2.0f / (right - left); projection.m11 = 2.0f / (top - bottom); projection.m22 = -1; projection.m30 = -(right + left) / (right - left); projection.m31 = -(top + bottom) / (top - bottom); projection.m32 = 0; } 

World-view Matrix

The camera's position is just a translation matrix which in this case I just offset by -w/2 and -h/2 to be zero relative to center.

1.0 0.0 0.0 -256.0 0.0 1.0 0.0 -224.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 

Solutions I have attempted

1. player.moveRight() would move 1-unit with the aspect ratio factored into the equation. So: gridWidth = 64 / 1.14f. Movement did not fit within the grid.

2. Forced a 512x512 window with a matching orthogonal projection.

3. Tried various magic numbers and tried to draw correlations between the two.

With that said, all I am left to believe is that I am munging up my actual projection. So, I am looking for any insight into maintaining the 1:1 pixel-to-world-unit projection.