# How to handle player slowness while moving up and down in a Top Down game with angled ortho camera and angled sprite due to stretching of ground?

So i'm making a 2D top down game setup in 3D using tilted Sprites and angled orthographic camera.

My camera setup is as shown.

In my game I have the floor flat on the X/Z plane with walls/characters rotated +45 degrees about the X axis. The orthographic camera is pointing down also at 45 degrees about the x axis, parallel with my walls/characters.

As a result, I dont see any distortion for players/characters since they face the camera directly on, while the ground however sees a distortion of sqrt(2) shorter. This makes sense considering how an orthographic camera works. To fix this, I've made my Tilemap set up with X:1 Y:1 Z:Sqrt(2) so that each tile is stretched on the Z axis by Sqrt(2) to compensate for this distortion.

All looks well with only one problem now... foreshortening with regards to movement: Forward and backwards movements of objects/characters along the z axis are perceived to be slower than movements left/right on the x axis. This makes sense because while each tile is perceived to be a square in the camera view thanks to scaling Z on the tilemap by sqrt(2), the real world tile is, well, sqrt(2) times taller than its width, so obviously it takes longer to travel forwards / backwards.

How do i correct this?

Myself, I'd recommend getting rid of the stretching and leaning in your game world.

Make the tilemap uniformly scaled 1x, and make any upright characters/walls/trees stand perpendicular, not leaned over.

That way both the z and y axis are equally foreshortened in your camera's view by a factor of $$\\frac 1 {\sqrt{2}}\$$.

Then, modify your camera's projection matrix to add a vertical scale factor of $$\\sqrt{2}\$$ to compensate. This applies the stretching in the render step alone, so it does not interfere with your gameplay/movement logic or force you to do fiddly things like leaning sprites diagonally.

In Unity it would look something like this:

Matrix4x4 mat  = camera.projectionMatrix;
mat[1, 1] = Mathf.sqrt(2) / camera.orthographicSize;
camera.projectionMatrix = mat;


If the tile is sqrt(2) times taller than wide, then multiply z-axis motion by sqrt(2)