Precision loss when transforming from cartesian to isometric
- by Justin Skiles
My goal is to display a tile map in isometric projection. This tile map has 25 tiles across and 25 tiles down. Each tile is 32x32. See below for how I'm accomplishing this.
World Space
World Space to Screen Space Rotation (45 degrees)
Using a 2D rotation matrix, I use the following:
double rotation = Math.PI / 4;
double rotatedX = ((tileWorldX * Math.Cos(rotation)) - ((tileWorldY * Math.Sin(rotation)));
double rotatedY = ((tileWorldX * Math.Sin(rotation)) + (tileWorldY * Math.Cos(rotation)));
World Space to Screen Space Scale (Y-axis reduced by 50%)
Here I simply scale down the Y value by a factor of 0.5.
Problem
And it works, kind of. There are some tiny 1px-2px gaps between some of the tiles when rendering. I think there's some precision loss somewhere, or I'm not understanding how to get these tiles to fit together perfectly. I'm not truncating or converting my values to non-decimal types until I absolutely have to (when I pass to the render method, which only takes integers). I'm not sure how to guarantee pixel perfect rendering precision when I'm rotating and scaling on a level of higher precision. Any advice? Do I need to supply for information?
