Finding the footprint of an isometric entity

Question

I'm working on making a 2D isometric engine in Java because I like suffering, I guess. Anyways, I'm getting into collision detection and I've hit a bit of a problem.

Characters in-game are not restricted to movement from tile to tile - they move freely. My problem is that I'm not sure how to stop a player from colliding with, say, a crate, without denying them access to the tile.

For instance, say the crate was on .5 of a tile, and then the rest of the crate was off the tile, I'd like the player to be able to move on to the free .5 of the tile instead of the entire tile becoming blocked.

The problem I've hit is that I'm not sure how to approximate the size of the footprint of the object. Using the image's dimensions don't work very well, since the object's "height" in gamespace translates to additional floorspace being taken up by the image.

How should I estimate an object's size? Mind, I don't need pixel-perfect detection. A rhombus would work fine.

I'm happy to provide any code you might need, but this seems like a math issue.

Answer 1

From the bounding rectangle of the sprite, you can infer the height of a rhombus that fits inside, but you cannot precisely determine the two dimensions on the floor, as each dimension contributes equally to width and height of the sprite. However, if you assume that the base of the rhombus square then you can determine the length of its side as well.

If the sprite is W pixels wide and H pixels high, the square base of the rhombus has a side of W / sqrt(3) and the height of the rhombus will be H - (W / sqrt(3)). This image of some shapes in isometric projection can be helpful to understand why these formulas work.