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How to find visible tiles using a perspective projection?

Mark Speir · 2013-04-07T00:49:10

I am working on a project that uses 3D tiles, all 1 unit in size, with a top-down perspective projection (think of a typical screen aligned 2D tile map, but with a perspective projection and tiles not constrained to 2D planes). I need to be able to find the minimum and maximum row and column extents to ensure that I am drawing only visible tiles. I've considered using bounding volumes, but that would require iterating over what could be a massive data set, in which only a tiny fraction would be visible. I could use a quad tree, but even that is overkill. With a 2D tile map using a orthographic projection, finding the row and column extents is easy. Take a rectangle in pixels corresponding to the location of the viewport in the tile map and divide the extents by the width and height of the tiles. This doesn't work so well with a perspective projection. How do I do this?

General and Gameplay Programming Programming

Started by MarkS_ March 23, 2013 12:58 AM

12 comments, last by MarkS_ 11 years ago

MichaelNIII

195

April 03, 2013 10:31 PM

Your issue I believe is that your doing soacahtoa with degrees and not radians.

MarkS_

3,509

Author

April 04, 2013 08:37 PM

I am using degrees, but am converting to radians.

30° in radians = 0.5235
tan(0.5235) = 0.57735
5 / 0.57735 = 8.66025
8.66025 * 2 = 17.32050

MichaelNIII

195

April 05, 2013 08:32 PM

I'm sorry. I feel like a tard. Anyways. X = (tan(fov/2)*height)*2

MarkS_

3,509

Author

April 07, 2013 12:49 AM

I was looking at my projection matrix and noticed that the location[0][0] was exactly 1/100 the correct projected tile width. Looking at glm::perspective, I came up with this:

range = tan(fov / 2) * z_near;
right = range * aspect;
left = -range * aspect;
width = ((2 * z_near) / (right - left)) * (z_far * z_near);

I would still like to know how to get the fov from the projected size.

How to find visible tiles using a perspective projection?

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How to find visible tiles using a perspective projection?

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