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L. Spiro

[Tutorial] Instant-Insertion Quadtrees

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Great tutorial!

Wit this technique, are my world coordinates forced to be from 0 - 256? And objects will only be spatially sorted at a resolution of (1/256)? Edited by web383

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Great tutorial!

Wit this technique, are my world coordinates forced to be from 0 - 256? And objects will only be spatially sorted at a resolution of (1/256)?

 

That would make it very limited, wouldn't it? It's 256 in his example since it's easier to show how it works in 8 bits. You can use 16 or 32 bit types if you want, for a much larger area.

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Wit this technique, are my world coordinates forced to be from 0 - 256?

No, you just need to apply a suitable conversion factor.

And objects will only be spatially sorted at a resolution of (1/256)?

Yes. That should be plenty to significantly speed up collision detection, or any other naive O(N^2) process.

You can use 16 or 32 bit types if you want, for a much larger area.

You will run out of memory - it's not feasible to preallocate enough storage. If you really need a quad-tree with depth greater than 8, then you need a sparse representation thereof.

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You can use 16 or 32 bit types if you want, for a much larger area.

You will run out of memory - it's not feasible to preallocate enough storage. If you really need a quad-tree with depth greater than 8, then you need a sparse representation thereof.


Oh right, I mixed up the world coordinates for depth representations. I forgot for a moment that the 8-bit value represents the tree levels, not coordinates.

Converting the coordinates as you said makes more sense.

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The world size can be any value.  In the code, m_fInvRadius is used to make the conversion from world units to internal units here:
		// Now to the range from [0..255].
		a2Shifted.m_vMin.x *= m_fInvRadius;
		a2Shifted.m_vMin.y *= m_fInvRadius;
		a2Shifted.m_vMax.x *= m_fInvRadius;
		a2Shifted.m_vMax.y *= m_fInvRadius;
You can use 16-bit values and some adjustments to the internal range to get 10 levels, but that would be 349,525 nodes and 18,175,300 megabytes of memory on 32-bit machines.

8 levels is usually enough. If your world is 10,000 meters square (10 kilometers), the smallest squares are 78.125 meters in size, which is very reasonable resolution. Remember that the smaller your nodes are the more frequently moving objects have to be re-inserted, so there is a trade-off with deeper trees.


L. Spiro

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Cool approach.  To manage the memory requirements in a large-yet-dense 3d world, it might make sense to store traditional oct-trees within this type of structure to have cache friendly step prior to a traditional broad phase collision detection.

Edited by Polarist

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I mention a few ideas on how to extend it into 3D at the bottom of the article and the way I am likely to do it when I get around to it is to use this method exactly as-is for the X and Z and use stacks for the Y (vertical).

To be honest, you don’t even necessarily need a vertical partition in most outdoor games, and indoor games use PVS’s, which you could couple with this type of quadtree (after testing to see if it makes sense for you), but even then you wouldn’t need a vertical partition most of the time.

 

Imagine a world that is 10 kilometers by 10 kilometers.  As a cube that means your octree would also be 10 kilometers tall, yet 90% of your level is likely to be in the root node or just the second node down, betrayed by its vertical proximity to the center of the octree.

 

So my feeling is that 3D should be handled by a mix of this method (completely as-is) for the X and Z and something entirely differently (if at all) for the Y.

And also, whatever method used for the Y (for me that will be stacks—just divide the world vertically by a fixed number of slices) can still benefit from better caching by being part of that same pool as the one used in the quadtree here.  Just extend the size of the pool by whatever is needed for the vertical slices and you should still keep decent caching.

 

 

L. Spiro

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Yup, I did read that part of the article, and it's a good observation for a 3d game which largely only expands in 2-dimensions.

 

But sometimes you need richness in that 3rd dimension, as well.  E.g. a space simulation.

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