Binary Space partitioning (https://en.wikipedia.org/wiki/Binary_space_partitioning) is an elegant algorithm that solves this issue. This has fallen out of popularity due to the invention of the depth buffer and the power of modern GPUs, but it was used in DOOM and Quake.
This technique, due to the unique limitation of the children's drag-and-drop coding platform, Scratch, has made it proliferate in the 3D community. https://scratch.mit.edu/projects/1203675921 is an example of such a project.
They seem to point out some examples in section 4 that can't be handled with space partioning. I'll confess I don't follow the reasoning. Figure 4.2 is the go-to example of a sorting problem that is handled with BSP trees.
Hi, it’s me, the author. In this thesis the focus was on techniques that don’t involve splitting the geometry into pieces, and the objects in Figure 4.2 can’t be partitioned without splitting. In later iterations of the implementation I have added splitting and I’ve detailed this in a talk I gave at Blanketcon 2025 (https://douira.dev/assets/document/presentation-blanketcon25...), but the algorithm still attempts to avoid it as much as possible since it can explode the amount of quads in the worst case.
Only slightly related, but since Minecraft seems to have a lot of community graphics programming associated with it I thought I'd ask here...
Does anyone know how those Minecraft realistic rendering mods work? I'm guessing today there's a lot of RTX, but e.g. in 2018 there was still fairly impressive global illumination in SEUS Renewed. Minecraft is the definition of a world with dynamic geometry, and I'm not aware of any decent realtime GI algorithms for 3d. The lighting in base Minecraft is a super basic and ugly hack. I've seen Unity's dynamic GI features and those are nowhere near as good either.
I don't know much about lighting, but looking at the source code of the shaders might give a clue. https://modrinth.com/discover/shaders has a lot of shaders that change the lighting. In other parts of the rendering pipeline, there are some very impressive mods utilizing GPU magic. One of them is Voxy (https://modrinth.com/mod/voxy), one that massively increases render distance with mesh shaders and level-of-detail based rendering.
Ah yeah, I was mostly interested in lighting, but that's really interesting too.
Voxy's LOD thing... so like, I guess what they do is when you're in an area so that area's high LOD assets are loaded, it computes the lower LOD and saves it, and then as you move around you get a library of more and more lower LODs? And since modifications to geometry only happen when you're nearby the LODs are static? I'd love to see a writeup of that too...
A lot of non raytracing GI solutions uses voxel grids on top of the world geometry, SVOGI is one of the fancy ones used in cry engine games. I imagine since minecraft essentially gives a voxel grid to you for "free" most of minecraft GI solutions also uses a similar technique.
This technique, due to the unique limitation of the children's drag-and-drop coding platform, Scratch, has made it proliferate in the 3D community. https://scratch.mit.edu/projects/1203675921 is an example of such a project.
I think this is particular to auto-partitioning BSPs where the splitting planes are aligned with scene geometry.
It inspired me so much back when I was graduating in mathematics, the author is a genius.
Does anyone know how those Minecraft realistic rendering mods work? I'm guessing today there's a lot of RTX, but e.g. in 2018 there was still fairly impressive global illumination in SEUS Renewed. Minecraft is the definition of a world with dynamic geometry, and I'm not aware of any decent realtime GI algorithms for 3d. The lighting in base Minecraft is a super basic and ugly hack. I've seen Unity's dynamic GI features and those are nowhere near as good either.
Voxy's LOD thing... so like, I guess what they do is when you're in an area so that area's high LOD assets are loaded, it computes the lower LOD and saves it, and then as you move around you get a library of more and more lower LODs? And since modifications to geometry only happen when you're nearby the LODs are static? I'd love to see a writeup of that too...
https://jacobdoescode.com/2025/05/18/precomputing-transparen...
- Multi-Fragment Effects on the GPU using the k-Buffer [2]
- Production Volume Rendering [3]
- Translucent Shadow Maps [4]
[1] https://developer.download.nvidia.com/presentations/2007/sig...
[2] https://www.sci.utah.edu/~stevec/papers/kbuffer.pdf
[3] https://graphics.pixar.com/library/ProductionVolumeRendering...
[4] https://www.scribd.com/document/657069029/Translucent-Shadow...
In general: https://en.wikipedia.org/wiki/Order-independent_transparency