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Triangle bounding boxes in a single byte

Just thought of a way to store the bounding box for a single triangle in only one byte. It's not really practical or something you'd ever really want to use, but what the hell.

Assume we have some kind of indexed mesh structure with a list of vertex positions and a list of triangle indices:

  struct Mesh {
    std::vector<vec3> verts;
    std::vector<uvec3> triangles;

We can find the bounding box of a triangle by taking the min and max of all three vertices:

  vec3 Mesh::lowerBound(uint32_t tri) const {
    vec3 v0 = verts[triangles[tri].x];
    vec3 v1 = verts[triangles[tri].y];
    vec3 v2 = verts[triangles[tri].z];
    return min(min(v0, v1), v2);

  vec3 Mesh::upperBound(uint32_t tri) const {
    vec3 v0 = verts[triangles[tri].x];
    vec3 v1 = verts[triangles[tri].y];
    vec3 v2 = verts[triangles[tri].z];
    return max(max(v0, v1), v2);

This is nice and simple and probably way better than what I'm about to suggest.

We can store a byte that tells us which of …
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If you ever find yourself needing to figure out a dynamic library loading problem on Linux, LD_DEBUG can be a massive help.

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We can fix this by appending the depth of the node to the morton encoding. If we have an octree of depth 9 then we need up to 27 bits for the morton encoding and 4 bits for the depth, which still fits nicely into a 32-bit integer. We'll shift the morton code up so that i…

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Here's a neat trick I discovered a couple of months back: given two signed or unsigned integers of the same bit width, you can calculate the length of their common prefix very efficiently:

int common_prefix_length(int a, int b) { return __builtin_clz(a ^ b); }
What's this doing? Let's break it down:

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Some helpful references
GPU-Based Importance Sampling, GPU Gems 3, Chapter 20.Real-Time Computation of Dynamic Irradiance Maps, GPU Gems 2, Chaper 10.Physically Based Shading in Theory and Practice, SIGGRAPH 2013 Course.In particular, the course notes for "Real Shading in Unreal Engine 4" are very helpful.

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Faster morton codes with compiler intrinsics

Today I learned that newer Intel processors have an instruction which is tailor-made for generating morton codes: the PDEP instruction. There's an instruction for the inverse as well, PEXT.

These exist in 32- and 64-bit versions and you can use them directly from C or C++ code via compiler intrinsics: _pdep_u32/u64 and _pext_u32/u64. Miraculously, both the Visual C++ and GCC versions of the intrinsics have the same names. You'll need an Intel Haswell processor or newer to be able to take advantage of them though.

Docs for the instructions:

Intel's docsGCC docsVisual C++ docs
This page has a great write up of older techniques for generating morton codes:

Jeroen Baert's blog ...but the real gold is hidden at the bottom of that page in a comment from Julien Bilalte, which is what clued me in to the existence of these instructions.
Update: there's some useful info on Wikipedia about these intructions too.

Awesome tools for Windows users

I moved back to Windows on my home computer a few months back. There are a few amazing free tools I've found since then that have been making my life better and I thought they deserved a shout-out. They are:

A fantastic PDF reader. Does everything I want and nothing I don't.

A sane way to edit environment variables. The simple joy of just being able to resize the window is... incredible.

The best tool for dealing with compressed files on windows, bar none.

A really handy way to see details about your GPU(s).

An amazingly good image viewer, which can also do bulk file format conversions.

If you haven't already got these... go get them!