Coder Vil

Let's say we have an octree and we want to come up with a unique integer that can identify any node in the tree - including interior nodes, not just leaf nodes. Let's also say that the octree has a maximum depth no greater than 9 levels, i.e. the level containing the leaf nodes divides space into 512 parts along each axis. The encoding The morton encoding of a node's i,j,k coordinates within the tree lets us identify a node uniquely if we already know it's depth. Without knowing the depth, there's no way to differentiate between cells at different depths in the tree. For example, the node at depth 1 with coords 0,0,0 has exactly the same morton encoding as the node at depth 2 with coords 0,0,0. 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 t...

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: a ^ b is the bitwise-xor of a and b. The boolean xor operation is true when one of it's inputs is true and the other is false; or false if both have the same value. Another way to put this is that xor returns true when its inputs are different and false if they're the same. The bitwise-xor operation then, returns a value which has zeros for every bit that is the same in both a and b; and ones for every bit that's different. __builtin_clz is a GCC intrisinc function which counts the number of leading zero bits of its argument. It compiles down to a single machine code instruction on hardware that supports it (which includes every Intel chip made i...