https://blog.jkoff.ca/ Recent content on Jonathan's Blog Hugo en-us Thu, 12 Sep 2024 00:00:00 +0100 https://blog.jkoff.ca/posts/octahedral/ Thu, 12 Sep 2024 00:00:00 +0100 https://blog.jkoff.ca/posts/octahedral/ The Physically Based Rendering 4th Edition book’s section on Octahedral Encoding shares an algorithm, but less of the intuition than I needed. Here’s what I’ve figured out. Dividing a vector by its L1 norm yields a vector whose L1 norm equals 1. # Octahedral encoding operates on unit vectors, i.e. vectors with $v_x^2 + v_y^2 + v_z^2 = 1$. To encode a vector with octahedral encoding, we first divide the vector by its L1 norm, $|v_x| + |v_y| + |v_z|$.