MBR blog-a-like http://marc-b-reynolds.github.io A normal/twist transform for TBN representation Covers a transform that converts the tangent and bitangent of a 3D frame to a point on the unit circle. Wed, 06 May 2026 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2026/05/06/NormalTwist.html http://marc-b-reynolds.github.io/math/2026/05/06/NormalTwist.html Item weights vs. the Paradox of Rarity This post describes using item weights to define the relative frequency of drop rates. Wed, 01 Jan 2025 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2025/01/01/Rarity.html http://marc-b-reynolds.github.io/math/2025/01/01/Rarity.html Comments on parameterized SplitMix and PCG style generators Builds up a rational for a presented method for generating the additive constant of a LCG or Weyl sequence based PRNG. Wed, 11 Dec 2024 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2024/12/11/LCGAddConst.html http://marc-b-reynolds.github.io/math/2024/12/11/LCGAddConst.html Popcount walks: next, previous, toward and nearest Informal (and by-example) derivation of walking adjacent integers with the same population count as the input. Thu, 09 Nov 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/11/09/PopNextPrev.html http://marc-b-reynolds.github.io/math/2023/11/09/PopNextPrev.html A fast path floating point underflow test elision from absorption A sketch of a fast path filter to avoid explicit underflow checking following an addition or subtraction. Wed, 12 Jul 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/07/12/FpAbsorbUnderflow.html http://marc-b-reynolds.github.io/math/2023/07/12/FpAbsorbUnderflow.html Stable look-at rotations Derives stable look-at computations for Yaw/Pitch, swing-twist and quaternions Thu, 15 Jun 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/06/15/LookAt.html http://marc-b-reynolds.github.io/math/2023/06/15/LookAt.html Weighted function approximation: angle trisection Example of a weighted sum of functions approximation: trisect an angle Sat, 21 Jan 2023 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2023/01/21/Trisect.html http://marc-b-reynolds.github.io/math/2023/01/21/Trisect.html An evil and odious map (partition into even/odd parity in increasing order) Presents a map that paritions integers into the even and odd parity subsets where each are in increasing order Fri, 16 Dec 2022 00:00:00 +0000 http://marc-b-reynolds.github.io/math/2022/12/16/ParityWalks.html http://marc-b-reynolds.github.io/math/2022/12/16/ParityWalks.html A fast perfect shuffle for n≤64 Describes a perfect shuffle using a bitset and the original pencil-and-paper Fisher-Yates method. Thu, 14 Jul 2022 00:00:00 +0000 http://marc-b-reynolds.github.io/distribution/2022/07/14/SmallPerfect.html http://marc-b-reynolds.github.io/distribution/2022/07/14/SmallPerfect.html Quaternion swing twist decomposition Given a unit quaternion $Q$ factor into a pair such that $Q = Q_rQ_a$ where $a$ is a predefined axis and $r$ is an orthogonal axis. This is commonly called swing-twist decomposition. Mon, 31 Jan 2022 00:00:00 +0000 http://marc-b-reynolds.github.io/quaternions/2022/01/31/QuatAxisFactor.html http://marc-b-reynolds.github.io/quaternions/2022/01/31/QuatAxisFactor.html