Life & fun · September 11, 2016
Attempting to use Norman Wildberger's rational trigonometry in WebGL
Attempting to use Norman Wildberger's rational trigonometry in WebGL launched on September 11, 2016 with 8 votes, #1,822 of 3,743 launches that month and more than 75% of that year's launches. The site was still online in September 2026, 10 years on.
What it does
Norman Wildberger suggests such transformation can and should be used to perform rotations in the plane, instead of using trigonometric functions ( wikipedia article ). Can it also be done in 3D space? That is, for any two non-colinear vectors \(\mathbf{u}\) and \(\mathbf{v}\), how can we algebraically parametrize rotations in the \((\mathbf{u},\mathbf{v})\) plane? It is known, notably as pointed out by David Hestenes , that \(\mathbf{uv}\) behaves as a complex number, with \(\mathbf{u}\cdot\mathbf{v}\) being the real part and \(\mathbf{u}\wedge\mathbf{v}\) the imaginary one. If we do it for three vectors of an orthonormal basis, we get the coefficients of the orthogonal matrix…from grondilu.github.io
Does a similar job
all alternatives →- FTFourier Transform Visualized via WebGL2021 · static.laszlokorte.de · ▲175
- SPSimple pendulum simulation with rational trigonometry2016 · grondilu.github.io · ▲52
Context: I'm looking at Norman Wildberger's rational trigonometry[1], and here I was wondering how useful it is in physics. So I thought about testing it with the famous simple pendulum exercise. It's not obvious we get any FPS gain, but still I find it cool to even be able to get the same result differently. 1. https://en.wikipedia.org/wiki/Rational_trigonometry
- WLWebGL low-poly saturn example2016 · whitestormjs.xyz · ▲19
- IAImplementing a trackball with rational numbers2017 · grondilu.github.io · ▲11
- STSVG Triangulation for WebGL2015 · mattdesl.github.io · ▲94
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