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www.themathdoctors.org | ||
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liorsinai.github.io
[AI summary] This blog post explains the different methods for representing and performing rotations in 2D space, including polar coordinates, Cartesian matrices, and complex numbers, while also introducing the concept of quaternions for future 3D rotations. |
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www.johndcook.com
Analogs of Euler's formula exp(ix) = cos(x) + i sin(x) in other number systems, namely dual numbers and double numbers. |
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www.kuniga.me
NP-Incompleteness: |
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thenumb.at
Or, where does that \(\sin\theta\) come from? Integrating functions over spheres is a ubiquitous task in graphicsand a common source of confusion for beginners. In particular, understanding why integration in spherical coordinates requires multiplying by \(\sin\theta\) takes some thought. The Confusion So, we want to integrate a function \(f\) over the unit sphere. For simplicity, lets assume \(f = 1\). Integrating \(1\) over any surface computes the area of that surface: for a unit sphere, we should end... |
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