marc-b-reynolds.github.io

MBR

MBR jack of no trades. Approximate concentric square to disc. A brief follow-up note to the square/disc post. A visualization of area/shape distortions and point distributions. A note on bias introduced by the pigeonhold principle. Uniform points on disc, circle, sphere and caps. A brief note on some basic uniform spatial distributions. Minimum magnitude angle rotation between two normals. Given two normals find the rotation from one to the other. Orthonormal basis from normal via quaternion similarity.

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MBR jack of no trades. Approximate concentric square to disc. A brief follow-up note to the square/disc post. A visualization of area/shape distortions and point distributions. A note on bias introduced by the pigeonhold principle. Uniform points on disc, circle, sphere and caps. A brief note on some basic uniform spatial distributions. Minimum magnitude angle rotation between two normals. Given two normals find the rotation from one to the other. Orthonormal basis from normal via quaternion similarity.

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MBR | marc-b-reynolds.github.io Reviews

https://marc-b-reynolds.github.io

MBR jack of no trades. Approximate concentric square to disc. A brief follow-up note to the square/disc post. A visualization of area/shape distortions and point distributions. A note on bias introduced by the pigeonhold principle. Uniform points on disc, circle, sphere and caps. A brief note on some basic uniform spatial distributions. Minimum magnitude angle rotation between two normals. Given two normals find the rotation from one to the other. Orthonormal basis from normal via quaternion similarity.

INTERNAL PAGES

marc-b-reynolds.github.io

1

Square/Disc mappings

http://marc-b-reynolds.github.io/math/2017/01/08/SquareDisc.html

January 8th, 2017. This note is for some auxilary information on some maps between the disc and square. A fair amount of the math is convered by Fong. And the survey by Lambers. A pair of animated plots between the various maps. Show the Jacobian matrices and determinates and visualize with interactive plots. Reduced complexity radial stretch in both directions. Reduced complexity concentric disc to square. Show a (perhaps) new radial approximate area preserving map. Define a signum like function:. A met...

2

Minimum magnitude angle rotation between two normals

http://marc-b-reynolds.github.io/quaternions/2016/08/09/TwoNormToRot.html

Minimum magnitude angle rotation between two normals. August 9th, 2016. Find the minimum magnitude angle rotation from $ hat{a}$ and $ hat{b}$, where both are unit vectors. The unit quaternion $Q$ that rotates (unit bivectors) $a$ to $b$ can be expressed as:. And solving for $Q$ gives:. This is well-covered material and if you’ve read my previous few posts then it is. Material. The bullet points are:. Ignoring the degenerate case this translates into:. 1 d)/sqrt(2 2d) (a x b)/sqrt(2 2d). Shows that the a...

3

Quaternion are really Complex

http://marc-b-reynolds.github.io/quaternions/2016/05/17/QuatAsComplex.html

Quaternion are really Complex. May 17th, 2016. If you cannot follow the formalism or if it is making your eyes bleed too much, I will give plane (da dum dum tish! English summaries marked in green. Newcommand{ hcomplex}[1]{ mathbb{C} {#1} $ $ newcommand{ pwrap}[1]{ left( #1 right)} $ $ newcommand{ set}[1]{ left{ #1 right} $. Preliminaries the really boring part. Complex numbers require two axiomatic definitions:. The product of the unit bivector: $ mathbf{i} 2=-1$. All other properties follow from these.

4

Uniform points on disc, circle, sphere and caps

http://marc-b-reynolds.github.io/distribution/2016/11/28/Uniform.html

Uniform points on disc, circle, sphere and caps. November 28th, 2016. Here I will only consider pseudo-random point generation. Well-spaced point generation is a different topic. The code examples are intended for clarity. Uniform points on the unit disc. One method to generate a uniform random point $p$ on the unit disc ($ mathbb{D}$) is as follows. Generate two uniform values: $a in left[ 0,1 right] $ , $ theta in left[ - pi, pi right) $ and apply. Lose one or both remaps (2*rng f32()-1). Uniform point...

5

Pigeonhole principle bias

http://marc-b-reynolds.github.io/math/2016/12/22/Pigeonhole.html

December 22nd, 2016. This is a quick note about how the Pigeonhole Principle applies to mapping integers to a smaller set. Let’s say we have 16 balls and 4 bins, then after distribution each has 4 balls. All is good. Each bin has a 4 in 16 chance of getting the ball each run which is a probability of $ frac{1}{n}$. Now we add an extra bin and things go abit wrong. Since 16 isn’t a multiple of 5 we end up with 4 bins of three balls and one with four:. The machine parts break down as follows:. Which is zer...

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MBR

MBR jack of no trades. Approximate concentric square to disc. A brief follow-up note to the square/disc post. A visualization of area/shape distortions and point distributions. A note on bias introduced by the pigeonhold principle. Uniform points on disc, circle, sphere and caps. A brief note on some basic uniform spatial distributions. Minimum magnitude angle rotation between two normals. Given two normals find the rotation from one to the other. Orthonormal basis from normal via quaternion similarity.

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