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Summary

This schema represents two rotations in the mathematical rotation space.It has been made by me to illustrate the article "quaternions and spatial rotation".

First rotation (yellow) is of 80 degrees and is represented by a short arrow. Second rotation (red) is of 160 degrees, around another axis, and is represented by a longer arrow.

Each rotation pertains to a "sphere" of all rotations by the same angle. Here we can see the yellow (inside) and red (outside) spheres.

The small circles are oriented conforming to the "positive" right hand convention for angles

The lengths of the arrows representing the rotations are proportional to the sine of their half-angle, so the represented spheres are "slices" of the 4 dimensions hypersphere : sin (80° / 2) = 0.6428 and sin (160° / 2) = 0.9848

Any better graphist than me (read : any graphist) is welcome to redo it.

Сводка

На схеме отображено два вращения в математическом пространстве. Рисунок был сделан участником Wikipedia:User:MathsPoetry в качестве иллюстрации к статье Wikipedia:Quaternions and spatial rotation.

Первое вращение (жёлтым) на 80° представлено короткой стрелкой. Второе вращение (красным) на 160° осуществлено вокруг другой оси и представлено линией длиннее.

Каждое вращение принадлежит к "сфере" всех возможных вращений на такой же угол. Здесь мы можем видеть жёлтую (внутренняя) и красную (внешняя) сферы.

Маленькие окружности расположены в положительной правосторонней системе координат.

Длины стрелок, представляющих вращения, пропорциональны синусу половины их угла, поэтому представленные сферы - это проекции (срезы) четырёхмерной гиперсферы : sin (80° / 2) = 0.6428 and sin (160° / 2) = 0.9848.

Автор рисунка будет рад, если другой художник доработает его.

Licensing

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