moonlord wrote:"is also deffined"... Aren't things supposed to only have a definition?
The_Science_Guy wrote:A clifford rotation is also defined as when every point in a 3D object rotates around the center point. So, according to that, it is possible to have a clifford rotation happen in 3D.
pat wrote:That depends on what you mean be a rotation.
The_Science_Guy wrote:A clifford rotation is also defined as when every point in a 3D object rotates around the center point. So, according to that, it is possible to have a clifford rotation happen in 3D.
That depends on what you mean be a rotation. There is no way that you can throw a ball up into the air with a spin that has only a single fixed point. Sure, you could hold the ball in your hands and spin it erraticly. But, you'd more or less be just doing a series of rotations where each rotation has a fixed axis of rotation, but you rapidly change which axis is fixed.
Unless, of course, you're talking about some non-rigid object, like a liquid mass.... then, I suppose you could have every point rotate around the center....
thigle wrote:well, what about acrobatic ski-jump ? when they are in the air, and do for ex. 720 with a twist...
also, could you add 3-simplex and 4-simplex to your clifford rotation applet ? people ususally skip these simpletons when doing multidimensional visualisation, byt i find that these minimal systems serve best to grasp the idea.
could you add to the applet a possibility of rotation about 3, 4 planes ? what that would be ? a hyperClifford ?
also please consider putting up a numeric input possibility in the interface together with the sliders.
also, what projection method is used for the applet ?
[ 1, 0, 0, 0, 0 ]
P43 = [ 0, 1, 0, 0, 0 ]
[ 0, 0, 1, 0, 0 ]
[ 0, 0, 0, 1, 1.5 ]
[ 10, 0, 0, -0.75 ]
P32 = [ 0, 10, 0, 0 ]
[ 0, 0, 10, 15 ]
p' = P32 * V * P43 * R * p
sx = sw/2 + x' * ss / d
sy = sh/2 - y' * ss / d
[ 1, 0, 0, 0, 0 ]
P43 = [ 0, 1, 0, 0, 0 ]
[ 0, 0, 0, 1, 0 ]
[ 0, 0,-1, 0, 1.5 ]
thigle wrote:a spherical body is set in rotation by a force F1 that hits it in tangential direction that cuts its radius r orthogonally at 1/4 from centre. now another force, F2, hits the rotating spherical body in direction orthogonal to plane rF.
[ x ]
[ y ]
p = [ z ]
[ w ]
[ 1 ]
[ 1, 0, 0, 0, 0 ]
[ 0, 0, 1, 0, 0 ]
[ 0,-1, 0, 0, 0 ]
[ 0, 0, 0, 0, 1 ]
[ 1, 0, 0, 0, a ]
[ 0, 1, 0, 0, 0 ]
[ 0, 0, 0, 1, 0 ]
[ 0, 0, 0, 0, 1 ]
[ x 2 6 ]
[ a, b, c, d ] * [ y 3 7 ]
[ e, f, g, h ] [ z 4 8 ]
[ w 5 9 ]
[ ax+by+cz+dw, 2a+3b+4c+5d, 6a+7b+8c+9d ]
[ ex+fy+gz+hw, 2e+3f+4g+5h, 6e+7f+8g+9h ]
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