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#Actualhaegarr

Posted 10 November 2013 - 01:10 PM


I am trying to rotate a point say (20,6,30) around a point (10,6,10) at a radius of 2

The above requirement can be fulfilled if the axis of rotation passes through (10,6,10) and passes through a point that is 2 length units away from (20,6,30).

 

Think of the rotational axis as a ray emanating at the center of rotation r0 (here (10,6,10)) along a direction d:

    r( t ) := r0 + t * d

The second point is at a distance t1 on this ray. The difference vector v from here to the point of interest p (here (20,6,30)) is:

    pr( t1 ) =: v

It is constrained because it is perpendicular to d

    v x d == 0

and its length should be 2

    || v || == 2

 

Try to solve this, but you'll see that there is an infinite amount of solutions to this. Think of a circle with radius 2 around p, and the 2nd point r( t1 ) on the ray may be any point of this circle. Whatever point you choose will have an influence on how the rotation looks like. EDIT: Ups, the figure isn't necessarily a circle, sorry. But it still may help as a gedanken experiment if thinking of a circle.


#1haegarr

Posted 10 November 2013 - 01:05 PM


I am trying to rotate a point say (20,6,30) around a point (10,6,10) at a radius of 2

The above requirement can be fulfilled if the axis of rotation passes through (10,6,10) and passes through a point that is 2 length units away from (20,6,30).

 

Think of the rotational axis as a ray emanating at the center of rotation r0 (here (10,6,10)) along a direction d:

    r( t ) := r0 + t * d

The second point is at a distance t1 on this ray. The difference vector v from here to the point of interest p (here (20,6,30)) is:

    pr( t1 ) =: v

It is constrained because it is perpendicular to d

    v x d == 0

and its length should be 2

    || v || == 2

 

Try to solve this, but you'll see that there is an infinite amount of solutions to this. Think of a circle with radius 2 around p, and the 2nd point r( t1 ) on the ray may be any point of this circle. Whatever point you choose will have an influence on how the rotation looks like.


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