How to rotate a point about an axis formed by 2 points
in [Matlab]
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From: jjspierx Spiering on 31 May 2010 17:34 Thank you very much Matt and James. M3D turned out to work perfectly for my purposes!
From: jjspierx Spiering on 31 May 2010 18:08 I have another question related to this same topic... Assuming now that I have 2 sets of the 3 points used previously to form an axis and then rotate about it. So now I have 2 axis and 2 points rotating about their respective axis. 2 planes are therefore formed, one between each set of 3 points. I am trying to figure out a way to find the axis formed by the intersection of those 2 planes. In 2-space this would be easy, I could just determine the slope of the planes (or lines in 2-space) and find the intersection point, ie the instant center. But in 3-space finding the equivalent instant axis is proving to be very difficult for me. Thanks in advance.
From: Matt J on 1 Jun 2010 00:59
"jjspierx Spiering" <jjspierx(a)gmail.com> wrote in message <hu1c03$qtu$1(a)fred.mathworks.com>... > I have another question related to this same topic... > > Assuming now that I have 2 sets of the 3 points used previously to form an axis and then rotate about it. So now I have 2 axis and 2 points rotating about their respective axis. 2 planes are therefore formed, one between each set of 3 points. I am trying to figure out a way to find the axis formed by the intersection of those 2 planes. In 2-space this would be easy, I could just determine the slope of the planes (or lines in 2-space) and find the intersection point, ie the instant center. But in 3-space finding the equivalent instant axis is proving to be very difficult for me. Thanks in advance. =================== Hints: (1) Suppose you have 3 points a,b,c. A normal N to the plane containing these points is N=cross(b-a,c-a) and the equation for this plane is dot(N,[x,y,z])=dot(N,a) (2) If 2 planes with normals N1 and N2 intersect in a line, a vector parallel to this line is cross(N1,N2) |