I am trying to construct a series of local coordinate systems and corresponding transformation matrices (x3) from a set of coordinates (x9)
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I have the coordinates of 9 points and I am trying to use them to construct 3 coordinate systems and determine the transformation matrices between the global and each local coordinate system. This is what I have so far (Not very filled in I know that's why I'm looking for help)
%Create 3 Local CS
or_Fm=
v1 = m1 - m2;
v2 = m3 - m2;
v3 = cross(v1,v2);
v4 = cross(v3,v1);
i_Fm = v1/norm(v1);
j_Fm = v4/norm(v4);
k_Fm = v3/norm(v3);
or_Fa=
v1 = m1 - m2;
v2 = m3 - m2;
v3 = cross(v1,v2);
v4 = cross(v3,v1);
i_Fa = v1/norm(v1);
j_Fa = v4/norm(v4);
k_Fa = v3/norm(v3);
or_Mm=
v1 = m1 - m2;
v2 = m3 - m2;
v3 = cross(v1,v2);
v4 = cross(v3,v1);
i_Mm = v1/norm(v1);
j_Mm = v4/norm(v4);
k_Mm = v3/norm(v3);
or_Ma=
v1 = m1 - m2;
v2 = m3 - m2;
v3 = cross(v1,v2);
v4 = cross(v3,v1);
i_Ma = v1/norm(v1);
j_Ma = v4/norm(v4);
k_Ma = v3/norm(v3);
%Compute Tranfromation Matrices
T_Fm=eye(4);
T_Fm(2:4,1)=or_Fm;
T_Fm(2:4,2:4)=[i_Fm j_Fm k_Fm]
T_Fa=eye(4);
T_Fa(2:4,1)=or_Fa;
T_Fa(2:4,2:4)=[i_Fa j_Fa k_Fa]
T_Mm=eye(4);
T_Mm(2:4,1)=or_Mm;
T_Mm(2:4,2:4)=[i_Mm j_Mm k_Mm]
T_Ma=eye(4);
T_Ma(2:4,1)=or_Ma;
T_Ma(2:4,2:4)=[i_Ma j_Ma k_Ma]
2 Comments
Matt Kindig
on 25 Oct 2012
What is the relationship between i_Fm and i_Fa? Similarly, what is the relationship between i_Mm and i_Ma? Which two coordinate systems is the transformation matrix T_Fm transforming between?
Image Analyst
on 26 Oct 2012
A diagram would help. What are you trying to do? Warp a 2D image into a "fixed up" image? I know you think the two comments you put in there explain it all, but they don't do it for me. What are x3 and x9 in your subject line - those variables do not seem to be in the code. Does that mean you have three transformation matrices and 9 coordinate pairs? Why are you not using maketform() or imtransform()? I suggest you look at this from our point of view and edit this to provide us with enough information to give us a fighting chance at helping you.
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