Matlab, visualize 3D rotational matrix - matlab

Question

I have a target coordinate (xyz) within a 3D rectangle. The target coordinate is set assuming the 3D rectangle is in a flat plane with x,y,z. The target coordinate is set to be on one terminal end of the rectangle, with the 'y' component set to be -2 from the top of the 3D square (Refer to image). However, in reality the 3D rectangle is not in a flat plane with x,y,z axes, it is skewed. We calculate the skew by measuring two reference points on the top surface of the rectangle and now want to recalculate the target coordinate. I do not know how to ensure I am computing the skew correctly or (more importantly) plot the old vs new 3D rectangle and target coordinate. Below is code to generate both the matrix and the target within said matrix.
For the two reference points used to calculate the skew of the 3D rectangle, we name one 'bregma' and one 'lamda'.
%% CONVENTIONS:
%1) numbers get lower when
% 1) going to left on x axis
% 2) going down y axis
% 3) going posterior (or towards you) on z axis,
% opposite of convention
%2) coordinate order is AP (anterior posterior), ML
%(medial lateral), DV
%(dorsal ventral)
%Bregma is the anterior reference point and
%Lambda is posterior reference point . The goal variables
%are the point in space I want to reach. I'm hoping the code creates new
%points for me as caused by a change in elevation between point "c" and "f"
%Note, for AP/ML/DV absolute values, the actual integers %are merely
%reference points in space. It is the delta between AP %and AP or ML and ML
%that is meaningful
%values a-f would be acquired from the stereotaxic frame
a= 43; %AP at bregma
b= 20; %ML at bregma
c= 22; %DV at bregma
d= 38.8; %AP at lambda
e= 20; %ML at Lambda
f= 21.5; %DV at lamda This variable causes the change %in which I want the rotation to correct
%Bregma =[b a c];
%Following three points are given relative to bregma, this is convention. So mathematically 'Bregma=[0 0 0];'
%These are also the coordinates I want altered from the rotation matrix
MLgoal=0; %ML to injection
APgoal=0; %AP to injection
DVgoal=-2.0; %DV to injection
DVgoal_zaxis_signconvention_correction = -DVgoal; %we want sign convention flipped for z axis[![enter image description here][1]][1]
A= a-d;
M= b-e;
D= c-f;
%Bregma =[0 0 0];
v = [A M D];
mv = norm(v);
u=[A 0 0]; %theoretical vector [ML,AP,DV] bregma to %lambda
mu = norm(u);
%angle in radians
X=acos(dot(u,v)/(mu*mv));
cu=cross(u,v);
w=cu/norm(cu); %unit vector
%rotate about this unit vector by angle X
wx=w(1);
wy=w(2);
wz=w(3);
%sustitute variables into general rotation for more %readable code
vx = 1-cos(X);
cx = cos(X);
sx = sin(X);
%rotation matrix about arbitrary unit vector [wx; wy; %wz] by angle X
r=[vx*wx*wx + cx, vx*wx*wy - wz*sx, vx*wx*wz + wy*sx;
vx*wx*wy + wz*sx, vx*wy*wy + cx, vx*wy*wz - wx*sx;
vx*wx*wz - wy*sx, vx*wy*wz + wx*sx, vx*wz*wz + cx];
%Newcoordinate output should tell you the change in %targeting coordinate
%after correcting for the output of rotational matrix. %The value for DV
%seems too large based on the subtle increase elevation %of reference point
%Bregma to reference point Lambda
Newcoordinates=r* [APgoal;MLgoal;DVgoal_zaxis_signconvention_correction]; %should give you the new coordinates for the injection %site