How to Extract 2D Plane Orthogonal to a LINE

Hello All, My Question is regarding extracting Plane/Slice of Data from Volume (Orthogonal to a line Passing through TWO Points). AFTER doin all the Vector manipulation, I have plotted LINE, as well as the SURFACE Plane (129*129) that is ORTHOGONAL to the LINE.

No I am stuck with the problem as the ORTHOGONAL PLANE that I have constructed have Coordinates accordingly:

x-coordinates=-64:64; y-coordinates=-64:64; z-coordinates=VALUES OBTAINED through the EQUATION of PLANE.

Now How to MAP these coordinate values to extract data around the given Point P1[5 18 10]. In case of applying simple translation, X and Y axes are mapped correctly, BUT Z coordinate varies and It does not remain the plane we want to access , as Plane must pass through given point P1[5 18 10];

I have tried new_x=old_x+5; new_y=old_y+18; new_z=old_z+10; But this shifts my whole PLANE , as I have already Obtained Z-VALUES for plane through equation of PLANE. ThankYou in Advance...

Kindly help me so that I could proce

clc;clear all; load mri; D=squeeze(D);volume=D;

P1=[5 18 10]; % Point P1, Picked from Skeleton Data P2=[6 19 11]; % Point P2, Picked from Skeleton Data dv_line=[P2(1)-P1(1) P2(2)-P1(2) P2(3)-P1(3)]; % Direction_Vector of Line t=linspace(-10,10); % Vector Equation of Line x=P1(1) +dv_line(1)*t; % X coordinate y=P1(2) +dv_line(2)*t; % Y coordinate z=P1(3) +dv_line(3)*t; % Z coordinate plot3(x,y,z,'LineWidth',2,'Color','r') % Plot LINEfor Validation of results in 3D grid on %LINE PLOTTING fINISHED

hold on pt=[5 18 10]; plot3(pt(1),pt(2),pt(3),'y.','MarkerSize',16)

radius=64 volSz=size(volume) epsilon=1e-12; x=linspace(-radius,radius,2*radius+1); y=linspace(-radius,radius,2*radius+1); z=zeros(2*radius+1); hsp=surf(x,y,z); rotate(hsp,[0 0 1],0) xdO=get(hsp,'XData'); ydO=get(hsp,'YData'); zdO=get(hsp,'ZData');

hold on syms x y z; dv_plane=[x-P1(1) y-P1(2) z-P1(3)] ; % Direction Vector of Plane Obtained with point passing through Plane dot_product=dot(dv_line,dv_plane); % Obtain Dot Product of two Direction Vectors (must be ZERO) z=solve(dot_product,'z'); % Solve Dot Product for Obtaining equation for z x=xdO;y=ydO; % Generate XY Range for Assignment z_value=eval(z);

delete(hsp) hsp2=surf(x,y,z_value);

xd=get(hsp2,'XData'); yd=get(hsp2,'YData'); zd=get(hsp2,'ZData');

% The yellow Point should lie on the plane as we have assumed that the Plane crosses through the point.

% Mathematical Validation Only clc; disp('Mathematical Validation of SURFACE');disp(' ') disp('Equation of PLANE is 1.X +1.Y +1.Z -33=0') for i=1:2*radius+1; valid=[xd(i,i) yd(i,i) zd(i,i) xd(i,i)+yd(i,i)+zd(i,i)-33 ] if valid(4)~=0 disp('EQUATION OF PLANE NOT SATISFIED'); break; end end disp('ALL POINTS VALIDATING PLANE EQUATION');

[John D'Errico]

Please learn to use the code formatting button. It says "{} CODE". Select your code, then click that button. It allows others to actually read your code instead of the headache that you have given us here.