MATLAB: Efficiency of a symbolic math loop

for loopMATLABspeedsymbolicSymbolic Math Toolbox

Hi all,
I have a piece of code I intend to run in real time with a camera and consequently I want to optimise everything as well as I can. The Symbolic Toolbox is something new to me, hopefully someone can point out where I might be able to increase the efficiency of the code.
The code is a little module I made for ray casting in another part of my project. Using the Sym math to get the 3D point of intersection between a ground plane and a ray from a camera. The main slowdown is in the for loop at the bottom.
Cheers guys
Code is: 
    P1 = [1,-1,0.1];
    P2 = [2,3,0.1];
    P3 = [-5,6,0.2];  %3 points define a plane
    cameraPosition = [0 0 0.5];
    pixel = [1:640;(ones(640,1)*320)']'; %Line of pixels from camera
    totalOps = length(pixel(:,1));
    normal = cross(P1-P2, P1-P3); 
    syms x y z xL yL zL m;
    P = [x,y,z];
    planefunction = dot(normal, P-P1);
      horFOV = deg2rad(57);
      vertFOV = deg2rad(43);
      horGaps = horFOV/640;   %rad/pixel

      vertGaps = vertFOV/480;  %rad/pixel
      alpha = (-pixel(:,2)+240)*vertGaps; 
      theta = (-pixel(:,1)+320)*horGaps+pi/2; 
      PL = [cameraPosition(1)+1*sin(theta), cameraPosition(2)-1*cos(theta), cameraPosition(3)+1*sin(alpha)];    
      R = PL-repmat(cameraPosition,totalOps,1);
      intercept = zeros(3,totalOps);
      digits(6);
      for i=1:totalOps
          xL = PL(i,1)+R(i,1)*m;
          yL = PL(i,2)+R(i,2)*m;
          zL = PL(i,3)+R(i,3)*m;
          subF = vpa(subs(planefunction,{x,y,z},[xL,yL,zL])); 
          subFcoeffs = double(coeffs(subF));
          mVar = linsolve(-subFcoeffs(2),subFcoeffs(1));
          intercept(:,i) = PL(i,:)+R(i,:)*mVar;
      end

Best Answer

P1 = [1,-1,0.1];
P2 = [2,3,0.1];
P3 = [-5,6,0.2];  %3 points define a plane
cameraPosition = [0 0 0.5];
pixel = [1:640;(ones(640,1)*320)']'; %Line of pixels from camera
totalOps = length(pixel(:,1));
normal = cross(P1-P2, P1-P3);
horFOV = deg2rad(57);
vertFOV = deg2rad(43);
horGaps = horFOV/640;   %rad/pixel

vertGaps = vertFOV/480;  %rad/pixel
alpha = (-pixel(:,2)+240)*vertGaps; 
theta = (-pixel(:,1)+320)*horGaps+pi/2;       
PL = [cameraPosition(1)+1*sin(theta), cameraPosition(2)-1*cos(theta), cameraPosition(3)+1*sin(alpha)];    
R = PL-repmat(cameraPosition,totalOps,1);
xyzL = PL + R*1i;
subF = bsxfun(@minus,xyzL,P1)*normal.';
mVar = real(subF)./-imag(subF);
intercept = (PL + bsxfun(@times,R,mVar)).';
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