def reflect(rays, surfMatrix):
#%reflect takes vectors hitting a surface, and returns them just after being reflected
#% there are two important requirements:
#% The rays must have already reached the surface
#% their direction vector must be toward the surface.
gradVec = getGrad(rays, surfMatrix);
rays['direction'] = rays['direction'] - 2* (np.sum(rays['direction']*gradVec,axis = 1)*gradVec.T).T;
#for i = 1:size(rays.direction,1)
# rays.direction(i,1:4) = rays.direction(i,1:4)-2*dot(rays.direction(i,1:4),gradVec(i,1:4))*gradVec(i,1:4);
#end
#%mirrors cause a pi phase shift in the wave phase:
rays['phase'] = (rays['phase'] + rays['wavelength']/2) % rays['wavelength']
return rays
def refract(rays, surfMatrix, n2 = 1):
#%refract(rays, surfMatrix, n2)
#%this function expects unit vectors to come in.
#%the equation is based on a derivation in the book Introduction to Ray Tracing by glassner
r = rays['n_index']/n2; #ratio n1/n2
rays['n_index'][:] = n2;
gradVec = getGrad(rays,surfMatrix);
cos1 = np.sum(-rays['direction']*gradVec,axis = 1);
gradVec[cos1<0,:] = -gradVec[cos1<0,:];
cos1 = np.sum(-rays['direction']*gradVec,axis = 1);
cos2 = np.lib.scimath.sqrt(1-r*r*(1-cos1*cos1)); #%if imaginary, there was internal reflection;
toRefl = cos2.imag != 0;
#cos1 = repmat(cos1,1,4); cos2 = repmat(cos2,1,4);
refl = rays['direction'] - (2*cos1*gradVec.T).T;
rays['direction'] = (r * ((rays['direction']-(cos1*gradVec.T).T) - (cos2*gradVec.T).T).T).T;#refract these rays
rays['direction'][:,toRefl] = refl[:,toRefl];#reflect these rays
#%I believe this is an unnecessary check to ensure that the result is
#% %normalized; it is guaranteed to be normalized by the equation above.
#% mag = sqrt(dot(rays.direction(1:3,:),rays.direction(1:3,:),1));
#% mag(mag == 0) = 1;
#% rays.direction(1:3,:) = rays.direction(1:3,:)./[mag;mag;mag];
#% rays.direction(4,:) = 0;
#%the 'rule of thumb' for phase reflections caused by refraction is:
#%n1 to n2: if high to low? Phase shift no!
#% if low to high? Phase shift pi!
if n1 < n2: #% := phase + 'pi'
rays['phase'] = (rays['phase'] + rays['wavelength']/2) % rays['wavelength'];
# %rays.wavephase = arrayfun(@(x,y) mod(x,y),rays.wavephase,rays.wavelength);
#end
reflected, refracted = hitAndMiss(rays, toRefl);
return refracted;