I have 2 curves, how do I evaluate all points of one curve at perpendicular to all points of the other curve?

Heres the code I'm currently using:

%% Normal Finder 
function [contour_worn_fitted, worn_distance, 
worn_index]=normal_finder(contour_unworn_fitted,contour_worn_fitted,contour_worn_curve)

dy_unworn=gradient(contour_unworn_fitted(2,:));
dz_unworn=gradient(contour_unworn_fitted(3,:));

m_unworn=-1./(dy_unworn./dz_unworn);
c_unworn=contour_unworn_fitted(2,:)-(m_unworn.*contour_unworn_fitted(3,:));
%y=mz+c
for i=1:length(contour_unworn_fitted(2,:))
unworn_y_values{i}=linspace(contour_unworn_fitted(2,i)-1.5,contour_unworn_fitted(2,i)+1.5,500);
unworn_z_values{i}=(unworn_y_values{i}-c_unworn(i))/m_unworn(i);
end

for i=1:length(contour_unworn_fitted)
  worn_z_values{i}=linspace(contour_unworn_fitted(3,i)-1.5,contour_unworn_fitted(3,i)+1.5,500);
  worn_y_values{i}=polyval(contour_worn_curve,worn_z_values{i});
end

point_distance=cell(length(unworn_y_values),1);
for j=1:length(unworn_y_values)
  for i=1:length(unworn_y_values{j})
      for ii=1:length(worn_y_values{j})
          point_distance{j}(i,ii)=sqrt((unworn_y_values{j}(i)-worn_y_values{j}(ii))^2+(unworn_z_values{j}(i)-worn_z_values{j}(ii))^2);
      end
  end
end

for i=1:length(point_distance)
  [distance{i},normal_index{i}]=min(point_distance{i},[],2);            
  [worn_distance(i),worn_index(i)]=min(distance{i});
end

for i=1:length(unworn_y_values)
  worn_y(i)=worn_y_values{i}(worn_index(i));
  worn_z(i)=worn_z_values{i}(worn_index(i));
end

figure
plot(worn_z,worn_y,'r*-',contour_unworn_fitted(3,:),contour_unworn_fitted(2,:),'*-k')

    hold on
for i=1:length(contour_worn_fitted(2,:))
    plot([worn_z(i) contour_unworn_fitted(3,i)],[worn_y(i) contour_unworn_fitted(2,i)])
end

end

I am tring to evaluate a fitted curve at perpendicular points to another curve which lies beside the aforementioned curve but I am having trouble finding a working solution. The current code shown above takes 16 mins to run, that is because there is little vectorization, I know the code I am using is in no way efficient, and the fact that I am using curves with thousands of points.

There are 2 curves, a 'worn' curve and 'unworn' curve. polyval is used to evaluate the curve. the x coordinates are referred to as z coordinates, as in the overall code that is the case.

Your help is very much appreciated. Thank you.

[Image Analyst]

Let us try it. But we can't (yet) because you forgot to include the input data contour_unworn_fitted, contour_worn_fitted, and contour_worn_curve. Please give a test harness m-file to run this function, along with any data files that it might need to read in.

[John D'Errico]

I honestly don't know what you mean by this: "evaluate all points of one curve at perpendicular to all points of the other curve".

Given curve A, you can pick any point, compute the line normal to the curve. Now, find the intersection of that line with the other curve (B). Whats the problem? Are you asking something different?

[Matthew Nargol]

Hi, thanks for the swift replies.

Sorry 'Image Analyst', I have attached a .m file with all the required data inputs.

'John D'Errico', You are right in your understanding of my problem, the problem is that the curve is a polynomial of 7th degree and so my attempt in finding intersection at normal to curve resulted in strange answers as I think this was due to the high degree of polynomial. That was my initial thought to solving this problem but I gave up on that.

[Matthew Nargol]

Also, I plan on increasing that polynomial degree to ~9 as my curve fitting is not perfect.