How to find Intersection of 2 surfaces ?

Hello

I have two surface made from discreate data. I want to find the cordinates of intersecting line. The surface are named as

Surface1 = (A1,A2,C)
Surface2 = (B1,B2,C)

My problem is that as data is discreate so I am not able to know the precise intersecting points of the surface.

For reference I have attached the file.

I want to find cordinates of this particular line.

Thanks in Advance

[Matt J]

Which is X, which is Y, and which is Z?

[Jay Talreja]

X is A1 and A2.

Y is B1 and B2

Z is C which is same for both graphs.

Answer 1

[Matt J]

One way,

load data

F1=griddedInterpolant({A1,A2},C,'linear','none');
F2=griddedInterpolant({B1,B2},C,'linear','none');


figure(1)
surf(A1,A2,C','FaceColor', [0 0 1],'EdgeColor','none','FaceAlpha',1)
hold on
surf(B1,B2,C','FaceColor', [1 0 0],'EdgeColor','none','FaceAlpha',1)
xlabel x; ylabel y; view(-30,50); axis vis3d

xl=xlim; yl=ylim;
x=linspace(xl(1),xl(2),500);
y=linspace(yl(1),yl(2),500);

C1=F1({x,y});
C2=F2({x,y});
cm=contourc(x,y,(C1-C2)',[0,0]);

[~,coords]=getContourLineCoordinates(cm);

for i=1:numel(coords)

  tmp=coords{i};
  tmp(:,3)=F2(tmp);
  coords{i}=num2cell(tmp,1); %coordinates of the surface intersection

end

for i=1:numel(coords)
 [x,y,z]=deal(coords{i}{:});
 line(x,y,z,'Color','g','LineWidth',3);
end
hold off

[Jay Talreja]

Thankyou very much. It helped me a lot.

I have a few questions regarding your answer.

1) Can you explain your code because It worked as expected but I was not able to understand below part of the code.

[~,h]=contour3(x,y,C1-C2,[0,0],'LineWidth',1,'Color','b');

XData=h.XData; %intersection x-coordinates

YData=h.YData; %intersection y-coordinates

2) The intersection line which I see from that I need their cordinates. I was unable to to find the variables where these values are stored. I had found a function whose reference i have given below

https://in.mathworks.com/matlabcentral/fileexchange/74010-getcontourlinecoordinates

This fuction gave me the exact cordinates of the contour line. But still was not able to understand the function as how it worked ?

3) I there a way that I can see this contour line on my actual graph. I tried to do but the counter level is zero which I couldnt change. Where as my graph is much about the zero level so, while viewing from XY plane I am not able to see the counter line.

Thanks in advance.

[Matt J]

The intersection line which I see from that I need their cordinates. I was unable to to find the variables where these values are stored

I had thought that XData, YData would give you the coordinates, but apparently I was wrong. I have updated my answer, using Adam Danz's File Exchange tool that you referenced. It works well, as the plot shows.

I there a way that I can see this contour line on my actual graph.

That is now demonstrated.

[Jay Talreja]

Yes now it is working as excepted. Thanks for help