how to find the intersection points of two 3d surfaces

i have one 3d function plot

function = 2.0346941376982715` (0.33000000000000007` - 0.5` V) (1/Lambda)^0.9523809523809523` where {Lambda, 1, 5}, {V, -5, 5}

and one 3d data plot of some data

my question is how can i find the intersection points of these two 3d plots

Answer 1

[Star Strider]

Try this —

fcn = @(Lambda,V) [2.0346941376982715 + (0.33000000000000007 - 0.5 * V); (1./Lambda).^0.9523809523809523];
%  where {Lambda, 1, 5}, {V, -5, 5}
[Lm,Vm] = ndgrid(1:5, -5:5);

fv = fcn(Lm,Vm);
fv1 = fv(1:5,:);
fv2 = fv((1:5)+5,:);
intsx = fv1 - fv2;

figure
[c,h] = contour3(Lm,Vm,intsx,[0 0], '-r');
xlabel('\Lambda')
ylabel('V')
title('Intersection Contour')
view(-120,30)

F = scatteredInterpolant(Lm(:),Vm(:),fv1(:));
Fisx = F(c(1,2:end),c(2,2:end));


figure
surf(Lm, Vm, fv1, 'FaceAlpha',0.8)
hold on
surf(Lm, Vm, fv2, 'FaceAlpha',0.5)
plot3(c(1,2:end),c(2,2:end),Fisx, '-r', 'LineWidth',8)
hold off
grid on
xlabel('\Lambda')
ylabel('V')
text(1,-5,1,'\Lambda Surface')
text(5,-5,5,'V Surface')
colormap(turbo)
view(-130,30)

This uses the (x,y) data provided by the contour3 function and the scatteredInterpolant function to calculate the z coordinate of the intersection, and plots the result.

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[jay verma]

thank you for your answer but actully my question is that i have one 3d surface of the equation mentioned above and one 3d surface made up of 55 descrete data points and i want to find the intersection points of these two 3d surfaces...

[Star Strider]

My pleasure!

The same approach would apply.

I cannot create code for missing or undefined problems.

[jay verma]

one 3d surface = 2.0346941376982715(0.33000000000000007 - 0.5 V) (1/Lambda)^0.9523809523809523 where {Lambda, 1, 5}, {V, -5, 5}

second 3d surface = data given in image below

and i need the list of intersection points of these two surfaces...

[Star Strider]

This is useless to me.

I cannot do anything with images of data. I need the actual data (preferably as a text file, since I cannot work with .mat files with the online Run feature).

I will also need an explanation of what the data are, since this makes no obvious sense. It also contains a strange sort of left single quote (`) that will have to be removed in order to use the data.

If these are the point data, what plane is it to intersect? The original ‘function’ makes no obvious sense either, because I have no idea how to intepret it in the context of the data. (I created two functions from it in the absence of any explanation as to exactly what it is supposed to do.) It also contains the strange (`) that I removed manually.

All of these issues need to be clarified.

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