How to apply any 2D lines on to a given 3D surface?

I will be given the dimension of a few lines on a 2D plane. I want to be able to apply them on any 3D curved surface made of a set of data points. It surface can be a set of data in a point cloud. This surface may not be represented by any equations. I just want to know if there is a way to fit these lines on to a surface and now the lines will have a curve based on that surface.

[Matt J]

To me at least, the question is not clear enough to be answered. Please provide an example set of input data and some description of what form the output should take.

Answer 1

[Star Strider]

This is actually straightforward with the griddedInterpolant function, providing the data are gridded to begin with. The surface can actually be random, since the funciton will interpolate essentially anything it is given. The llines to be drawn on the surface have to have enough data points to fit any of the surface irregularities.

Here, the black ine is straight and the magenta line is a sine curve —

x = linspace(-5, 5, 20);
y = linspace(0, 10, 25);
[X,Y] = ndgrid(x,y);
z = randn(20, 25);

F = griddedInterpolant(X,Y,z);
x1v = linspace(-2, 3.5, 1500);
y1v = linspace(3, 7, 1500);
z1v = F(x1v,y1v);

x2v = linspace(-4, 4, 2500);
y2v = 4+2*sin(2*pi*x2v/5);
z2v = F(x2v,y2v);

figure
surf(x, y, z.')
hold on
plot3(x1v, y1v, z1v, 'k', 'LineWidth',3)
plot3(x2v, y2v, z2v, 'm', 'LineWidth',3)
hold off
grid on
xlabel('X')
ylabel('Y')
view(35,80)

The griddedInterpolant funciton would have fewer problems with a more regular surface. The number of data points in the lines is important in order to provide the function with good enough resolution to map all the irregularities. I gave it a real challenge here, and it seems to have done quite well.

EDIT — Aesthetic fix.

.

[Bojia Lan]

Thank you. This is exactly the concept I wanted to know. However, the tricky thing is that would it be possible to do the same thing if I am provided a surface of pointcloud or just (x,y,z) coordinates?

[Star Strider]

My pleasure!

I’m not absolutely certain because I don’t have those to work with. However it should work with either scatteredInterpolant or griddedInterpolant, as it did here. I would experiment with both of them to see which gives the best results. The calling syntax is the same.

Try it with those. If you have problems, post back here and I’ll see if I can help solve them.

Testing both, scatteredInterpolant definitely works better than griddedInterpolant in this particular example, so it would likely be preferable to use it with your data —

x = linspace(-5, 5, 20);
y = linspace(0, 10, 25);
[X,Y] = ndgrid(x,y);
z = randn(20, 25);

F = griddedInterpolant(X,Y,z);
x1v = linspace(-2, 3.5, 1500);
y1v = linspace(3, 7, 1500);
z1v = F(x1v,y1v);

x2v = linspace(-4, 4, 2500);
y2v = 4+2*sin(2*pi*x2v/5);
z2v = F(x2v,y2v);

figure
surf(x, y, z.')
hold on
plot3(x1v, y1v, z1v, 'k', 'LineWidth',3)
plot3(x2v, y2v, z2v, 'm', 'LineWidth',3)
hold off
grid on
xlabel('X')
ylabel('Y')
title('griddedInterpolant')
view(35,80)

F = scatteredInterpolant(X(:),Y(:),z(:));
x1v = linspace(-2, 3.5, 1500);
y1v = linspace(3, 7, 1500);
z1v = F(x1v,y1v);

x2v = linspace(-4, 4, 2500);
y2v = 4+2*sin(2*pi*x2v/5);
z2v = F(x2v,y2v);

figure
surf(x, y, z.')
hold on
plot3(x1v, y1v, z1v, 'k', 'LineWidth',3)
plot3(x2v, y2v, z2v, 'm', 'LineWidth',3)
hold off
grid on
xlabel('X')
ylabel('Y')
title('scatteredInterpolant')
view(35,80)

The griddedInterpolant result appears to ‘tunnel’ through some of the irregular peaks, while the scatteredInterpolant result remains on the surface everywhere.

.

[Bojia Lan]

Thank you! I will work on it.

[Star Strider]

As always, my pleasure!