How to project a line on a surface?

Hi,

I am plotting a 3D surface and a straight line together. The line is not on the surface nor intersecting the surface. Now I want to project that line onto the surface.

Anyone can help me how to do this?

Thank you!

[Sargondjani]

What is the shape of your surface? Is it a function? And how do you want to project it?

I assume your surface consists of a finite number of data points, and you use vertical projection. You could use interpolation to let the line closely follow the surface. Assume your surface consists of vectors X,Y,Z

If the line consists of a vectors with x,y coordinates in pairs xp, yp, you could do:

F=scatteredInterpolant(X,Y,Z);

Proj_line = F(xp,yp);

Otherwise you could try to change your data to something like this.

[Sachal Hussain]

It's an anatomical shape, not a function. The line is above the surface so I want to project it straight down on the surface.

The line is plotted in a space so it has X,Y,Z coordinates.

Answer 1

[KSSV]

Let X, Y, Z be your surface data. And (x,y) be the coordinates of the line data. Use interpolation to get the z values of line from surface and then plot.

z = interp2(X,Y,Z,x,y) ;
surf(X,Y,Z)
shading interp
plot3(x,y,z,'r')

[Sachal Hussain]

But in my case X Y Z are column vectors, how to grid them?

[KSSV]

Let X, Y, Z be your column data.

F=scatteredInterpolant(X,Y,Z) ;
z=F(x, y) ;

[Sachal Hussain]

I tried to follow your suggested way but the result is still not correct. Below is the code I wrote, Please have a look and point out where I am doing wrong. Thak you!

import_stl = stlread('mesh_40_tagli.stl');

figure,hold on,trisurf(import_stl, 'FaceColor','flat', 'LineStyle', 'none');view(3),

% Adding noise to x,y,z coordinates of surface to make them 'unique'

a = import_stl.Points(:,1); t = a == unique(a)'; out1 = sum(cumsum(.0001*t).*t,2)-.0001 + a; % x-coordinates

a = import_stl.Points(:,2); t = a == unique(a)'; out2 = sum(cumsum(.0001*t).*t,2)-.0001 + a; % y-coordinates

a = import_stl.Points(:,3); t = a == unique(a)'; out3 = sum(cumsum(.0001*t).*t,2)-.0001 + a; % z-coordinates

X = [133.4843 131.3938]; Y = [70.1121 66.5661]; Z = [51.3541 27.6482]; % query points

xq = linspace(X(1),X(2),50); yq = linspace(Y(1),Y(2),50); % sampling of query points

F=scatteredInterpolant(out1,out2,out3) ;

zq=F(xq,yq) ;

plot3(xq,yq,zq);