How to project and fit a 2D path onto a 3D surface?

I want to project a 2D spiral path on a 3D surface as in the attached image. How can this be done? Any help would be appreciated.

Answer 1

[Adam Danz]

> I want to project a 2D spiral path on a 3D surface

Inputs:

• (x,y) coordinates of the 2D spiral
• (X,Y,Z) coordinates of the 3D surface

Produce 2D spiral.

t = linspace(0,12*pi,201);
x = t/pi.*cos(t);
y = t/pi.*sin(t);
zBase = -8; 
z = zBase * ones(size(x)); 

cla()
plot3(x,y,z, '-', 'Color', [0.5 0.5 0.5])

Produce 3D surface

% Define surface
hold on
[X,Y,Z] = peaks(25);
X = X*4; 
Y = Y*4;
% surf(X,Y,Z)

Interpolate the 3D surface so it shares the same x,y grid values as the spiral.

F = griddedInterpolant(X',Y',Z');
[Xq,Yq] = ndgrid(x,y);
Vq = F(Xq,Yq);

% Plot the interpolated surface
surf(Xq,Yq,Vq,'FaceAlpha',.1,'EdgeAlpha',0)

Add the 3D spiral to the surface

z3D = Vq(logical(eye(size(Vq)))); 
plot3(x,y,z3D, 'k-', 'LineWidth', 1)

Answer 2

[DGM]

Something like

N = 1000;
nturns = 10;
rmax = pi;
zscale = 0.1;
zoffset = 0.5;

r = linspace(0,rmax,N);
th = linspace(0,nturns*2*pi,N);
[x y] = pol2cart(th,r);

z = zoffset + zscale*sin(x);

plot(x,y); hold on
plot3(x,y,z);
view(3)
zlim([0 1])

view(-15,14)