Here is an example
[x,y,z] = peaks(20); % surface
% curve coordinates
x1 = linspace(-3,2,20);
y1 = linspace(-1,1,20);
z1 = interp2(x,y,z,x1,y1);
surf(x,y,z,'edgecolor',[1 1 1]*0.8)
line(x1,y1,z1,'color','red','linewidth',2)
% calculate curve length
L = sum(sqrt(diff(x1).^2+diff(y1).^2+diff(z1).^2))
