Contour Line and Surface Matlab - matlab

Question

I want to produce a surface plot with a predefined contour line on the surface, in Matlab. I have already produced the plot in Mathematica, and want to create the equivalent figure in Matlab.
With the following functions I defined a surface
k2[G_, V_] = Sqrt[G]*Exp[-V];
k1[G_] = Sqrt[G]*Exp[-10];
L1[G_, V_] = -0.5*(k1[G_] + 2*k2[G, V]) + 0.5*Sqrt[k1[G_]^2 + 4*k2[G, V]^2];
and a parametric curve over the surface
hike=ParametricPlot3D[{10, 0, 0} + {x^2, x, -(1/L1[10 + x^2, x])}, {x, 0, 12},PlotStyle -> Directive[Thick, Red]];
hikeHeight=ParametricPlot3D[{10, 0, 0} + {x^2,x, -z*(1/L1[10 + x^2, x])}, {x, 0, 12}, {z, 0, 1},PlotStyle -> Directive[Gray], Mesh -> None];
Then I plot the surface and the contour line together:
surf= Plot3D[-1/L1[G, V], {G, 10, 100}, {V, 0, 12}];
Show[surf, hike, hikeHeight, AxesLabel -> {G, V,Z}, Boxed -> False]
What is the process for evaluating the function and producing the same plot in Matlab?
This how far i get with my matlab attempt
[X,Y,Z] = peaks(25);
curvX=diag(X);
curvY=diag(Y);
curvZ=diag(Z);
nn = 401;
xi = linspace(-3.0, 3.0, nn);
yi = xi;
[xi, yi] = meshgrid(xi, yi);
zi = interp2(X, Y, Z, xi, yi, 'spline');
figure()
surf(xi, yi, zi,'LineStyle', 'none', 'FaceColor', 'interp')
colormap(parula)
alpha 0.7
hold on
surf(diag(curvX),diag(curvY),diag(curvZ),'LineStyle', 'none')
the surface and the parametric curve are obviously not the same but the idea is the same to plot an slice of the surface

Answer 1

Let's start by defining the functions, as inline, vectorised function handles:
k2 = #(g, v)sqrt(g).*exp(-v);
k1 = #(g)sqrt(g).*exp(-10);
l1 = #(g, v) -.5 .* (k1(g) + 2.*k2(g, v)) + 0.5 * sqrt(k1(g).^2 + 4.*k2(g, v).^2);
Now we need to define a mesh, since Matlab isn't smart enough to do automatic discretisation like Mathematica:
nMeshPoints = 50;
vfG = linspace(10, 100, nMeshPoints);
vfV = linspace(0, 12, nMeshPoints);
[mfG, mfV] = ndgrid(vfG, vfV);
Ok, now we can evaluate the surface over the mesh, and make a surface plot:
hSurf = surf(mfG, mfV, -1./l1(mfG, mfV));
shading interp;
hold on;
hSurf.FaceAlpha = 0.5;
Now we need to build and plot your parametric line, also via explicit discretisation:
vfX = linspace(0, 12, nMeshPoints);
vfZ = linspace(0, 1, nMeshPoints);
vfLX = 10 + vfX.^2;
vfLY = vfX;
vfLZ = -(1 ./ l1(10 + vfX.^2, vfX));
vfLHeight = vfLZ .* vfZ;
plot3(vfLX, vfLY, vfLZ, 'r-');
plot3(vfLX, vfLY, vfLHeight, 'k-');
Now we can make the plot a little more beautiful:
xlim([10 100]);
ylim([0 12]);
zlim([0 20000]);
caxis([0 20000]);
xlabel('G');
ylabel('V');
zlabel('Z');
view([60, 30]);
The result: not quite as beautiful as Mathematica, but at least equivalent.