Find gradient ascent for 3D surface

• I have a 3D surface (x,y,z) plotted using the following code (excel sheet attached):

clear; clc; clearvars;

% Read table:

T = readtable('full-nov26th.csv');

rows = (T.(3)== 3);

T = T(rows, :);

% Define Variables

x = T.(1);

y = T.(2);

z = T.(4);

xi = linspace(min(x),max(x), 200);

yi = linspace(min(y),max(y), 200);

[X,Y] = meshgrid(xi,yi);

Z = griddata(x,y,z,X,Y);

surf(X,Y,Z);

• The generated surface looks as follows:

• I am trying to plot a line that incrementally goes from the starting point (0,0,14.19) to the highest point on the surface.

• I have seen other answers on the forums dealing with analytical functions. However, in here, I only have the surface generated from points. Hence, how could I be able to do it from these points?

Answer 1

[Star Strider]

This code finds the maximum of the surface and then uses griddedInterpolant with the calculated ‘xv’ and ‘yv’ vectors to draw the interpolated line, following the ‘Z’ contours.

T = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/815814/full-nov26th.csv', 'VariableNamingRule','preserve')

T = 161599×6 table
    in:xrot    in:yrot    in:n    out:PE    out:ARM    out:r
    _______    _______    ____    ______    _______    _____

        0         0        3      14.19         0      0.63 
     0.01         0        3      14.19      0.33      0.63 
     0.02         0        3      14.19      0.67      0.63 
     0.03         0        3       14.2         1      0.63 
     0.04         0        3      14.21      1.33      0.63 
     0.05         0        3      14.22      1.67      0.63 
     0.06         0        3      14.24         2      0.63 
     0.07         0        3      14.25      2.33      0.63 
     0.08         0        3      14.27      2.67      0.63 
     0.09         0        3      14.29         3      0.63 
      0.1         0        3      14.32      3.34      0.63 
     0.11         0        3      14.35      3.65      0.63 
     0.12         0        3      14.38      3.95      0.63 
     0.13         0        3      14.41      4.21      0.63 
     0.14         0        3      14.44      4.46      0.63 
     0.15         0        3      14.48      4.68      0.63 

rows = (T.(3)== 3);
T = T(rows, :); 

% Define Variables
x = T.(1);
y = T.(2);
z = T.(4);

xi = linspace(min(x),max(x), 200);
yi = linspace(min(y),max(y), 200);
[X,Y] = ndgrid(xi,yi);
Z = griddata(x,y,z,X,Y);
zmix = find(Z == max(Z(:)))                      % There Is More Than One Maximum

zmix = 4×1

17202 17402 18005 18204

Xc = X(zmix);
Yc = Y(zmix);
Zc = Z(zmix);

Xcm = mean(Xc);
Ycm = mean(Yc);
Zcm = mean(Zc);

xv = linspace(0, Xcm, 100);
yv = linspace(0, Ycm, 100);
Zi = griddedInterpolant(X,Y,Z);
zv = Zi(xv,yv);

figure
surf(X,Y,Z, 'EdgeColor','none', 'FaceAlpha',0.5);
hold on
stem3(Xcm,Ycm,Zcm,'-^r', 'filled')
plot3(xv, yv, zv, '-m', 'LineWidth',2)
hold off
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('Z')
title('Original: Complete Surface & Requested Line')

figure
surf(X,Y,Z, 'EdgeColor','none', 'FaceAlpha',0.5);
hold on
stem3(Xcm,Ycm,Zcm,'-^r', 'filled')
plot3(xv, yv, zv, '-m', 'LineWidth',2)
hold off
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('Z')
xlim([0 2*Xcm])
ylim([0 2*Ycm])
zlim([10 20])
view(290,30)
title('Detail: Zoomed Surface Section & Requested Line')

Choose different lime colours & colormap options to get the desired result.

.

[HAMID]

Thank you so much. This is extremely helpful.

[Star Strider]

As always, my pleasure!

.

Answer 2

[Alan Weiss]

You might be interested in this example: Pattern Search Climbs Mount Washington

Alan Weiss

MATLAB mathematical toolbox documentation