Plot 3D surface within nonlinear bounds

Let's say I have bounds as follows in the 2D plot below:

xmin1 = 0;  xmax1 = 1; xmax2 = 2;
ymin1 = @(x)0.25* x.^2; ymax1 = @(x) x.^(1/3);
x1 = 0:0.05:1; x2 = 1.05:0.05:2; xAll = 2:-0.05:0;
yTop1 = ymax1(x1); yTop2 = ones(1,length(x2)); yBot = ymin1(xAll);
figure
fill([x1 x2 xAll],[yTop1 yTop2 yBot],'b')

I want to plot surf() with , but only in the bounds above. That's to say, the projection of the surface plot matches the 2D fill above. How do I program this?

Just adding the surface with fill for reference:

fun = @(x,y) sin(4.*x) + y.^2 + 2;
[X,Y] = meshgrid(0:0.05:2,0:0.05:1);
Z = fun(X,Y);
figure
surf(X,Y,Z); hold on
fill([x1 x2 xAll],[yTop1 yTop2 yBot],'b'); hold off

Answer 1

[Abhinaya Kennedy]

To plot the surface only within the specified bounds, you need to mask the values outside the bounds. This can be achieved by setting the Z values to NaN where the points fall outside the desired region. Here's how you can do it:

1. Define the bounds as logical conditions.
2. Apply these bounds to mask out the unwanted parts of the surface.

xmin1 = 0;  
xmax1 = 1; 
xmax2 = 2;
ymin1 = @(x) 0.25 * x.^2; 
ymax1 = @(x) x.^(1/3);

x1 = 0:0.05:1; 
x2 = 1.05:0.05:2; 
xAll = 2:-0.05:0;

yTop1 = ymax1(x1); 
yTop2 = ones(1, length(x2)); 
yBot = ymin1(xAll);

% Define the function
fun = @(x, y) sin(4 .* x) + y.^2 + 2;

% Create meshgrid
[X, Y] = meshgrid(0:0.05:2, 0:0.05:1);
Z = fun(X, Y);

% Mask Z values outside the bounds
mask = false(size(X));

% Apply the bounds to create the mask
for i = 1:length(X(:))
    x = X(i);
    y = Y(i);
    if (x >= xmin1 && x <= xmax1 && y >= ymin1(x) && y <= ymax1(x)) || ...
       (x > xmax1 && x <= xmax2 && y >= ymin1(x) && y <= 1)
        mask(i) = true;
    end
end

Z(~mask) = NaN;

% Plot the surface
figure
surf(X, Y, Z);
hold on

% Plot the 2D fill for reference
fill([x1 x2 xAll], [yTop1 yTop2 yBot], 'b');
hold off

• The "mask" array is created to identify the points within the specified bounds.
• The Z values outside the bounds are set to "NaN" to mask them.

Answer 2

[Mathieu NOE]

hello

this is a job for inpolygon

Points located inside or on edge of polygonal region - MATLAB inpolygon - MathWorks France

as you have already created the x,y data defining this polygon , the answer is quite simple to implement :

NB I have slightly modified your code to use xmax1 and xmax2 instead of hard coded 1's and 2's in multiple locations

xmin1 = 0;
xmax1 = 1;
xmax2 = 2;


%% main code 
ymin1 = @(x)0.25* x.^2;
ymax1 = @(x) x.^(1/3);

% slightly modified these lines (1 replaced by xmax1, 2 replaced by xmax2);
dx = 0.05;
x1 = 0:dx:xmax1;
x2 = xmax1+dx:dx:xmax2;
xAll = xmax2:-dx:0;

yTop1 = ymax1(x1);
yTop2 = ones(1,length(x2));
yBot = ymin1(xAll);

% create polygon x,y data 
xx = [x1 x2 xAll];
yy = [yTop1 yTop2 yBot];

fun = @(x,y) sin(4.*x) + y.^2 + 2;
[X,Y] = meshgrid(0:dx:xmax2,0:dx:xmax1); % (1 replaced by xmax1, 2 replaced by xmax2);
Z = fun(X,Y);
IN = inpolygon(X,Y,xx,yy);

figure
Z(~IN) = NaN; % remove Z data outside polygon
surf(X,Y,Z); hold on
plot(xx,yy,'b')
hold off