plotting a surface between 2D curves

Hello Experts,

I need to fill/fill a curve between the 2D curves in 3D space. I've seen some comments with the surf command, but would the command help where the extremeties of the curve are defined? My script looks something like this for 2D curves spaced in 3D-

Hoping to get some advice on it.

clc

clear all

figure(2)

x = linspace(28,224);

y = repelem(1,100); y2 =repelem(2,100);

eq1 = 0.0645*log(x)+0.9221;

eq2 = 0.0225*log(x)+0.9441;

plot3(y,x,eq1)

hold on

plot3(y2,x,eq2)

view([35 25])

grid on

legend

Answer 1

[Star Strider]

One option is a patch object for this and another is surf —

figure(2)
x = linspace(28,224);
y1 = repelem(1,100); y2 =repelem(2,100); 
eq1 = 0.0645*log(x)+0.9221;
eq2 = 0.0225*log(x)+0.9441;
plot3(y1, x, eq1, '-b', 'LineWidth',2)
hold on
plot3(y2, x, eq2, '-r', 'LineWidth',2)
% patch([y1 flip(y2)], [x flip(x)], [eq1 flip(eq2)], 'g', 'FaceAlpha',0.25, 'EdgeColor','none')     % 'patch'
surf([y1; y2], [x; x], [eq1; eq2], 'MeshStyle','row')                                             % 'surf'
view([35 25])
grid on
legend('eq1', 'eq2', 'Included Surface')
xlabel('X')
ylabel('Y')

I included working calls for both, so experiment to see which is best.

.

[Chaman Srivastava]

Thank you very much!!!

[Star Strider]

As always, my pleasure!

Thank you for posing an interesting problem!

.

[Chaman Srivastava]

Thanks! Just out of curiosity, is it possible to create a mesh on the plot? it may look better :D

[Star Strider]

I considered that. It‘s slightly difficult, however not impossible.

It took a bit to figure it out. I used three different approaches before I finally got one that I liked.

The first one (figure(2)) simply draws the grid lines that surf provides in the original code.

The second (figure(3)) uses gridded interpolation techniques to construct the surface, however it also creates a connectig surface underneath the intended surface that I couldn’t get rid of, and only provide one set of grid lines as well.

The third (figure(4)) intrepolates all the matrices to create a surface, and finally does what I want! The ‘Ym’ and ‘Zm’ matrices had to be transposed from the way I originally created them in order to plot it correctly, however that code has the advantage of producing the result I want, with grid lines in both directions. I also plotted it as surfc in order to describe the surface in more detail.

x = linspace(28,224);
y1 = repelem(1,100); y2 =repelem(2,100); 
eq1 = 0.0645*log(x)+0.9221;
eq2 = 0.0225*log(x)+0.9441;

xv = linspace(min(x), max(x), 25);
y1v = linspace(min(y1), max(y1), 25);
y2v = linspace(min(y2), max(y2), 25);
[Xm,Ym] = ndgrid([xv(:); xv(:)], [y1v(:); y2v(:)]);
Zm = griddata([x(:); x(:)], [y1(:); y2(:)], [eq1(:); eq2(:)], Xm, Ym);


figure(2)
plot3(y1, x, eq1, '-b', 'LineWidth',2)
hold on
plot3(y2, x, eq2, '-r', 'LineWidth',2)
% patch([y1 flip(y2)], [x flip(x)], [eq1 flip(eq2)], 'g', 'FaceAlpha',0.25, 'EdgeColor','none')       % 'patch'
surf([y1; y2], [x; x], [eq1; eq2])                                                                  % 'surf'
% surf(Ym, Xm, Zm)
view([35 25])
grid on
legend('eq1', 'eq2', 'Included Surface')
xlabel('Y')
ylabel('X')

xv = linspace(min(x), max(x), 25);
y1v = linspace(min(y1), max(y1), 25);
y2v = linspace(min(y2), max(y2), 25);
[Xm,Ym] = ndgrid([xv(:); xv(:)], [y1v(:); y2v(:)]);
Zm = griddata([x(:); x(:)], [y1(:); y2(:)], [eq1(:); eq2(:)], Xm, Ym);

figure(3)
surf(Ym, Xm, Zm)
grid on
view([35 25])
xlabel('Y')
ylabel('X')

N = 25;
Xm = (ones(25,1) * linspace(28,224,N));
Ym = (ones(N,1) * linspace(1, 2, N));
k1 = linspace(0.0645, 0.0225, N);
k2 = linspace(0.9221, 0.9441, N);
Zm = k1(:).*log(Xm) + k2(:);

figure(4)
surfc(Ym, Xm', Zm')
grid on
view([35 25])
zlim([1 1.3])
xlabel('Y')
ylabel('X')

figure(5)
hsc = surfc(Ym, Xm', Zm');
hold on
hp3(1) = plot3(y1, x, eq1, '-b', 'LineWidth',2);
hp3(2) = plot3(y2, x, eq2, '-r', 'LineWidth',2);
hold off
grid on
view([35 25])
zlim([1 1.3])
xlabel('Y')
ylabel('X')
legend([hsc(1) hp3], 'Interpolated Surface', 'eq1', 'eq2', 'Location','best')

I created the matrices as square matrices, and changing‘N’ changes the number of grid lines, and accordingly the grid spacing and the surface resolution.

I’m happy with figure(4) ! Adding back the original lines creates figure(5).

.