3D surf plot for more than two quantities

Question

yogeshwari patel on 19 Jun 2025

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https://se.mathworks.com/matlabcentral/answers/2177900-3d-surf-plot-for-more-than-two-quantities

Answered: Star Strider on 19 Jun 2025

I want to plot the value in the same 3D graph .

syms x t r b %alpha
% Parameter values 
a=(pi)/3;
g=9.8;
U=2.5;
O=7.29*10^(-5);
f=2*O*sin(a);
H=-(f/g)*U;
alpha=0.75; % fractional order 
%%%%%%%%%initalization of variable 
u_l=sym(zeros(1));
v_l=zeros(1,'sym');
h_l=zeros(1,'sym');
A_l=zeros(1,2,'sym');
B_l=zeros(1,2,'sym');
C_l=zeros(1,2,'sym');
D_l=zeros(1,2,'sym');
series1_l(x,t)=sym(zeros(1,1));
series2_l(x,t)=sym(zeros(1,1));
series3_l(x,t)=sym(zeros(1,1));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
u_up=sym(zeros(1));
v_up=zeros(1,'sym');
h_up=zeros(1,'sym');
A_up=zeros(1,2,'sym');
B_up=zeros(1,2,'sym');
C_up=zeros(1,2,'sym');
D_up=zeros(1,2,'sym');
series1_up(x,t)=sym(zeros(1,1));
series2_up(x,t)=sym(zeros(1,1));
series3_up(x,t)=sym(zeros(1,1));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
u_cr=sym(zeros(1));
v_cr=zeros(1,'sym');
h_cr=zeros(1,'sym');
A_cr=zeros(1,2,'sym');
B_cr=zeros(1,2,'sym');
C_cr=zeros(1,2,'sym');
D_cr=zeros(1,2,'sym');
series1_cr(x,t)=sym(zeros(1,1));
series2_cr(x,t)=sym(zeros(1,1));
series3_cr(x,t)=sym(zeros(1,1));
%%%%%%%% Initial condition  fuzzy condition
R=0.5;
b_l=0 % lower bound 
b_cr=0.5 % middle value
b_u=1 % upper value 
%%%%%%%%%%%%%%%%%% lOWER VALUE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
u_l(1)=(2*b_l*(1-R)+R)*exp(x)*(sech(x))^2;
v_l(1)=(2*b_l*(1-R)+R+1)*2*x*(sech(2*x))^2;
h_l(1)=(2*b_l*(1-R)+R)*x^2*(sech(2*x))^2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%UPPER VALUE 
u_up(1)=(2*b_u*(1-R)+R)*exp(x)*(sech(x))^2;
v_up(1)=(2*b_u*(1-R)+R+1)*2*x*(sech(2*x))^2;
h_up(1)=(2*b_u*(1-R)+R)*x^2*(sech(2*x))^2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Middle valur %%%%%%%%%%%%%%%%%%%%
u_cr(1)=(2*b_cr*(1-R)+R)*exp(x)*(sech(x))^2;
v_cr(1)=(2*b_cr*(1-R)+R+1)*2*x*(sech(2*x))^2;
h_cr(1)=(2*b_cr*(1-R)+R)*x^2*(sech(2*x))^2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%lOWER VALUR %%%%%%%%%%%%%%%%%%%%%%%%%
for k=1:2
    A_l=0;
    B_l=0;
    C_l=0;
    D_l=0;
    if k==1
        E=1;
    else
        E=0;
    end
    for r=1:k
        A_l=A_l+u_l(r)*diff(u_l(k-r+1),x,1);
        B_l=B_l+u_l(r)*diff(v_l(k-r+1),x,1);
        C_l=C_l+u_l(r)*diff(h_l(k-r+1),x,1);
        D_l=D_l+h_l(r)*diff(u_l(k-r+1),x,1);
    end
    u_l(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_l+f*v_l(k)-g*diff(h_l(k),x,1)));
    v_l(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_l-f*u_l(k)-g*H*E);
    h_l(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_l-H*v_l(k)-D_l);
end
% t1=simplify(u(2))
% var2 = vpa(t1)
% t2=simplify(v(2))
% var = vpa(t2)
% t3=simplify(h(2))
for k=1:3
    series1_l(x,t)=simplify(series1_l(x,t)+u_l(k)*(power(t,k-1)));
    series2_l(x,t)=simplify(series2_l(x,t)+v_l(k)*(power(t,k-1)));
    series3_l(x,t)=simplify(series3_l(x,t)+h_l(k)*(power(t,k-1)));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UPPER  VALUE %%%%%%%%%%%%%%%%
for k=1:2
    A_up=0;
    B_up=0;
    C_up=0;
    D_up=0;
    if k==1
        E=1;
    else
        E=0;
    end
    for r=1:k
        A_up=A_up+u_up(r)*diff(u_up(k-r+1),x,1);
        B_up=B_up+u_up(r)*diff(v_up(k-r+1),x,1);
        C_up=C_up+u_up(r)*diff(h_up(k-r+1),x,1);
        D_up=D_up+h_up(r)*diff(u_up(k-r+1),x,1);
    end
    u_up(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_up+f*v_up(k)-g*diff(h_up(k),x,1)));
    v_up(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_up-f*u_up(k)-g*H*E);
    h_up(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_up-H*v_up(k)-D_up);
end
% t1=simplify(u(2))
% var2 = vpa(t1)_u
% t2=simplify(v(2))
% var = vpa(t2)
% t3=simplify(h(2))
for k=1:3
    series1_up(x,t)=simplify(series1_up(x,t)+u_up(k)*(power(t,k-1)));
    series2_up(x,t)=simplify(series2_up(x,t)+v_up(k)*(power(t,k-1)));
    series3_up(x,t)=simplify(series3_up(x,t)+h_up(k)*(power(t,k-1)));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%middle value %%%%%%%%%%%%%%
for k=1:2
    A_cr=0;
    B_cr=0;
    C_cr=0;
    D_cr=0;
    if k==1
        E=1;
    else
        E=0;
    end
    for r=1:k
        A_cr=A_cr+u_cr(r)*diff(u_up(k-r+1),x,1);
        B_cr=B_cr+u_cr(r)*diff(v_up(k-r+1),x,1);
        C_cr=C_cr+u_cr(r)*diff(h_up(k-r+1),x,1);
        D_cr=D_up+h_cr(r)*diff(u_up(k-r+1),x,1);
    end
    u_cr(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_cr+f*v_up(k)-g*diff(h_cr(k),x,1)));
    v_cr(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_cr-f*u_cr(k)-g*H*E);
    h_cr(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_cr-H*v_cr(k)-D_cr);
end
% t1=simplify(u(2))
% var2 = vpa(t1)_u
% t2=simplify(v(2))
% var = vpa(t2)
% t3=simplify(h(2))
for k=1:3
    series1_cr(x,t)=simplify(series1_cr(x,t)+u_cr(k)*(power(t,k-1)));
    series2_cr(x,t)=simplify(series2_cr(x,t)+v_cr(k)*(power(t,k-1)));
    series3_cr(x,t)=simplify(series3_cr(x,t)+h_cr(k)*(power(t,k-1)));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C1_l=zeros(1)
C2_l=zeros(1)
C3_l=zeros(1)
C1_up=zeros(1)
C2_up=zeros(1)
C3_up=zeros(1)
C1_cr=zeros(1)
C2_cr=zeros(1)
C3_cr=zeros(1)
row=0;
x=0:0.04:2
t=0:0.002:0.1
for i=1:length(x)
    row=row+1;
    col=0;
    for j=1:length(t)
        col=col+1;
        C1_l(row,col)=series1_l(x(i),t(j));
        C2_l(row,col)=series2_l(x(i),t(j));
        C3_l(row,col)=series3_l(x(i),t(j));
        %----------------------------------
        C1_up(row,col)=series1_up(x(i),t(j));
        C2_up(row,col)=series2_up(x(i),t(j));
        C3_up(row,col)=series3_up(x(i),t(j));
        %------------------------------------
        C1_cr(row,col)=series1_cr(x(i),t(j));
        C2_cr(row,col)=series2_cr(x(i),t(j));
        C3_cr(row,col)=series3_cr(x(i),t(j));
        
    end
end
%--------------------------------------------------------
surf(x,t,C1_l,C1_up,C1_cr)
surf(x,t,C2_l,C2_up,C2_cr)
surf(x,t,C3_l,C3_up,C3_cr)

I want to plot all the graph in the same 3D plot. I dont want different graph using subplot. and I am using MATLAB version 2023a

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Matt J on 19 Jun 2025

So, then why not use hold ?

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Answer 1

Star Strider on 19 Jun 2025

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https://se.mathworks.com/matlabcentral/answers/2177900-3d-surf-plot-for-more-than-two-quantities#answer_1566846

Open in MATLAB Online

One problem is thta your surf calls have the wrong syntax. This works. I made the surfaces partially transparent (the FaceAlpha arguments), however you can change that by changing or removing the FaceAlpha arguments

Try this --

syms x t r b %alpha

% Parameter values

a=(pi)/3;

g=9.8;

U=2.5;

O=7.29*10^(-5);

f=2*O*sin(a);

H=-(f/g)*U;

alpha=0.75; % fractional order

%%%%%%%%%initalization of variable

u_l=sym(zeros(1));

v_l=zeros(1,'sym');

h_l=zeros(1,'sym');

A_l=zeros(1,2,'sym');

B_l=zeros(1,2,'sym');

C_l=zeros(1,2,'sym');

D_l=zeros(1,2,'sym');

series1_l(x,t)=sym(zeros(1,1));

series2_l(x,t)=sym(zeros(1,1));

series3_l(x,t)=sym(zeros(1,1));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

u_up=sym(zeros(1));

v_up=zeros(1,'sym');

h_up=zeros(1,'sym');

A_up=zeros(1,2,'sym');

B_up=zeros(1,2,'sym');

C_up=zeros(1,2,'sym');

D_up=zeros(1,2,'sym');

series1_up(x,t)=sym(zeros(1,1));

series2_up(x,t)=sym(zeros(1,1));

series3_up(x,t)=sym(zeros(1,1));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

u_cr=sym(zeros(1));

v_cr=zeros(1,'sym');

h_cr=zeros(1,'sym');

A_cr=zeros(1,2,'sym');

B_cr=zeros(1,2,'sym');

C_cr=zeros(1,2,'sym');

D_cr=zeros(1,2,'sym');

series1_cr(x,t)=sym(zeros(1,1));

series2_cr(x,t)=sym(zeros(1,1));

series3_cr(x,t)=sym(zeros(1,1));

%%%%%%%% Initial condition fuzzy condition

R=0.5;

b_l=0 % lower bound

b_l = 0

b_cr=0.5 % middle value

b_cr = 0.5000

b_u=1 % upper value

b_u = 1

%%%%%%%%%%%%%%%%%% lOWER VALUE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

u_l(1)=(2*b_l*(1-R)+R)*exp(x)*(sech(x))^2;

v_l(1)=(2*b_l*(1-R)+R+1)*2*x*(sech(2*x))^2;

h_l(1)=(2*b_l*(1-R)+R)*x^2*(sech(2*x))^2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%UPPER VALUE

u_up(1)=(2*b_u*(1-R)+R)*exp(x)*(sech(x))^2;

v_up(1)=(2*b_u*(1-R)+R+1)*2*x*(sech(2*x))^2;

h_up(1)=(2*b_u*(1-R)+R)*x^2*(sech(2*x))^2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Middle valur %%%%%%%%%%%%%%%%%%%%

u_cr(1)=(2*b_cr*(1-R)+R)*exp(x)*(sech(x))^2;

v_cr(1)=(2*b_cr*(1-R)+R+1)*2*x*(sech(2*x))^2;

h_cr(1)=(2*b_cr*(1-R)+R)*x^2*(sech(2*x))^2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%lOWER VALUR %%%%%%%%%%%%%%%%%%%%%%%%%

for k=1:2

A_l=0;

B_l=0;

C_l=0;

D_l=0;

if k==1

E=1;

else

E=0;

end

for r=1:k

A_l=A_l+u_l(r)*diff(u_l(k-r+1),x,1);

B_l=B_l+u_l(r)*diff(v_l(k-r+1),x,1);

C_l=C_l+u_l(r)*diff(h_l(k-r+1),x,1);

D_l=D_l+h_l(r)*diff(u_l(k-r+1),x,1);

end

u_l(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_l+f*v_l(k)-g*diff(h_l(k),x,1)));

v_l(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_l-f*u_l(k)-g*H*E);

h_l(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_l-H*v_l(k)-D_l);

end

% t1=simplify(u(2))

% var2 = vpa(t1)

% t2=simplify(v(2))

% var = vpa(t2)

% t3=simplify(h(2))

for k=1:3

series1_l(x,t)=simplify(series1_l(x,t)+u_l(k)*(power(t,k-1)));

series2_l(x,t)=simplify(series2_l(x,t)+v_l(k)*(power(t,k-1)));

series3_l(x,t)=simplify(series3_l(x,t)+h_l(k)*(power(t,k-1)));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% UPPER VALUE %%%%%%%%%%%%%%%%

for k=1:2

A_up=0;

B_up=0;

C_up=0;

D_up=0;

if k==1

E=1;

else

E=0;

end

for r=1:k

A_up=A_up+u_up(r)*diff(u_up(k-r+1),x,1);

B_up=B_up+u_up(r)*diff(v_up(k-r+1),x,1);

C_up=C_up+u_up(r)*diff(h_up(k-r+1),x,1);

D_up=D_up+h_up(r)*diff(u_up(k-r+1),x,1);

end

u_up(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_up+f*v_up(k)-g*diff(h_up(k),x,1)));

v_up(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_up-f*u_up(k)-g*H*E);

h_up(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_up-H*v_up(k)-D_up);

end

% t1=simplify(u(2))

% var2 = vpa(t1)_u

% t2=simplify(v(2))

% var = vpa(t2)

% t3=simplify(h(2))

for k=1:3

series1_up(x,t)=simplify(series1_up(x,t)+u_up(k)*(power(t,k-1)));

series2_up(x,t)=simplify(series2_up(x,t)+v_up(k)*(power(t,k-1)));

series3_up(x,t)=simplify(series3_up(x,t)+h_up(k)*(power(t,k-1)));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%middle value %%%%%%%%%%%%%%

for k=1:2

A_cr=0;

B_cr=0;

C_cr=0;

D_cr=0;

if k==1

E=1;

else

E=0;

end

for r=1:k

A_cr=A_cr+u_cr(r)*diff(u_up(k-r+1),x,1);

B_cr=B_cr+u_cr(r)*diff(v_up(k-r+1),x,1);

C_cr=C_cr+u_cr(r)*diff(h_up(k-r+1),x,1);

D_cr=D_up+h_cr(r)*diff(u_up(k-r+1),x,1);

end

u_cr(k+1)=simplify(gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-A_cr+f*v_up(k)-g*diff(h_cr(k),x,1)));

v_cr(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-B_cr-f*u_cr(k)-g*H*E);

h_cr(k+1)=gamma(((k-1)*alpha)+1)/gamma((alpha*(k+1-1))+1)*(-C_cr-H*v_cr(k)-D_cr);

end

% t1=simplify(u(2))

% var2 = vpa(t1)_u

% t2=simplify(v(2))

% var = vpa(t2)

% t3=simplify(h(2))

for k=1:3

series1_cr(x,t)=simplify(series1_cr(x,t)+u_cr(k)*(power(t,k-1)));

series2_cr(x,t)=simplify(series2_cr(x,t)+v_cr(k)*(power(t,k-1)));

series3_cr(x,t)=simplify(series3_cr(x,t)+h_cr(k)*(power(t,k-1)));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

C1_l=zeros(1)

C1_l = 0

C2_l=zeros(1)

C2_l = 0

C3_l=zeros(1)

C3_l = 0

C1_up=zeros(1)

C1_up = 0

C2_up=zeros(1)

C2_up = 0

C3_up=zeros(1)

C3_up = 0

C1_cr=zeros(1)

C1_cr = 0

C2_cr=zeros(1)

C2_cr = 0

C3_cr=zeros(1)

C3_cr = 0

row=0;

x=0:0.04:2

x = 1×51

0 0.0400 0.0800 0.1200 0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 0.4000 0.4400 0.4800 0.5200 0.5600 0.6000 0.6400 0.6800 0.7200 0.7600 0.8000 0.8400 0.8800 0.9200 0.9600 1.0000 1.0400 1.0800 1.1200 1.1600

<mw-icon class=""></mw-icon>

t=0:0.002:0.1

t = 1×51

0 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140 0.0160 0.0180 0.0200 0.0220 0.0240 0.0260 0.0280 0.0300 0.0320 0.0340 0.0360 0.0380 0.0400 0.0420 0.0440 0.0460 0.0480 0.0500 0.0520 0.0540 0.0560 0.0580

<mw-icon class=""></mw-icon>

for i=1:length(x)

row=row+1;

col=0;

for j=1:length(t)

col=col+1;

C1_l(row,col)=series1_l(x(i),t(j));

C2_l(row,col)=series2_l(x(i),t(j));

C3_l(row,col)=series3_l(x(i),t(j));

%----------------------------------

C1_up(row,col)=series1_up(x(i),t(j));

C2_up(row,col)=series2_up(x(i),t(j));

C3_up(row,col)=series3_up(x(i),t(j));

%------------------------------------

C1_cr(row,col)=series1_cr(x(i),t(j));

C2_cr(row,col)=series2_cr(x(i),t(j));

C3_cr(row,col)=series3_cr(x(i),t(j));

end

%--------------------------------------------------------

figure

surf(x,t,C1_l, FaceAlpha=0.5)

hold on

surf(x,t,C1_up, FaceAlpha=0.5)

surf(x,t,C1_cr, FaceAlpha=0.5)

hold off

colormap(turbo)

% colorbar

xlabel('x')

ylabel('t')

text(2, 0, C1_l(1,1), "\leftarrow C1_l", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C1_up(1,1), "\leftarrow C1_{up}", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C1_cr(1,1), "\leftarrow C1_{cr}", FontWeight='bold', Horiz = 'left', Vert='middle')

●

figure

surf(x,t,C2_l, FaceAlpha=0.5)

hold on

surf(x,t,C2_up, FaceAlpha=0.5)

surf(x,t,C2_cr, FaceAlpha=0.5)

hold off

colormap(turbo)

% colorbar

xlabel('x')

ylabel('t')

text(2, 0, C2_l(1,1), "\leftarrow C2_l", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C2_up(1,1), "\leftarrow C2_{up}", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C2_cr(1,1), "\leftarrow C2_{cr}", FontWeight='bold', Horiz = 'left', Vert='middle')

figure

surf(x,t,C3_l, FaceAlpha=0.5)

hold on

surf(x,t,C3_up, FaceAlpha=0.5)

surf(x,t,C3_cr, FaceAlpha=0.5)

hold off

colormap(turbo)

% colorbar

xlabel('x')

ylabel('t')

text(2, 0, C3_l(1,1), "\leftarrow C3_l", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C3_up(1,1), "\leftarrow C3_{up}", FontWeight='bold', Horiz = 'left', Vert='middle')

text(2, 0, C3_cr(1,1), "\leftarrow C3_{cr}", FontWeight='bold', Horiz = 'left', Vert='middle')

% surf(x,t,C1_l,C1_up,C1_cr)

% surf(x,t,C2_l,C2_up,C2_cr)

% surf(x,t,C3_l,C3_up,C3_cr)

.

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3D surf plot for more than two quantities

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3D surf plot for more than two quantities

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