Help with 3D-plotting?

Question

Lewis Hancox 2018-3-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/388276-help-with-3d-plotting

评论： Star Strider 2018-3-14

So I have made this code that creates the shape I desire, but the top is open, and I want it to flat on the top. Any help would be appreciated. Thanks

if true
  % code
end
%Constants
A=7/4;
L=1;
R=1;
%Solve for u_2
syms u 
u_2=vpasolve(u*(-A-log(u)+u^2+3*u^4/4)*(1+u^2)^(-2)== L/R, u)
%x(u_2)=R rearranges to get C=...,
C=R*u_2/(1+u_2^2)^2
syms u
u_1=vpasolve(-log(u)+u^2+3*u^4/4 == A, u)
x_1=(C*(1+u_1^2)^2)/u_1
v= linspace (u_1,u_2);
  X= C*((1+v.^2).^2)./v;
  Y= L-C*(-A-log(v)+v.^2+(3*v.^4)/4);
  plot(X,Y)
 figure(1)
figure(2)  
u1 = double(u_1)
u2 = double(u_2)
syms r v
colormap(bone)
x=fsurf(cos(r)*C*((1+v.^2).^2)./v, sin(r)*C*((1+v.^2).^2)./v,(L-C*(-A-log(v)+v.^2+(3*v.^4)/4)),[0,2*pi u1, u2])
title('R=1 L=1')

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Answer 1

Star Strider 2018-3-14

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Tweak figure(2) by adding a patch call:

figure(2)  
u1 = double(u_1)
u2 = double(u_2)
syms r v
colormap(bone)
x=fsurf(cos(r)*C*((1+v.^2).^2)./v, sin(r)*C*((1+v.^2).^2)./v,(L-C*(-A-log(v)+v.^2+(3*v.^4)/4)),[0,2*pi u1, u2])
hold on
rv = linspace(0,2*pi);
Radius = 0.35;
patch(Radius*cos(rv), Radius*sin(rv), ones(size(rv)), 'r')              % <— ADD THIS ‘patch’ CALL, REFINE ‘Radius’
hold off
title('R=1 L=1')

I don’t know how you define the value for the radius of the top, so I guessed at one that sort of works. Tweak that, change the colour to something you want, and it should work. See the documentation for patch to tweak its properties.

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Lewis Hancox 2018-3-14

Thanks again! I can't get the colormap to work on the patch, but I'll just make it all one colour I suppose.

Star Strider 2018-3-14

As always, my pleasure!

I’m not sure what to advise with respect to the colormap. That you’re using symbolic calculations and fplot makes that something of a challenge. Experiment using the last row of the colormap for the patch object colour. It could work!

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Answer 2

Lewis Hancox 2018-3-14

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Sorry to bug you again, but when I change the height the patch doesn't sit on top properly. I've changed the code so the radius matched but I can't get it to sit on correctly. Thanks again

if true
  % code
end
%Constants
u1=1; %Assume minimum occurs here
L=1/2;
R=1;
%Solve for u_2
syms A 
A=-log(u1)+u1^2+3*u1^4/4
syms u2 
u2=vpasolve(u2*(-A-log(u2)+u2^2+3*u2^4/4)*(1+u2^2)^(-2)== L/R, u2)
C=u2*R/(1+u2^2)^2
x1=C*((1+u1^2)^2)/u1
u= linspace (u1,u2);
  X= C*((1+u.^2).^2)./u;
  Y= L-C*(-A-log(u)+u.^2+(3*u.^4)/4);
  plot(X,Y)
 figure(1)
figure(2)  
u_1 = double(u1)
u_2 = double(u2)
syms r u
x=fsurf(cos(r)*C*((1+u.^2).^2)./u, sin(r)*C*((1+u.^2).^2)./u,(L-C*(-A-log(u)+u.^2+(3*u.^4)/4)),[0,2*pi u_1, u_2],'b')
title('R=1 L=5')
figure(2)  
u1 = double(u_1)
u2 = double(u_2)
x_1=double(x1)
syms r v
colormap(autumn)
x=fsurf(cos(r)*C*((1+u.^2).^2)./u, sin(r)*C*((1+u.^2).^2)./u,(L-C*(-A-log(u)+u.^2+(3*u.^4)/4)),[0,2*pi u1, u2])
hold on
rv = linspace(0,2*pi);
Radius = x_1;
patch(Radius*cos(rv), Radius*sin(rv), ones(size(rv)),'y')
% <— ADD THIS ‘patch’ CALL, REFINE ‘Radius’
hold off
title('R=1 L=1')