MATLAB: How to optimize this code

coslinspacesin

u = (0:1500).*(96*(2*pi)/1500); % spiral with 96 waves

r=u./2; % spiral radius

x=r.* cos(u); % X

y=r.* sin(u); % Y

Best Answer

Your code is already pretty optimized. However, you can replace the first line with

u = linspace(0, 96*2*pi, 1501)

I think this line is more readable compared to the one in your code.

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MATLAB: Can someone help me with these 3D plots

you can plot these shapes in the following two ways(you can choose better way you like):

%%Seashell

[u, v] = meshgrid(linspace(0, 6 * pi, 100), linspace(0, 2 * pi, 100));
x = 2 * (1 - exp(u / (6 * pi))) .* cos(u) .* (cos(0.5 * v))^2;
y = 2 * (-1 + exp(u / (6 * pi))) .* sin(u) .* (cos(0.5 * v))^2;
z = 1 - exp(u / (3 * pi)) - sin(v) + exp(u / (6 * pi)) .* sin(v);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Seashell')
%%Eight torus

c = 1;
[u, v] = meshgrid(linspace(-pi, pi, 100));
x = cos(u) .* (c + sin(v) .* cos(u) - sin(2 * v) .* (sin(u) / 2));
y = sin(u) .* (c + sin(v) .* cos(u) - sin(2 * v) .* (sin(u) / 2));
z = sin(u) .* sin(v) + cos(u) .* (sin(2 * v) / 2);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Eight torus')
%%Helical spring

r1 = 0.25;
r2 = 0.25;
T = 2;
n = 6;
[u, v] = meshgrid(linspace(0, 2 * n * pi, 100), linspace(0, 2 * pi, 100));
x = (1 - r1 * cos(v)) .* cos(u);
y = (1 - r1 * cos(v)) .* sin(u);
z = r2 * (sin(v) + T * u / pi);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Helical spring')
%%Cornucopia

a = 0.3;
b = 0.5;
[u, v] = meshgrid(linspace(0, 2 * pi, 100), linspace(-3, 3, 100));
x = exp(b * v) .* cos(v) + exp(a * v) .* cos(u) .* cos(v);
y = exp(b * v) .* sin(v) + exp(a * v) .* cos(u) .* sin(v);
z = exp(a * v) .* sin(u);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Cornucopia')

Or alternatively you can also plot them using ezsurf as follows:

syms u v
%%Seashell
x = 2 * (1 - exp(u / (6 * pi))) * cos(u) * (cos(0.5 * v))^2;
y = 2 * (-1 + exp(u / (6 * pi))) * sin(u) * (cos(0.5 * v))^2;
z = 1 - exp(u / (3 * pi)) - sin(v) + exp(u / (6 * pi)) * sin(v);
figure, ezsurf(x, y, z)
%%Eight torus
c = 1;
x = cos(u) * (c + sin(v) * cos(u) - sin(2 * v) * (sin(u) / 2));
y = sin(u) * (c + sin(v) * cos(u) - sin(2 * v) * (sin(u) / 2));
z = sin(u) * sin(v) + cos(u) * (sin(2 * v) / 2);
figure, ezsurf(x, y, z)
%%Helical spring
r1 = 0.25;
r2 = 0.25;
T = 2;
n = 6;
x = (1 - r1 * cos(v)) .* cos(u);
y = (1 - r1 * cos(v)) .* sin(u);
z = r2 * (sin(v) + T * u / pi);
figure, ezsurf(x, y, z)
%%Cornucopia
a = 0.3;
b =0.5;
x = exp(b * v) .* cos(v) + exp(a * v) .* cos(u) .* cos(v);
y = exp(b * v) .* sin(v) + exp(a * v) .* cos(u) .* sin(v);
z = exp(a * v) .* sin(u);
figure, ezsurf(x, y, z)

I hope it helps. Good luck!

MATLAB: How to shift a fsurf plot

r = @(u,v) 2 + sin(7.*u + 5.*v);
funx = @(u,v) r(u,v).*cos(u).*sin(v);
funy = @(u,v) r(u,v).*sin(u).*sin(v);
funz = @(u,v) r(u,v).*cos(v);
% fsurf(funx,funy,funz,[0 2*pi 0 pi]); % This plot should be shifted
xshift = 2; yshift = -2;
% fsurf( @(u,v)funx(u-xshift,v-yshift), @(u,v)funy(u-xshift,v-yshift), @(u,v)funz(u-xshift,v-yshift), [0 2*pi 0 pi])
M = 100 ; N =100 ;
u = linspace(0,2*pi,M) ;
v = linspace(0,pi,N) ;
[U,V] = meshgrid(u,v) ;
X = funx(U,V)-2 ;
Y = funy(U,V)+2 ;
Z = funz(U,V) ;
surf(X,Y,Z)

Best Answer

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MATLAB: Can someone help me with these 3D plots

MATLAB: How to shift a fsurf plot

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