Lituus
t=linspace(0.1,14*pi,500);
r=0.2./sqrt(t);
x=r.*cos(t);
y=r.*sin(t);
plot(x,y);
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Fermat spiral
%MATLAB Code for Fermat spiral
t1=linspace(-15*pi,0.1,2000);
r1=sqrt(t1);
x1=-r1.*cos(t1);
y1=r1.*sin(t1);
t2=linspace(0,15*pi,2000);
r2=sqrt(t2);
x2=r2.*cos(t2);
y2=r2.*sin(t2);
line(imag(x1),imag(y1),'linewidth',2,'color',[0.2 0.3 0.4])
line(x2,y2,'linewidth',2,'color',[0.2 0.3 0.4])
axis square
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Maurer Rose
Formula taken from Wikipedia . MATLAB code given below . Varying 'n' and 'd' in code give different curves .
%Maurer rose
n=2;
d=39/180*pi;
k=0:360;
[x,y]=pol2cart( k*d , sin(n*d*k) );
line(x,y);
axis equal off
 n=2,d=39 |
n=3,d=47
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n=2,d=29
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n=3,d=17
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Super Ellipse
Generalized formula for super ellipse is abs(x/a)^m+abs(y/b)^n=1,m>0,n>0. Formula taken from Wikipedia
m = 1 , n = 2 , a =1 , b = 1.
%MATLAB Code
ezplot( ' abs(x)^1 + abs(y)^2 - 1 ' ) ;
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m = 0.5 , n = 5 , a =1 , b = 1.
%MATLAB Code
ezplot( ' abs(x)^0.5 + abs(y)^5 - 1 ' ) ;
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m = 1.5 , n = 1.5 , a =1 , b = 1.
%MATLAB Code
ezplot( ' abs(x)^1.5 + abs(y)^1.5 - 1 ' ) ;
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m = 0.5 , n = 2 , a =1 , b = 1.
%MATLAB Code
ezplot( ' abs(x)^0.5 + abs(y)^2 - 1 ' ) ;
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Spiral Mandala
t=0:sqrt(pi)/pi^2:5*pi;
r=sqrt(t);
lent=length(t);
x=zeros(lent,8);
y=zeros(lent,8);
x2=zeros(lent,8);
y2=zeros(lent,8);
pd=-0.75:0.25:1;
for n=1:8
x(:,n)=r.*cos(t+pd(n)*pi);
y(:,n)=r.*sin(t+pd(n)*pi);
x2(:,n)=-r.*cos(t+pd(n)*pi);
y2(:,n)=r.*sin(t+pd(n)*pi);
end
h_s=scatter(x(:)',y(:)',50+10*((x(:)').^2+(y(:)').^2),...
((x(:)').^2+(y(:)').^2),'filled');
colormap( fliplr(hsv) );
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Cornu spiral (Euler spiral) and some of its variants
(MATLAB code for cornu spiral is here)
3D Curves
Spherical Helix
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Slinky
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Chrysanthemum
formula taken from Paul Bourke website . MATLAB code given below .
u=linspace(0,21*pi,5000);
r=5*(1+sin(11*u/5))-4*sin(17*u/3).^4.*sin(2*cos(3*u)-28*u).^8;
x=r.*cos(u);
y=r.*sin(u);
z=(r/20+0.2).*sin(r*2*pi/7);
%plot3(x,y,z,'LineWidth',1,'Color',[.5 0.2 0.5]);
verts = {[x' y' z']};
h=streamtube(verts,0.15);
shading interp,colormap(cool)
axis off equal,view(3)
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