Curve

    • Maurer Rose

Formula taken from Wikipedia . MATLAB code given below . Varying 'n' and 'd' in code give different curves.

n = 2;

d = 39;

k = (0:120)/180*pi;

[x,y] = pol2cart( k*d , sin(n*d*k) );

line(x,y);

axis equal off

n = 3;

d = 47;

k = (0:180)/180*pi;

[x,y] = pol2cart( k*d , sin(n*d*k) );

line(x,y);

axis equal off

n = 2;

d = 29;

k = (0:360)/180*pi;

[x,y] = pol2cart( k*d , sin(n*d*k) );

line(x,y);

axis equal off

n = 3;

d = 17;

k = (0:180)/180*pi;

[x,y] = pol2cart( k*d , sin(n*d*k) );

line(x,y);

axis equal off

    • 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

% MATLAB Code

% m = 1, n = 2, a = 1, b = 1

ezplot('abs(x)^1 + abs(y)^2 - 1',[-1.5 1.5 -1.5 1.5]);

axis equal

% MATLAB Code

% m = 0.5, n = 5, a = 1 ,b = 1

ezplot('abs(x)^0.5 + abs(y)^5 - 1',[-1.5 1.5 -1.5 1.5]);

axis equal

% MATLAB Code

% m = 1.5, n = 1.5, a = 1 ,b = 1

ezplot('abs(x)^1.5 + abs(y)^1.5 - 1',[-1.5 1.5 -1.5 1.5]);

axis equal

% MATLAB Code

% m = 0.5, n = 2, a = 1 ,b = 1

ezplot('abs(x)^0.5 + abs(y)^2 - 1',[-1.5 1.5 -1.5 1.5]);

axis equal

    • Chrysanthemum

Formula taken from Paul Bourke website . MATLAB code given below .

u = linspace(0,21*pi,2000);

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);

figure

line(x,y,z);

axis equal off

view(3)

figure

verts = {[x' y' z']};

h = streamtube(verts,0.15);

shading interp,colormap(cool)

axis off equal

view(3)