Plot elipses with a foci based on equations to plot flowers
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Ahmed Mohamed Mansoor
le 6 Oct 2022
Commenté : Ahmed Mohamed Mansoor
le 10 Oct 2022
I am trying to practice with matlab with various equations out there. Does anyone know how to plot this picture (see image below) based on these equations? I have coded the equations (see below picture), but have no idea how to plot it.
I have coded the equations A(k), B(k), C(k), D(k), E(k) but I do not know where to go from here.
Any help would be appreciated.
close all; clc; clear;
sin48 =@(k) sin((48*pi*k)./1000000);
cos48 =@(k) cos((48*pi*k)./1000000);
sin8 =@(k) sin((8*pi*k)./1000000);
cos8 =@(k) cos((8*pi*k)./1000000);
sin24 =@(k) sin((24*pi*k)./1000000);
cos24 =@(k) cos((24*pi*k)./1000000);
sin72 =@(k) sin((72*pi*k)./1000000);
cos72 =@(k) cos((72*pi*k)./1000000);
cos648=@(k) cos((648*pi*k)./1000000);
cos64 =@(k) cos((64*pi*k)./1000000);
Ek = 0.1 + 0.25*sin48(x).^2 + 0.2*cos18(x).^18 *...
(1 + (1/3)*cos24(x).^8 + 0.1*cos24(x)^20) + (1/6)*sin8(x).^16 +...
(8/20)*sin8(x).*(1 - 0.4*cos72(x).^4) + 0.0625*sin(x).^18.*...
sin24(x).^20.*sin72(x).^30 - (0.1*sin24(x).^6 + (1/6)*sin24(x).^30)...
(1-sin8(x));
Dk = (pi/2) + (1686*pi*x/1000000);
Ck = 0.003 + 0.097*cos648(x).^40;
Bk = -cos64(x).*Ek - 0.1*cos64(x);
Ak = 1.2*sin64(x)*Ek;
2 commentaires
Sam Chak
le 6 Oct 2022
Hmm... Didn't you have few examples posted on the last few days?
Can you put the scatter() and colormap(jet) functions in the code?
Réponse acceptée
Davide Masiello
le 6 Oct 2022
The code below does the job drawing the figure, but not the coloring.
I can't run it online (takes too long).
clear,clc
figure(1)
hold on
for k = 1:1000000
plotEllipse(k)
end
function plotEllipse(k)
e = 98/100;
sin48 = sin((48*pi*k)/1000000);
sin8 = sin((8*pi*k)/1000000);
cos8 = cos((8*pi*k)./1000000);
sin24 = sin((24*pi*k)/1000000);
cos24 = cos((24*pi*k)/1000000);
sin72 = sin((72*pi*k)/1000000);
cos72 = cos((72*pi*k)/1000000);
cos648 = cos((648*pi*k)/1000000);
sin64 = sin((64*pi*k)/1000000);
cos64 = cos((64*pi*k)/1000000);
Ek = 0.1 + 0.25*sin48^2 + 0.2*cos8^18 *...
(1 + (1/3)*cos24^8 + 0.1*cos24^20) + (1/6)*sin8^16 +...
(8/20)*sin8*(1 - 0.4*cos72^4) + 0.0625*sin8^18.*...
sin24^20*sin72^30 - (0.1*sin24^6 + (1/6)*sin24^30)*...
(1-sin8);
Dk = (pi/2) + (1686*pi*k/1000000);
Ck = 0.003 + 0.097*cos648^40;
Bk = -cos64*Ek - 0.1*cos64;
Ak = 1.2*sin64*Ek;
F1 = Ak + 1i*Bk + Ck*exp(1i*Dk) ; % Focus 1
F2 = Ak + 1i*Bk - Ck*exp(1i*Dk) ; % Focus 2
centre = mean([F1,F2]); % ellipse centre
angle = atan(abs(imag(F1)-imag(F2))/abs(real(F1)-real(F2))); % angle between ellipse horizontal axis and x-axis
c = sqrt((real(F1)-real(F2))^2+(imag(F1)-imag(F2))^2)/2; % distance from centre to foci
a = c/e; % ellipse horizontal axis
b = a^2-c^2; % ellipse vertical axis
t = linspace(0,2*pi,100); % parametric coordinate
x0 = a*cos(t); % x-coordinates of ellipse if centered with reference axis and horizontal
y0 = b*sin(t); % y-coordinates of ellipse if centered with reference axis and horizontal
x = x0*cos(angle)-y0*sin(angle)+real(centre); % Absolute x-coordinates (rotation+translation)
y = y0*cos(angle)+x0*sin(angle)+imag(centre); % Absolute y-coordinates (rotation+translation)
plot(x,y)
end
8 commentaires
Davide Masiello
le 10 Oct 2022
Modifié(e) : Davide Masiello
le 10 Oct 2022
@Ahmed Mohamed Mansoor Happy to help, please post the plot if you ever manage to produce it. Also, since you are interested in this cool plots, I suggest you check this out.
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