How can I construct delauany's disc in matlab??

This is the code which I did for displaying delanauys disc in matlab, however I am not getting the accurate output. Please find below my code and output for that. Kindly help me out with this.

% Script for delaunay's disc

clc

close all

figure

axis on;

hold on

n=5; % Declaring the value of n

% Calculation of concentric circles

x = linspace(0,n,1000);

y1 = sqrt(n^2-x.^2); % Calculation of circle equation for the top circle

% y2 = -y1; % Constructing the Bottom circle

fill([x 0],[y1 0],rand(1,3)) % Filling the top circle with red color

% fill([x 0],[y2 0],rand(1,3)) % Filling the bottom circle with white color

n1 = -5;

x1 = linspace(0,n1,1000);

y2 = sqrt(n1^2-x1.^2);

fill([x1 0],[y2 0],rand(1,3))

x2 = linspace(n1,n1,10);

y3 = sqrt(n1^2-x2.^2);

fill([x2 0],[y3 0],rand(1,3))

x3 = linspace(n1,0,10);

y4 = sqrt(n1^2-x3.^2);

fill([x3 0],[y4 0],rand(1,3))

Output:

Kindly help me with the correct code for this problem. Let me know if there is any concerns or questions.

Thanks in advance.

[KALYAN ACHARJYA]

however I am not getting the accurate output.

Expected accurate result?

[Ashis Jana]

This is delaunays disc, which I am supposed to construct. I tried to write a code for this, however I didnt get this. Its not working, please help me out in fixing my code. Thanks!!

Answer 1

[John D'Errico]

Hmm, if that was what you were expecting, you did not come very close. :)

Let me suggest a trick though.

Write a little helper function that will plot a quarter arc of a circular reqion, with an inner and outer radius specified, and you would tell the code which quadrant to create this in. You will be using fill for the plot. Then just call it repeatedly. I might write it like this:

function quarterarc(R1,R2,quadrant,arccolor)
% R1 and R2 are radii for the arcs. R1 can be zero, in which case
%    the arc will fill all the way to the origin.
% quadrant is expected to be a number from the set {1,2,3,4}.
%    It will denote the quadrant the arc will live in.
% arccolor must be a row vector of length 3, indicating a color in RGB.

if ~ismember(quadrant,[1,2,3,4])
  error('The sky is falling!. quadrant was an unexpected value')
end

% create the arc, in the form of a polygonal region with n points along
% each the inner and outer edges
t1 = (quadrant - 1)*pi/2;
t2 = quadrant*pi/2;
n = 100;
theta = [linspace(t1,t2,n),linspace(t2,t1,n),t1];
R = [repmat(R1,1,n),repmat(R2,1,n),R1];

% Convert to carteisna coordinates
[X,Y] = pol2cart(R,theta)

The nice thing is, that little helper function can be tested first, BEFORE you write the rest of your code. Make sure that it does what you expected. This act of encompassing important pieces of code in a function is an incredibly valuable one, that you will frequently find of use in your programming efforts. It allows you to break a problem up into small pieces. Then test and debug each piece. Verify that it works, and works correctly, BEFORE putting it all together.

But then, it seems trivial to write the plot code.

figure
hold on
axis([-5,5,-5,5])
axis equal
 
for R1 = 0:4
  R2 = R1 + 1;
  for quadrant = 1:4
    quarterarc(R1,R2,quadrant,100,rand(1,3));
  end
end

Sadly, I have a funny feeling if you turn in my solution as your homework that your teacher will know you copied it. But it may give you a hint as to how to write your own code.

[Ashis Jana]

Thanks a lot for your response and help. My instructor is not concerned about that so dont worry. :P :D

I wont copy your code either, I will definitely make some changes. However, I wanted to let you know that I got some errors in your code while trying to run it.

[X,Y] = pol2cart(R,theta): Its showing an error but I fixed it.

There was a problem with the functions but I fixed that too.

I ran the code in following way:

clc

close all

figure

hold on

axis([-5,5,-5,5])

axis equal

function ashis(R1,R2,quadrant,~)

% R1 and R2 are radii for the arcs. R1 can be zero, in which case

% the arc will fill all the way to the origin.

% quadrant is expected to be a number from the set {1,2,3,4}.

% It will denote the quadrant the arc will live in.

% arccolor must be a row vector of length 3, indicating a color in RGB.

if ~ismember(quadrant,[1,2,3,4])

error('The sky is falling!. quadrant was an unexpected value')

end

% create the arc, in the form of a polygonal region with n points along

% each the inner and outer edges

t1 = (quadrant - 1)*pi/2;

t2 = quadrant*pi/2;

n = 100;

theta = [linspace(t1,t2,n),linspace(t2,t1,n),t1];

R = [repmat(R1,1,n),repmat(R2,1,n),R1];

% Convert polar to cartesian coordinates

[~,~] = pol2cart(R,theta);

for R1 = 0:4

R2 = R1 + 1;

for quadrant = 1:4

ashis(R1,R2,quadrant,100,rand(1,3));

end

end

end

It shows no error but I am getting no output either. Its showing just the x and y axis witht white color inside which means we are not getting the disc properly. Its my earnest request to kindly run your code so that you get output and share it to me. That will be good for me. Thanks in advance.