Cutting a Circular Ring at particular points using angle-theta

Hello,

I am drawing a circular ring using the following code:

clear all; close all;

p = linspace(-1/2,1/2,100);

[X,Y] = meshgrid(p,p); % box mesh

R = p(size(p,2))/2;
r = R/1.5;

alpha = deg2rad(15);
alpha = linspace(-alpha,alpha,50);

[alpha_X,alpha_Y] = meshgrid(alpha,alpha);

theta = atan2(Y,X);

active = (X.^2 + Y.^2  <= R^2 & X.^2 + Y.^2 >= r^2);


figure()

plot(X(active),Y(active),'o','MarkerFaceColor','red');

hold on

This code is incomplete because I have to use alpha and theta to cut the ring at particular points.

The inequalities that I have are:

x^2+y^2<=R^2

x^2+y^2>=r^2

-alpha <=taninv(y/x)<=+alpha.

i have plotted the first two, I am confused as how to plot the third one, alpha one.

Does any on know how to plot the third inequality or how to use it to cut the ring at a particular angle.

the result which i get from above code is:

Answer 1

[Les Beckham]

You were pretty close. See if you can adapt this to get what you want.

p = linspace(-1/2,1/2,100);
[X,Y] = meshgrid(p,p); % box mesh
R = p(size(p,2))/2;
r = R/1.5;
alpha = deg2rad(15);
theta = atan2(Y,X); % check size of theta; note it is already a mesh grid because X and Y are
% the whole circle (radius constraints only)
active = (X.^2 + Y.^2  <= R^2) & (X.^2 + Y.^2 >= r^2);
plot(X(active),Y(active),'o','MarkerFaceColor','red');
% the portion that satisfies the alpha constraint as well
active = (X.^2 + Y.^2  <= R^2) & (X.^2 + Y.^2 >= r^2) & (abs(theta) < alpha); 
hold on
plot(X(active),Y(active),'o','MarkerFaceColor','blue');

Answer 2

[Simon Chan]

Try to add the follwoing lines:

alphaA = 15*pi/180;                                     % Set the margin, 15 degree here
[thetaA,~] = cart2pol(X,Y);
angleA = abs(thetaA)<=alphaA;
active = (X.^2 + Y.^2  <= R^2 & X.^2 + Y.^2 >= r^2 & angleA);