Cutting a Circular Ring at particular points using angle-theta

Question

Chris Dan 2022-3-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1680519-cutting-a-circular-ring-at-particular-points-using-angle-theta

编辑： Les Beckham 2022-3-25

采纳的回答： Les Beckham

在 MATLAB Online 中打开

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:

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Answer 1

Les Beckham 2022-3-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1680519-cutting-a-circular-ring-at-particular-points-using-angle-theta#answer_926874

编辑：Les Beckham 2022-3-25

在 MATLAB Online 中打开

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');

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Answer 2

Simon Chan 2022-3-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1680519-cutting-a-circular-ring-at-particular-points-using-angle-theta#answer_926869

在 MATLAB Online 中打开

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);