Programmatically calculate indices of the outline of a circle and all points within in it

I am trying to establish a programmatic means of calculating the indices of the outline of a circle and all points within in it.

Of course, this is can be done manually (very tediously) but I would grateful if anybody had any suggestions.

I can then apply logical indexing to variables of interest.

Thank you.

Daniel

r = 0.3; % radius
x = 0; % central x coordinate of domain
y = 0; % central y coordinate of domain
[xunit,yunit] = circle(x,y,r);

X = 0.375:-0.125:-0.375; % x coordinates
Y = -0.375:-0.125:-.375; % y coordinates
npoints = [99 99]; % define improved resolution for contour plots later
Xfine = linspace(X(1),X(end),npoints(1)); % y coords
Yfine = linspace(Y(1),Y(end),npoints(2)); % z coords
[Xfine Yfine] = meshgrid(Xfine,Yfine); % create mesh

function [xunit,yunit] = circle(x,y,r)
    th = 0:pi/50:2*pi;
    xunit = r * cos(th) + x;
    yunit = r * sin(th) + y;
end

[Matt J]

You appear to have code already. Were you going to tell us that something is wrong with it?

Answer 1

[Walter Roberson]

X = 0.375:-0.125:-0.375; % x coordinates
Y = -0.375:-0.125:-.375; % y coordinates
npoints = [99 99]; % define improved resolution for contour plots later
Xfine = linspace(X(1),X(end),npoints(1)); % y coords
Yfine = linspace(Y(1),Y(end),npoints(2)); % z coords
[Xfine Yfine] = meshgrid(Xfine,Yfine); % create mesh

r = 0.3; % radius
x = 0; % central x coordinate of domain
y = 0; % central y coordinate of domain

mask = (Xfine - x).^2 + (Yfile - y).^2 <= r.^2;

indices = find(mask);      % but typically it is better to use the mask directly

[Daniel]

Thank you.

Answer 2

[John D'Errico]

Wait. You want to compute the list of all points within a circle? There are infinitely many.

Ok, I guess given a MESH of points, you want to know how many lie inside? That is trivial.

For example, given a circle of radius 0.3, with center at (0,0), which points from your fine mesh lie inside? No loops needed. Just the equation of a circle.

r = 0.3; % radius
C = [0,0]; % LEARN TO USE VECTORS

[X,Y] = meshgrid(linspace(-0.375,0.375,99));

insideind = (X-C(1)).^2 + (Y - C(2)).^2 < r.^2;
XYinside = [X(insideind),Y(insideind)]

XYinside = 4825×2

-0.2985 -0.0230 -0.2985 -0.0153 -0.2985 -0.0077 -0.2985 0 -0.2985 0.0077 -0.2985 0.0153 -0.2985 0.0230 -0.2908 -0.0689 -0.2908 -0.0612 -0.2908 -0.0536

size(XYinside,1)

ans = 4825

So 4825 nodes from that mesh lie inside. None will lie EXACTLY on the perimeter of the circle due to the use of floating point arithmetic.

sum((X-C(1)).^2 + (Y - C(2)).^2 == r.^2,'all')

ans = 0

[Daniel]

Thank you.