Generate a circular array of gridpoints inside a given contour.

Hello Everyone,

Say I have a contour that needs to be filled with discrete individual gridpoints, as illustrated in the figure. However, the gridpoints are of circular orientation, i.e, the gridpoints, when joined together forms a circle and this progressively gets bigger as we move radially outwards, untill the contour is reached.

I understand an 'inpolygon' test is to be done somewhere, but I cannot create the grid.

The size of the points have nothing to do here. Points are nothine but XY cordinates. The red circle marks the contour.

Thank you.

Answer 1

[Voss]

r = 1;
x = linspace(-r,r,100);
y = linspace(-r,r,100).';

figure
[~,h] = contour(x,y,x.^2+y.^2, ...
    'LevelList',r, ...
    'EdgeColor','r', ...
    'LineWidth',1.5);
axis padded
axis square
axis off

hold on
rr = linspace(0,r,10);
rr([1 end]) = [];
for ii = 1:numel(rr)
    th = linspace(0,2*pi,ceil(5.4*ii))+2*pi*rand();
    th(end) = [];
    plot(rr(ii)*cos(th),rr(ii)*sin(th),'o', ...
        'MarkerSize',9, ...
        'MarkerEdgeColor','k', ...
        'MarkerFaceColor','k');
end

Answer 2

[Voss]

Here's a function that fills an aribitrary contour (i.e., not necessarily a single circle) with random points (i.e., not necessarily in a circular grid) within each pair of contour levels.

x = linspace(-1,1,100);
y = linspace(-1,1,100).';

figure
[~,h] = contour(x,y,x.^2+y.^2, ...
    'LevelList',1, ...
    'EdgeColor','r', ...
    'LineWidth',1.5);
axis padded
axis square
axis off
fill_contour_with_points(h);

figure
[~,h] = contour(x,y,x.^2+y.^2, ...
    'EdgeColor','r', ...
    'LineWidth',1.5);
axis padded
axis square
axis off
fill_contour_with_points(h,0.24);

figure
[~,h] = contour(x,y,abs(x)+0.3*abs(y), ...
    'LevelList',[0.7 1 1.4], ...
    'EdgeColor','r', ...
    'LineWidth',1.5);
axis padded
axis square
axis off
fill_contour_with_points(h,0.12,true);

figure
[~,h] = contour(x,y,cos(x*10)+cos(y*4), ...
    'EdgeColor','k', ...
    'LineWidth',1);
axis padded
axis square
axis off
fill_contour_with_points(h,0.65,true);

function fill_contour_with_points(h,density,do_include_last)
if nargin < 2 || isempty(density)
    density = 0.1;
end
if nargin < 3
    do_include_last = false;
end
zd = get(h,'ZData');
xd = get(h,'XData');
yd = get(h,'YData');
if isvector(xd)
    xd = xd(:).';
    xd = xd(ones(size(zd,1),1),:);
end
if isvector(yd)
    yd = yd(:);
    yd = yd(:,ones(size(zd,2),1));
end
hold on
level_list = get(h,'LevelList');
level_list = [-Inf; level_list(:); Inf];
if ~do_include_last
    level_list(end) = [];
end
for ii = 1:numel(level_list)-1
    idx = find(zd >= level_list(ii) & zd < level_list(ii+1));
    n_idx = numel(idx);
    idx = idx(randperm(n_idx,ceil(density*n_idx)));
    plot(xd(idx),yd(idx),'.');
end
end