SAMPLEDISK - Sampling disks over a grid.

Description
Syntax
Inputs
Outputs
Reference
See also
Function implementation
Subfunction

Description

Sample lattice points (ie. with integer coordinates) inside disks given by their respective centers and radii.

Syntax

  SAMPLEDISK(center, radius);
  [x, y, w] = SAMPLEDISK(center, radius, method, samp, disp);

Inputs

center : matrix (k,2) of the (X,Y) integer coordinates of the centers of k disks.

radius : matrix (k,1) of the radii of the k disks.

method : (optional) string defining the method used for sampling the lattice points inside the disks; it can be:

'full' for all lattice points included in the disks,
'grid' for all lattices points regularly sampled on a 2D grid with size equal to samp (see below) and included in the disks,
'radi' for points sampled on internal circles inside the disks (by default, at half the size of the disk, otherwise depending on samp) plus the center of the circle itself,
'rand' for randomly selected points inside the disks;

   default: |method='full'|.

samp : (optional) scalar or vector of size (k,1) giving (of no use when method='full' or 'scale'):

for method='grid', the sampling rate of the grid when samp>1 or the proportion of desired sampled points on this grid when 0<=samp<1,
for method='rand', the total number of sampled points when samp>=1 and the proportion of sampled points when 0<=samp<1,
for method='radi', (i) when samp>1, the total number of points regularly sampled on the border of the disk, (ii) when samp<-1, the total number of sampled points around an internal circle at a distance radius/2 from the disk's center, (iii) when 0<samp<=1, the ratio of the radius of an internal circle on which as many lattice points as possible are sampled; in particular, points are sampled around the disk border when samp=1;

note that in the latter case ('radi'), the total number of points in the disk is estimated using Gauss formula; default: samp=0.5 for all chosen methods.

disp : (optional) flag for drawing (discrete) lines; default: disp=false.

Outputs

x, y : (X,Y) coordinates of the sampled points.

Reference

See discussions at http://mathworld.wolfram.com/DiskPointPicking.html http://mathworld.wolfram.com/GausssCircleProblem.html

Function implementation

%--------------------------------------------------------------------------
function varargout = sampledisk(center, radius, method, samp, disp)

settting/checking variables

% check errors in muber of input/output variables
error(nargchk(3, 5, nargin, 'struct'));
error(nargoutchk(0, 3, nargout, 'struct'));

% set default
if nargin<5
    if nargout==0,  disp = true;
    else            disp = false;     end
    if nargin<4,  samp = [];
        if nargin<3,  method = 'full';  end
    end
end

if ~any(strcmpi(method,{'full','grid','scale','radi','rand'}))
    error('sampledisk:methoderror',['unknown method ' method]);
end

if isempty(samp) && any(strcmpi(method,{'grid','radi','rand'}))
    % error('sampledisk:errorinput', ...
    %  'samp parameter must be entered with methods ''grid'', ''radi'' or ''rand''');
   samp = 0.5;
elseif ~isempty(samp) && any(strcmpi(method,{'full','scale'}))
    warning('sampledisk:warninginput', ...
        ['samp parameter ignored with method ' method]);
end

main computation

[x, y, w] = sampledisk_base(center, radius, method, samp);

if disp
    plotsampledisk(x, y, center, radius);
end

if nargin>=1,  varargout{1} = x;
    if nargin>=2,  varargout{2} = y;
        if nargin==3,  varargout{3} = w;  end
    end
end

end % end of sampledisk

Subfunction

%--------------------------------------------------------------------------
function plotsampledisk(x, y, center, radius)
ndisks = size(center,1);

for i=1:ndisks
    figure
    plot(x(i,:),y(i,:),'g.')
    axis([center(i,1)-1.1*radius(i) center(i,1)+1.1*radius(i) ...
        center(i,2)-1.1*radius(i) center(i,2)+1.1*radius(i)])
    hold on
    t = linspace(0,2*pi,1000);  r = ones(1,1000)*radius(i);
    [xx,yy] = pol2cart(t,r);
    xx=xx+center(i,1);   yy=yy+center(i,2);
    plot(xx,yy,'--');
    hold off
    axis square
end
end