SAMPLETRIANGLE - Sampling triangles over a grid.

Contents

Description

Sample lattice points (ie. with integer coordinates) inside triangles given by their respective faces and vertices coordinates.

Syntax

  SAMPLETRIANGLE(tri, vertex);
  [x,y] = SAMPLETRIANGLE(tri, vertex, method, samp, disp);

Inputs

tri : matrix (n,3) storing the faces of n triangles; this is typically the output of a triangulation.

vertex : matrix (k,2) storing the (X,Y) coordinates of the k vertices indexed by the faces in tri.

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

note that in the cases method='vista', 'grid' or 'rand', the sample points may lay outside of the triangles (small triangles), not in the case 'full'; default: method='full'.

samp : (optional) scalar used when method='vista', 'grid' or 'rand' (of no use when method='full'); it gives the number of sampled points when samp>=1, or the proportion of sampled points when 0<samp<1; in the latter case, the total number of points in a triangle is 'guessed' using Pick's theorem; default: samp=0.5.

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

Outputs

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

Reference

See discussion at http://mathworld.wolfram.com/TrianglePointPicking.html

See also

Ressembles: SAMPLEDISK, BRESENHAMLINE. Requires: SAMPLETRIANGLE_BASE.

Function implementation

%--------------------------------------------------------------------------
function varargout = sampletriangle(tri, vertex, method, samp, disp)

check arguments

error(nargchk(2, 5, nargin, 'struct'));
error(nargoutchk(0, 2, 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','vista','rand'}))
    error('sampletriangle:methoderror',['unknown method ' method]);

elseif isempty(samp) && any(method,{'grid','vista','rand'})
    % error('sampledisk:errorinput', ...
    %  'samp parameter must be entered with methods ''grid'', ''vista'' or ''rand''');
   samp = 0.5;

elseif samp<=0
    error('sampletriangle:errorinput', 'samp parameter must be >0');
end

main computation

[x, y] = sampletriangle_base(tri, vertex, method, samp);

display

if disp
    plotsampletriangle(x, y, tri, vertex);
end

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

end % end of sampletriangle

Subfunction

%--------------------------------------------------------------------------
function plotsampletriangle(x, y, tri, vertex)
ntri = size(tri,1);

for i=1:ntri
    figure % plot the triangles in red, the  sampled points as yellow dots
    plot(vertex(tri(i,[1 2 3 1]),1)',vertex(tri(i,[1 2 3 1]),2)','ro', ...
        vertex(tri(i,[1 2 3 1]),1)',vertex(tri(i,[1 2 3 1]),2)','r-', ...
      x(i,:),y(i,:),'b.')
    % axis([]);
end
end