Points Inside Convex Polygon

We define a pentagon and a set of points. Then, determine which points lie inside, outside, or on the edge of the pentagon.

Contents

Data

Create polygon vertices that form a pentagon

t = linspace(0, 2*pi, 6).';
ct = [cos(t) sin(t)];

Create 250 random query points

pt = randn(250,2);
pt = [pt; ct];  % add points on edge, to ensure all cases are represented

OpenCV

Determine whether each point lies inside, outside, or on the edge of polygon

tic
if false
    loc = zeros(size(pt,1),1);
    for i=1:size(pt,1)
        loc(i) = cv.pointPolygonTest(ct, pt(i,:));
    end
else
    % vectorized call
    loc = cv.pointPolygonTest(ct, pt);
end
toc

Elapsed time is 0.022040 seconds.

MATLAB

Same using MATLAB function

tic
[in, on] = inpolygon(pt(:,1), pt(:,2), ct(:,1), ct(:,2));
loc2 = zeros(size(in));
loc2(~in) = -1;      % outside
loc2(in & ~on) = 1;  % inside
loc2(on) = 0;        % on edge
toc

Elapsed time is 0.154738 seconds.

Results

Compare results, and show the number of points of each case

assert(isequal(loc(:), loc2(:)))
fprintf('%d inside, %d outside, %d on edge\n', ...
    nnz(loc>0), nnz(loc<0), nnz(loc==0));

80 inside, 170 outside, 6 on edge

Plot the polygon and the query points

clr = eye(3) * 0.8;
figure
plot(ct(:,1), ct(:,2), 'g', 'LineWidth',2), hold on
if ~mexopencv.isOctave() && mexopencv.require('stats')
    gscatter(pt(:,1), pt(:,2), loc, clr)
else
    %HACK: GSCATTER not implemented in Octave
    scatter(pt(:,1), pt(:,2), [], clr(loc+2,:), 'filled')
end
hold off, axis equal
xlabel('X'), ylabel('Y'), title('pointPolygonTest')