— Function File: voronoi (x, y)
— Function File: voronoi (x, y, options)
— Function File: voronoi (..., "linespec")
— Function File: voronoi (hax, ...)
— Function File: h = voronoi (...)
— Function File: [vx, vy] = voronoi (...)

Plot the Voronoi diagram of points (x, y). The Voronoi facets with points at infinity are not drawn.

If "linespec" is given it is used to set the color and line style of the plot. If an axis graphics handle hax is supplied then the Voronoi diagram is drawn on the specified axis rather than in a new figure.

The options argument, which must be a string or cell array of strings, contains options passed to the underlying qhull command. See the documentation for the Qhull library for details http://www.qhull.org/html/qh-quick.htm#options.

If a single output argument is requested then the Voronoi diagram will be plotted and a graphics handle h to the plot is returned. [vx, vy] = voronoi(...) returns the Voronoi vertices instead of plotting the diagram.

            x = rand (10, 1);
            y = rand (size (x));
            h = convhull (x, y);
            [vx, vy] = voronoi (x, y);
            plot (vx, vy, "-b", x, y, "o", x(h), y(h), "-g")
            legend ("", "points", "hull");

See also: voronoin, delaunay, convhull.

— Function File: [C, F] = voronoin (pts)
— Function File: [C, F] = voronoin (pts, options)

Compute N-dimensional Voronoi facets. The input matrix pts of size [n, dim] contains n points in a space of dimension dim. C contains the points of the Voronoi facets. The list F contains, for each facet, the indices of the Voronoi points.

An optional second argument, which must be a string or cell array of strings, contains options passed to the underlying qhull command. See the documentation for the Qhull library for details http://www.qhull.org/html/qh-quick.htm#options.

See also: voronoi, convhulln, delaunayn.

     rand("state",9);
     x = rand(10,1);
     y = rand(10,1);
     tri = delaunay (x, y);
     [vx, vy] = voronoi (x, y, tri);
     triplot (tri, x, y, "b");
     hold on;
     plot (vx, vy, "r");

— Function File: polyarea (x, y)
— Function File: polyarea (x, y, dim)

Determine area of a polygon by triangle method. The variables x and y define the vertex pairs, and must therefore have the same shape. They can be either vectors or arrays. If they are arrays then the columns of x and y are treated separately and an area returned for each.

If the optional dim argument is given, then polyarea works along this dimension of the arrays x and y.

     rand ("state", 2);
     x = rand (10, 1);
     y = rand (10, 1);
     [c, f] = voronoin ([x, y]);
     af = zeros (size(f));
     for i = 1 : length (f)
       af(i) = polyarea (c (f {i, :}, 1), c (f {i, :}, 2));
     endfor

— Function File: area = rectint (a, b)

Compute the area of intersection of rectangles in a and rectangles in b. Rectangles are defined as [x y width height] where x and y are the minimum values of the two orthogonal dimensions.

If a or b are matrices, then the output, area, is a matrix where the i-th row corresponds to the i-th row of a and the j-th column corresponds to the j-th row of b.

See also: polyarea.

— Function File: [in, on] = inpolygon (x, y, xv, yv)

For a polygon defined by vertex points (xv, yv), determine if the points (x, y) are inside or outside the polygon. The variables x, y, must have the same dimension. The optional output on gives the points that are on the polygon.

     randn ("state", 2);
     x = randn (100, 1);
     y = randn (100, 1);
     vx = cos (pi * [-1 : 0.1: 1]);
     vy = sin (pi * [-1 : 0.1 : 1]);
     in = inpolygon (x, y, vx, vy);
     plot(vx, vy, x(in), y(in), "r+", x(!in), y(!in), "bo");
     axis ([-2, 2, -2, 2]);