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polybool

Set operations on polygonal regions

Syntax

  • [x,y] = polybool(flag,x1,y1,x2,y2)
    example

Description

example

[x,y] = polybool(flag,x1,y1,x2,y2) performs the polygon set operation identified by flag. The result is output using the same format as the input. Geographic data that encompasses a pole cannot be used directly. Use flatearthpoly to convert polygons that contain a pole to Cartesian coordinates.

Most Mapping Toolbox™ functions adhere to the convention that individual contours with clockwise-ordered vertices are external contours and individual contours with counterclockwise-ordered vertices are internal contours. Although the polybool function ignores vertex order, follow this convention when creating contours to ensure consistency with other functions.

Examples

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theta = linspace(0, 2*pi, 100);
x1 = cos(theta) - 0.5;
y1 = -sin(theta);    % -sin(theta) to make a clockwise contour
x2 = x1 + 1;
y2 = y1;
[xa, ya] = polybool('union', x1, y1, x2, y2);
[xb, yb] = polybool('intersection', x1, y1, x2, y2);
[xc, yc] = polybool('xor', x1, y1, x2, y2);
[xd, yd] = polybool('subtraction', x1, y1, x2, y2);

subplot(2, 2, 1)
patch(xa, ya, 1, 'FaceColor', 'r')
axis equal, axis off, hold on
plot(x1, y1, x2, y2, 'Color', 'k')
title('Union')

subplot(2, 2, 2)
patch(xb, yb, 1, 'FaceColor', 'r')
axis equal, axis off, hold on
plot(x1, y1, x2, y2, 'Color', 'k')
title('Intersection')

subplot(2, 2, 3)
% The output of the exclusive-or operation consists of disjoint
% regions.  It can be plotted as a single patch object using the
% face-vertex form.  Use poly2fv to convert a polygonal region
% to face-vertex form.
[f, v] = poly2fv(xc, yc);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, hold on
plot(x1, y1, x2, y2, 'Color', 'k')
title('Exclusive Or')

subplot(2, 2, 4)
patch(xd, yd, 1, 'FaceColor', 'r')
axis equal, axis off, hold on
plot(x1, y1, x2, y2, 'Color', 'k')
title('Subtraction')

Ax = {[1 1 6 6 1], [2 5 5 2 2], [2 5 5 2 2]};
Ay = {[1 6 6 1 1], [2 2 3 3 2], [4 4 5 5 4]};
subplot(2, 3, 1)
[f, v] = poly2fv(Ax, Ay);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Ax), plot(Ax{k}, Ay{k}, 'Color', 'k'), end
title('A')

Bx = {[0 0 7 7 0], [1 3 3 1 1], [4 6 6 4 4]};
By = {[0 7 7 0 0], [1 1 6 6 1], [1 1 6 6 1]};
subplot(2, 3, 4);
[f, v] = poly2fv(Bx, By);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Bx), plot(Bx{k}, By{k}, 'Color', 'k'), end
title('B')

subplot(2, 3, 2)
[Cx, Cy] = polybool('union', Ax, Ay, Bx, By);
[f, v] = poly2fv(Cx, Cy);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Cx), plot(Cx{k}, Cy{k}, 'Color', 'k'), end
title('A \cup B')

subplot(2, 3, 3)
[Dx, Dy] = polybool('intersection', Ax, Ay, Bx, By);
[f, v] = poly2fv(Dx, Dy);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Dx), plot(Dx{k}, Dy{k}, 'Color', 'k'), end
title('A \cap B')

subplot(2, 3, 5)
[Ex, Ey] = polybool('subtraction', Ax, Ay, Bx, By);
[f, v] = poly2fv(Ex, Ey);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Ex), plot(Ex{k}, Ey{k}, 'Color', 'k'), end
title('A - B')

subplot(2, 3, 6)
[Fx, Fy] = polybool('xor', Ax, Ay, Bx, By);
[f, v] = poly2fv(Fx, Fy);
patch('Faces', f, 'Vertices', v, 'FaceColor', 'r', ...
  'EdgeColor', 'none')
axis equal, axis off, axis([0 7 0 7]), hold on
for k = 1:numel(Fx), plot(Fx{k}, Fy{k}, 'Color', 'k'), end
title('XOR(A, B)')

Input Arguments

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Polygon set operation, specified as one of the following character vectors.

Operation     
Region intersection'intersection''and''&'  
Region union'union''or''|''+''plus'
Region subtraction'subtraction''minus''-'  
Region exclusive or'exclusiveor''xor'   

Data Types: char

Polygon contours, specified as a NaN-delimited vector or cell array.

Data Types: double

Polygon contours, specified as a NaN-delimited vector or cell array.

Data Types: double

Polygon contours, specified as a NaN-delimited vector or cell array.

Data Types: double

Polygon contours, specified as a NaN-delimited vector or cell array.

Data Types: double

Output Arguments

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Polygon contour after set operation, returned as the same format as the input, that is, a NaN-delimited vector or cell array.

Polygon contour after set operation, returned as the same format as the input, that is, a NaN-delimited vector or cell array.

More About

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Tips

  • Numerical problems can occur when the polygons have a large offset from the origin. To avoid this issue, translate the coordinates to a location closer to the origin before performing the operation. Then, undo the translation after completing the operation. For example:

    [x,y] = polybool(flag,x1-xt,y1-yt,x2-xt,y2-yt);

    x = x+xt;

    y = y+yt;

Introduced before R2006a

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