# polybool

Set operations on polygonal regions

`polybool` is not recommended. Use `polyshape` instead. For more information, see Version History.

## Syntax

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

## Description

``````[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.```

example

## 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 values.

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

Data Types: `char` | `string`

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 a `NaN`-delimited vector or cell array. The output returns in the same format as the input.

Polygon contour after set operation, returned as a `NaN`-delimited vector or cell array. The output returns in the same format as the input.

## 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;`

## Version History

Introduced before R2006a

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### R2018a: `polybool` is not recommended

`polybool` is not recommended. Use `polyshape` instead.

To replace calls to `polybool`, create `polyshape` objects to represent the shapes, call the appropriate `polyshape` object function for the equivalent Boolean operation, and then call the `polyshape` `boundary` object function. For example, this call to `polybool` specifies the union operation as the first argument.

`[Cx,Cy] = polybool('union',Ax,Ay,Bx,By)`
To update this usage, create separate `polyshape` objects for each shape and then use the `union` object function associated with the `polyshape` object. `polyshape` supports the Boolean operations supported by `polybool`: union, intersection, subtraction, and exclusive OR. Use the `polyshape` `boundary` object function to return `Cx` and `Cy`. See `polyshape` for a complete list of object functions, including `plot`.
```A = polyshape(Ax,Ay,'Simplify',false); B = polyshape(Bx,By,'Simplify',false); C = union(A,B); [Cx,Cy] = boundary(C);```
Note that the polygon vertex order is likely to differ between the output from `polybool` and the output from the call to `boundary`, because there is no single right answer. (Even in a simple one-region polygon, the vertices can be permuted cyclically without affecting the underlying geometry.) In addition, if the geometries of the inputs are not perfectly clean (free from self-intersections, etc.), then the `polyshape` `union` operation may make small changes that are not necessarily performed in `polybool`.