Points located inside or on edge of polygonal region

Define a pentagon and a set of points. Then, determine which points lie inside (or on the edge) of the pentagon.

Define the x and y coordinates of polygon vertices to create a pentagon.

L = linspace(0,2*pi,6); xv = cos(L)'; yv = sin(L)';

Define x and y coordinates of 250 random query points. Initialize the random-number generator to make the output of `randn`

repeatable.

```
rng default
xq = randn(250,1);
yq = randn(250,1);
```

Determine whether each point lies inside or on the edge of the polygon area. Also determine whether any of the points lie on the edge of the polygon area.

[in,on] = inpolygon(xq,yq,xv,yv);

Determine the number of points lying inside or on the edge of the polygon area.

numel(xq(in))

ans = 80

Determine the number of points lying on the edge of the polygon area.

numel(xq(on))

ans = 0

Since there are no points lying on the edge of the polygon area, all 80 points identified by `xq(in)`

, `yq(in)`

are strictly inside the polygon area.

Determine the number of points lying outside the polygon area (not inside or on the edge).

numel(xq(~in))

ans = 170

Plot the polygon and the query points. Display the points inside the polygon with a red plus. Display the points outside the polygon with a blue circle.

figure plot(xv,yv) % polygon axis equal hold on plot(xq(in),yq(in),'r+') % points inside plot(xq(~in),yq(~in),'bo') % points outside hold off

Find the points inside a square with a square hole.

Define a square region with a square hole. Specify the vertices of the outer loop in a counterclockwise direction, and specify the vertices for the inner loop in a clockwise direction. Use `NaN`

to separate the coordinates for the outer and inner loops.

xv = [1 4 4 1 1 NaN 2 2 3 3 2]; yv = [1 1 4 4 1 NaN 2 3 3 2 2];

Define x and y coordinates of 500 random points. Initialize the random-number generator to make the output of `randn`

repeatable.

```
rng default
xq = rand(500,1)*5;
yq = rand(500,1)*5;
```

Determine whether each point lies inside or on the edge of the polygon area.

in = inpolygon(xq,yq,xv,yv);

Plot the polygon and the query points. Display the points inside the polygon with a red plus. Display the points outside the polygon with a blue circle.

figure plot(xv,yv,'LineWidth',2) % polygon axis equal hold on plot(xq(in),yq(in),'r+') % points inside plot(xq(~in),yq(~in),'bo') % points outside hold off

Query points in the square hole are outside the polygon.

Define the x and y coordinates for a pentagram.

xv = [0.5;0.2;1.0;0;0.8;0.5]; yv = [1.0;0.1;0.7;0.7;0.1;1];

Define the x and y coordinates of 12 query points.

xq = [0.1;0.5;0.9;0.2;0.4;0.5;0.5;0.9;0.6;0.8;0.7;0.2]; yq = [0.4;0.6;0.9;0.7;0.3;0.8;0.2;0.4;0.4;0.6;0.2;0.6];

Determine whether each point lies inside or on the edge of the polygon area. Also determine whether any of the points lie on the edge of the polygon area.

[in,on] = inpolygon(xq,yq,xv,yv);

Determine the number of points lying inside or on the edge of the polygon area.

numel(xq(in))

ans = 8

Determine the number of points lying on the edge of the polygon area.

numel(xq(on))

ans = 2

Determine the number of points lying outside the polygon area (not inside or on the edge).

numel(xq(~in))

ans = 4

Plot the polygon and the points. Display the points strictly inside the polygon with a red plus. Display the points on the edge with a black asterisk. Display the points outside the polygon with a blue circle.

figure plot(xv,yv) % polygon hold on plot(xq(in&~on),yq(in&~on),'r+') % points strictly inside plot(xq(on),yq(on),'k*') % points on edge plot(xq(~in),yq(~in),'bo') % points outside hold off

Six points lie inside the polygon. Two points lie on the edge of the polygon. Four points lie outside the polygon.

`xq`

— x-coordinates of query pointsscalar | vector | matrix | multidimensional array

x-coordinates of query points, specified as a scalar, vector, matrix, or multidimensional array.

The size of `xq`

must match the size of `yq`

.

**Data Types: **`double`

| `single`

`yq`

— y-coordinates of query pointsscalar | vector | matrix | multidimensional array

y-coordinates of query points, specified as a scalar, vector, matrix, or multidimensional array.

The size of `yq`

must match the size of `xq`

.

**Data Types: **`double`

| `single`

`xv`

— x-coordinates of polygon verticesvector

x-coordinates of polygon vertices, specified as a vector.

The size of `xv`

must match the size of `yv`

.

To specify vertices of multiply connected or disjoint polygons,
separate the coordinates for distinct loops with `NaN`

.
Additionally for multiply connected polygons, you must orient the
vertices for external and internal loops in opposite directions.

The polygon cannot be self-intersecting and multiply connected due to the ambiguity associated with self-intersections and loop orientations.

**Data Types: **`double`

| `single`

`yv`

— y-coordinates of polygon verticesvector

y-coordinates of polygon vertices, specified as a vector.

The size of `yv`

must match the size of `xv`

.

To specify vertices of multiply connected or disjoint polygons,
separate the coordinates for distinct loops with `NaN`

.
Additionally for multiply connected polygons, you must orient the
vertices for external and internal loops in opposite directions.

The polygon cannot be self-intersecting and multiply connected due to the ambiguity associated with self-intersections and loop orientations.

**Data Types: **`double`

| `single`

`in`

— Indicator for points inside or on edge of polygon arealogical array

Indicator for the points inside or on the edge of the polygon
area, returned as a logical array. `in`

is the same
size as `xq`

and `yq`

.

A logical

`1`

(`true`

) indicates that the corresponding query point is inside the polygonal region or on the edge of the polygon boundary.A logical

`0`

(`false`

) indicates that the corresponding query point is outside the polygonal region.

Therefore, you can use `in`

to index into `xq`

and `yq`

to
identify query points of interest.

`xq(in)` , `yq(in)` | Query points inside or on the edge of the polygon area |

`xq(~in)` , `yq(~in)` | Query points outside the polygonal region |

`on`

— Indicator for points on edge of polygon arealogical array

Indicator for the points on the edge of the polygon area, returned
as a logical array. `on`

is the same size as `xq`

and `yq`

.

A logical

`1`

(`true`

) indicates that the corresponding query point is on the polygon boundary.A logical

`0`

(`false`

) indicates that the corresponding query point is inside or outside the polygon boundary.

Therefore, you can use `on`

and `in`

to
index into `xq`

and `yq`

identify
query points of interest.

`xq(on)` , `yq(on)` | Query points on the polygon boundary |

`xq(~on)` , `yq(~on)` | Query points inside or outside the polygon boundary |

`xq(in&~on)` , `yq(in&~on)` | Query points strictly inside the polygonal region |

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