within

Returns true if geometry a lies in geometry b and their interiors intersect.

Geometry a is within geometry b if all points of a are in the interior or at the boundary of b and the interiors of a and b have at least one point in common.

note

According to the definition above, a geometry does not contain its boundary, so for example, a LineString that is completely contained in the boundary of a Polygon is not considered to be within that Polygon.

In most cases coveredBy should be used, as it has a simpler definition and allows for additional optimizations.

within is the converse of contains: within(a, b) === contains(b, a).

warning

Do not use this function with invalid geometries. You will get unexpected results.

Parameters

Name	Type	Description
a	Geometry | Prepared<Geometry>	First geometry
b	Geometry	Second geometry

Returns

boolean

true if geometry a is within geometry b

Throws

• GEOSError on unsupported geometry types (curved)

See also

• contains converse of within
• coveredBy more inclusive within
• prepare improves performance of repeated calls against a single geometry

Examples

const a = point([ 2, 10 ]);
const b = lineString([ [ 0, 13 ], [ 4, 15 ], [ 2, 10 ] ]);
const ab_within = within(a, b); // false

const c = lineString([ [ 10, 13 ], [ 14, 15 ] ]);
const d = lineString([ [ 10, 13 ], [ 14, 15 ], [ 12, 10 ] ]);
const cd_within = within(c, d); // true

const e = point([ 3, 3 ]);
const f = polygon([
    [ [ 0, 0 ], [ 0, 5 ], [ 5, 5 ], [ 5, 0 ], [ 0, 0 ] ],
    [ [ 2, 2 ], [ 4, 2 ], [ 4, 4 ], [ 2, 4 ], [ 2, 2 ] ],
]);
const ef_within = within(e, f); // false

const g = polygon([ [ [ 13, 0 ], [ 13, 2 ], [ 15, 2 ], [ 15, 0 ], [ 13, 0 ] ] ]);
const h = polygon([
    [ [ 10, 0 ], [ 10, 5 ], [ 15, 5 ], [ 15, 0 ], [ 10, 0 ] ],
    [ [ 12, 2 ], [ 14, 2 ], [ 14, 4 ], [ 12, 4 ], [ 12, 2 ] ],
]);
const gh_within = within(g, h); // true

const a = point([ 2, 10 ]); const b = lineString([ [ 0, 13 ], [ 4, 15 ], [ 2, 10 ] ]); const ab_within = within(a, b); // false const c = lineString([ [ 10, 13 ], [ 14, 15 ] ]); const d = lineString([ [ 10, 13 ], [ 14, 15 ], [ 12, 10 ] ]); const cd_within = within(c, d); // true const e = point([ 3, 3 ]); const f = polygon([ [ [ 0, 0 ], [ 0, 5 ], [ 5, 5 ], [ 5, 0 ], [ 0, 0 ] ], [ [ 2, 2 ], [ 4, 2 ], [ 4, 4 ], [ 2, 4 ], [ 2, 2 ] ], ]); const ef_within = within(e, f); // false const g = polygon([ [ [ 13, 0 ], [ 13, 2 ], [ 15, 2 ], [ 15, 0 ], [ 13, 0 ] ] ]); const h = polygon([ [ [ 10, 0 ], [ 10, 5 ], [ 15, 5 ], [ 15, 0 ], [ 10, 0 ] ], [ [ 12, 2 ], [ 14, 2 ], [ 14, 4 ], [ 12, 4 ], [ 12, 2 ] ], ]); const gh_within = within(g, h); // true