Point in polygon checker

A point-in-polygon test answers a basic computational geometry question: given one query location and a closed shape defined by an ordered ring of vertices, does that location fall in the interior of the shape? Surveying, mapping products, game collision masks, logistics geofences, and classroom geometry labs all need the same deterministic answer rather than a hand-drawn sketch. This checker implements the classical even-odd ray casting algorithm on planar coordinates: a horizontal half-line is cast from the test point toward positive infinity, each polygon edge is tested for a proper crossing, and the parity of the crossing count decides inside versus outside. Points that land exactly on an edge or vertex are treated as inside and flagged with an on-boundary marker so closed-set consumers do not need a second pass. The polygon is closed implicitly—you do not have to repeat the first vertex at the end—and vertices may be supplied as objects with x and y fields or as two-element arrays.

How the even-odd ray casting test works

Start with a finite query point with coordinates x and y and an ordered list of at least three planar vertices that form a simple closed polygon when consecutive vertices are connected and the last vertex joins back to the first. The algorithm does not require you to choose clockwise or counter-clockwise order; both orientations are valid under the even-odd rule. From the query point, imagine a horizontal ray that travels only to the right, never to the left.

Walk every edge of the polygon and decide whether that edge crosses the ray. Horizontal edges are ignored so they do not create ambiguous double counts. If the query x lies strictly left of that intersection, the edge contributes one crossing; if the intersection coincides with the query within a tiny numerical tolerance, the point is classified as lying on the boundary.

After all edges are processed, an odd crossing count means the point is inside and an even count means outside, which is the classic Jordan-curve parity argument specialized to a horizontal ray. Coordinates must be finite; NaN and Infinity are rejected. Degenerate rings with fewer than three vertices are rejected with invalid input rather than silently treating a line segment as a polygon.

Where point-in-polygon checks show up in real work

Logistics and delivery products ask whether a courier GPS fix falls inside a neighborhood polygon before offering a zone-specific rate, and they need a deterministic answer that does not drift between the browser map preview and the server. Games and interactive media use axis-aligned or free-form collision masks defined as vertex rings and test player or projectile positions every frame without pulling a heavy GIS stack.

Classroom computational geometry modules teach ray casting, the Jordan curve theorem intuition, and floating-point edge cases; a single trusted oracle that returns both the inside flag and the raw crossing count helps students verify homework step by step. Urban planning and cadastral tools classify sample points against building footprints or zoning polygons during early design reviews when full topology databases are not yet connected.

If you later need polygon perimeter, polygon area, great-circle geodesy, multipolygon holes with the nonzero winding rule, or spherical containment on the WGS84 ellipsoid, treat those as separate search intents and landings rather than overloading this planar point-in-polygon checker page.