Use this mathematical tool to inspect or reproduce the stated operation with inputs that satisfy its dimensional and domain requirements.

Point x

Optional number. X coordinate of the test point.

Point y

Optional number. Y coordinate of the test point.

X coordinates

Optional list. Vertex x coordinates in order around the polygon.

Y coordinates

Optional list. Vertex y coordinates matching xs.

The cited overview of Computational geometry supplies background for the terminology and domain context used by this tool.^[1]

Even-odd ray-casting test of whether a point lies inside a simple polygon given as parallel vertex coordinate lists, with exact boundary detection. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Inside

Returned boolean. True when the point is inside the polygon or on its boundary.

On boundary

Returned boolean. True when the point lies exactly on a polygon edge.

• Floating-point rounding, ill-conditioned inputs, singular cases, tolerance choices, and rapidly growing output sets can affect numerical accuracy or feasibility.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Check the result analytically on a small case and use an established numerical or symbolic library with suitable precision and diagnostics for consequential work.

• Polygon Area Calculator

  Compute the area of a simple polygon from parallel vertex coordinate lists using the shoelace formula.

• Polyline Length Calculator

  Sum the Euclidean distances between consecutive points of a polyline given as parallel coordinate lists.

• Chebyshev Distance Calculator

  Find the greatest coordinate difference between two equal-length points or vectors.