Geometry

Areas on the ellipsoid.

• Polygon area and perimeter on the ellipsoid

  The area and perimeter of a polygon with geodesic edges on WGS 84 (or any ellipsoid), with holes, across the antimeridian or around a pole, and its ring orientation.

Zones a set distance around points, lines, and polygons.

• Buffer a point, line, or polygon

  The area within a distance of a point, line, or polygon on the ellipsoid, or a polygon shrunk inward, with round, mitre, or bevel corners, measured back against the input.

How far apart lines and tracks are.

• Compare two tracks

  How far apart two GPS tracks or routes are: the discrete Fréchet distance (the leash two walkers need, with where it is tightest), the Hausdorff distance, and their closest approach.

Triangles and nearest-point regions from scattered points.

• Delaunay triangulation of points

  Triangles joining a set of points so no point sits inside any triangle's circumcircle: planar on a local map for a regional set, or on the sphere for a global one.

• Voronoi cells around points

  The region nearest each point (its Voronoi cell), planar on a local map within a box around the points, or on the whole sphere for a global set.

Overlaps, unions, and differences of polygons.

• Overlap, union, or difference of two polygons

  Where two areas overlap, their combined outline, what one has that the other lacks, or both, as valid polygons with geodesic areas, like the overlap of two geofences.

Tests of where points and shapes sit against each other.

• Point in polygon

  Whether points are inside a polygon with geodesic edges, by the winding rule and the even-odd rule, with holes, on the boundary within 1 mm, and how far each is from the edge.

Centers, interior points, and envelopes of shapes.

• Bounding box, antimeridian-aware

  The smallest latitude and longitude box around points, a line, or a polygon, written west-south-east-north, crossing the antimeridian when that is shorter and reaching a pole a polygon circles.

• Polygon centroid and interior point

  The center of mass of a polygon on the ellipsoid, a warning when it falls outside the shape, and a point guaranteed inside, as far from the edges as possible, for a label or a pin.

• Add vertices along geodesic edges (densify)

  Adds vertices along each edge of a line or polygon so no piece is longer than a set length, each on the true geodesic, so maps that draw straight segments still follow the Earth's curve.

• Hull, bounding rectangle, and enclosing circle

  Around a set of points: the convex hull, the smallest rotated rectangle, and the smallest circle that holds them all, with its center and geodesic radius.

Fewer vertices, with the shape kept.

• Simplify a line or polygon (Douglas-Peucker)

  Removes vertices from a line or polygon while keeping every removed vertex within a distance tolerance of the simplified geodesic edges, optionally without letting edges cross, and reports the largest deviation.

• Simplify a line or polygon (Visvalingam)

  Removes the vertices that make the smallest triangles with their neighbors, down to an area threshold or a target number of vertices, optionally without letting edges cross, and reports the largest deviation.

Checks that polygons are well formed, and repairs them.

• Check and repair a polygon

  Finds what is wrong with a polygon (crossed or touching edges, duplicate corners, spikes, holes outside the outline, clockwise rings), says where, and returns a repaired version: a bow-tie becomes two triangles.