The statement is still true, but non-trivial, if the fundamental group is only assumed to be infinite abelian (the most difficult case being when it is $\mathbb Z$) it was proved by Bangert-Hingston in the 1980s. On non-simply connected closed Riemannian or Finsler manifolds, it is very easy to find infinitely many closed geodesics when, for instance, the fundamental group is abelian and has rank larger than 1. For the other CROSSes, Hingston and Rademacher proved that a suitably generic Riemannian metric has infinitely many closed geodesics. The case of $S^2$ was settled in a combination of celebrated papers by Bangert, Franks, and Hingston. Poincaré's conjecture that any Riemannian metric on $\mathbbP^2$. Read more here.Lyusternik and Shnirel'man were the first to prove Therefore values returned from expressions using this function may change after zooming between scales. Returns the centroid of the given polygon ring var ringPoints = Geometry( $feature).rings Ĭlip Clip( geometry, envelope ) -> GeometryĬalculates the clipped geometry from a target geometry by an envelope.īe aware that using $feature as input to this function will yield results only as precise as the view's scale resolution. Returns: Point Example Returns the centroid of the given polygon Centroid( $feature) The polygon or array of points composing a polygon. Returns the centroid of the input geometry. Returns: Polygon Example Returns a polygon representing a 1/2-mile buffer around the input geometry BufferGeodetic( $feature, 0.5, 'miles') Support is limited to geometries with a Web Mercator (wkid 3857) or a WGS 84 (wkid 4326) spatial reference. This is a geodesic measurement, which calculates distances on an ellipsoid. Returns the geodetic buffer at a specified distance around the input geometry. Use one of the string values listed in the Units reference.Įxample Returns a polygon representing a 1/2-mile buffer around the input geometry Buffer( $feature, 0.5, 'miles')īufferGeodetic BufferGeodetic( geometry, distance, unit? ) -> Polygon Optional Measurement unit of the buffer distance. The distance to buffer from the geometry. This is a planar measurement using Cartesian mathematics.īe aware that using $feature as input to this function will yield results only as precise as the view's scale resolution.
Returns the planar (or Euclidean) buffer at a specified distance around the input geometry. The second point used to calculate the angle.Įxample Returns the angle from a point to the feature, in degrees var pointA = Point() īuffer Buffer( geometry, distance, unit? ) -> Polygon The first point used to calculate the angle. If the points are identical, then an angle of 0 degrees is returned. Point features can be used instead of any or both Point geometries. Only the x-y plane is considered for the measurement.
For example, an angle of 90 degrees points due north. The angle is measured in a counter-clockwise direction relative to east. Returns the arithmetic angle of a line between two points in degrees (0 - 360). Angle( pointA, pointB, pointC ) -> Number.* Indicates the unit may only be used for calculating areas. Yard, yd, square-yards, square-yard, squareyards, squareyard Meter, m, square-meters, square-meter, squaremeters, squaremeter Nautical-mile, square-nautical-miles, square-nautical-mile, squarenauticalmiles, squarenauticalmile Mile, square-miles, square-mile, squaremiles, squaremile Kilometer, km, square-kilometers, square-kilometer, squarekilometers, squarekilometer Unit valueįoot, ft, square-feet, square-foot, squarefeet, squarefoot For example, if calculating an area and meters is specified as the unit, then the unit will be treated as square-meters and vice versa. Where appropriate, linear and areal units may be used interchangeably. If the value is a number, it will be based on the standard referenced here. Units can either be identified as a number or a string. If a function references units, then any of the values described in the table below may be used. Geometry functions are not supported in the Dashboard formatting profile.