Introduction
This page contains the summary of discussions on the correct interpretation of ArcByCenterPoint.
Angle Measuring Convention in GML
GML implements the semantics of ISO 19107. As such, the semantics for an angle encoded in GML is given by ISO 19107 clause:
In this variant of Bearing usually used for 2D coordinate systems, the first angle (azimuth) is measured from the first coordinate axis (usually north) in a counterclockwise fashion parallel to the reference surface tangent plane.
General Direction of Increasing and Decreasing Angle Values
ISO 19107 thus defines in which direction angle values increase and in which direction they decrease - see the following diagram:
Depending upon the "up" and the orientation of the first two axes, we have a left-handed or right handed coordinate system (see wikipedia and the following figure).
(Note: you can try this yourself with the following convention: thumb=x, index=y, middle=z)
Left-handed systems have a clockwise rotation from first to second axis (positive axis to
positive axis). Right-handed systems have a counterclockwise rotation from first to second axis
(positive axis to positive axis).
Note: the direction of "clockwise" and "counterclockwise" therefore depends on the "up", not
the order of the first two axes in the coordinate system. Swapping the order of the first and
second axis does not affect the direction of clockwise, just the direction of the rotation between
the two axes.
In a left-handed system, angle values increase in clockwise direction. In a right-handed system,
angle values increase in counterclockwise direction
The following diagram shows how angles are measured in WGS 84 2D with different
coordinate systems:
Note: The planes in geographic information are representations of the ground, and as such have
a "natural" up direction (usually represented by a normal vector). In a 3D system, "up" is given
by the definition of the third axis in the chosen CRS. In a 2D system "up" is usually implied.
Angle Measurement in Different Coordinate Systems
Apparently the way that angle values are expressed heavily depends upon the axis order
defined by the coordinate system that is used.
(A) GeodeticCRS: urn:ogc:def:crs:OGC:1.3:CRS84 (right-handed)
¿ Datum: WGS84
¿ Ellipsoidal 2D CS.
o Axes: (1st) longitude, (2nd) latitude.
o Orientations: east, north. UoM: degree
(B) GeodeticCRS: urn:ogc:def:crs:EPSG::4326 (left-handed)
¿ Datum: WGS84
¿ Ellipsoidal 2D CS.
o Axes: (1st) latitude, (2nd) longitude.
o Orientations: north, east. UoM: degree
The order of the axes determines where 0° is located.
Definition: The 0° angle is located on the positive part of the coordinate system's first axis.
Note: As explained in the previous section, the order of the first two axes and their location "on
the ground" in combination with the "up" direction defines in which directions the angle values
increase/decrease.