Basics of Coordinate Metrology
Unit 2:  2-D Coordinate systems - Polar Coordinates

Digression
  Back

       

Instead of the Cartesian coordinates x and y, the position of a point P in the plane can also be characterized by
  • its distance from the origin (usually designated with the letter r) and
  • the direction in which it is "seen" from the origin. This direction is defined as the angle, relative to the x axis (measured counter-clockwise). It is designated by the Greek letter f (phi), j (other variant of phi) or q (theta) also often being used.

These coordinates are called (planar) polar coordinates. The position of a point is defined by a pair (r, f) of numbers. r is always ³ 0 and 0° £ f < 360°. (Please note: an angle of 360° is the same as 0°).

This is not entirely true of the origin: At the origin, r = 0, but the angle f is completely undetermined. All other points have unambiguously determined values of r and f, and in turn each pair (r, f) for which r > 0 and 0° £ f < 360° specifies exactly one point.

Some geometric problems can be solved more easily if the drawing plane is seen through polar coordinates. In technical drawings, for example rounded-off corners of parts are preferentially specified in polar coordinates.