Generating angular coordinate of raster scan of polar-coordinate

Abstract

Graphics for television display which emphasize circles, ellipses, circular or elliptical arcs, and the radii of circles or ellipses are conveniently stored in image memories addressable in polar coordinates. Television images which are to be rotated are conveniently stored in such memories, so the angular coordinate of the image memory addresses can be incremented or decremented to rotate the image with hardware as simple as a single adder. To read image memories addressed in polar coordinates, the Cartesian coordinates descriptive of television raster display are scan-converted to polar coordinates. This scan conversion takes place in real time at video sampling rates. The generation of the angular coordinate of the polar coordinates is facilitated by dividing one Cartesian coordinate by another by differentially combining their logarithms as found from read-only-memory table look-up, then finding an arc tangent from the logarithm of their difference as found from further read-only-memory table look-up. Since the non-linearities of the logarithm and arc tangent functions tend to track each other to a degree, combining the anti-logarithm and arc tangent look-up steps in a single read-only memory provides greater angular resolution for number of bits used in the read-only-memory input addresses.