1. A color image data processing method comprising the steps of: receiving, as input data, a plurality of color component values representing a color picture element to be reproduced; performing in parallel a plurality of operations for a respective plurality of predetermined regions in a color coordinate system on the chromaticity chart of the color of the picture element, wherein areas for a predetermined number of colors to reproduce the picture element are determined by applying the operations to the plurality of color component values; and selecting a result of an operation that provides positive values for the areas for using those areas to reproduce the picture element.