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The objective of CNC machining is to produce mechanical parts with designed quality most efficiently. To generate CNC tool paths for machining a sculptured part using a three-axis CNC machine, surface geometry, cutter shape and size, as well as tool path interval and direction need to be considered. In this work, the relation between the direction of a tool motion and cutting efficiency is studied. A new measure of cutting efficiency in three-axis CNC milling - the length of effective cutting edge (ECE) is introduced. The ECE length is mathematically proven to reach its maximum when the tool cuts a sculptured surface along its steepest tangent direction at the cutter contact point. The steepest tangent direction is thus proven to be the most efficient tool feed direction in three-axis sculptured part machining. The study identifies tool feed direction as a new control parameter in CNC tool path planning, and forms the foundation for further research on three-axis tool path generation of sculptured parts. [PUBLICATION ABSTRACT]