Planing, also called "parallelism", is a technique in which harmonic interval relationships between notes are kept the same in relation to the melodic line. This is a very common technique in today's jazz writing - listen to Maria Schneider's work. Planing has its origins in the impressionistic styles of Debussy and Ravel.
There are two types of planing; diatonic and chromatic.
The example below demonstrates chromatic planing. The harmonic intervals are exact from one voicing to the next. If we analyze the interval structure of the right hand piano part we see exact intervals maintained - a P4 (F-C) and a M2 (C-Bb) moving to a P4 (G-D) and a M2 (D-C) and so forth.
The left hand and bass are planing P5 intervals.
This example uses diatonic planing. The harmonic intervals are not chromatically exact from one voicing to the next but diatonically exact. All of the notes used to harmonize the melody are diatonic to the chord.