The three values are leftDirection, the anchor point, and rightDirection. 'leftDirection' and 'rightDirection' compete in the competition for worst property names, because they have nothing to do with left and right. Font editors and other programs that deal with Bézier curves use the perfectly transparent 'incoming' and 'outgoing'. These terms make sense. Adobe's don't.
To find out what the values stand for, draw a simple curve with three points, then use a script to write the values to the ESTK's console. Open the Transform panel and check the values there what what you printed in the console.
A major problem in all this is that when you select a point with the direct selection tool, app.selection[0] doesn't return that point (I forget now what it does return), and getting a handle on a selected point is an ugly hack.
Peter