I have had this experience when "scanning" a line from target back to ball. Athough my head turns properly to run my line of sight in a straight line, just as the scan get about 3-4 feet from the ball, the "line" I appear to be scanning takes on a curvature (bowed with the middle of the bowing away from me). I've had to learn a special care and slowness to "get through" this troublesome area of the return scan.
Going away from the putter and ball at the start of the scan, I guess there is a similar problem, as I have to be careful to assess what is really straight off the putter face before I start the head turn to drive the line of sight along the ground.
Nice of you to explain it in such detail. Maybe I can get a handle on this and make something out of it useful for golfers. Thanks.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
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