I'm not quite sure what you are asking, but I think you want to know that if you have the following:

          * C 
           \
            \ 
             \
              * B
             /
            /
           /
          /
         *  A
[download]

and you travel from A to C, whether at B you go "right" or "left". There's a simple formula for that.

Let A, B and C have coordinates (x_a,y_a), (x_b,y_b), and (x_c,y_c).

Then you turn "left" or "counter-clockwise" at B if, and only if, the determinant

                 
    |                 |
    | xa - xb  xc - xb |
    |                 |  =
    | ya - yb  yc - yb |
    |                 |

    (xa - xb) * (yc - yb) - (xc - xb) * (ya - yb)

is negative. If it's positive, you turn "right", or "clockwise". If the result is 0, you continue in a straight line.

Abigail

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