Ranking Points for Evaluation (cont.)

• Point b shadows point a from point d if:

• b is closer to d than a, and
• the slope between a and b is greater than the slope between a and d.

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Notes:

For this segment of a parabola, suppose we've evaluated points a, b,and c. Given the assumptions previously stated, one might most likely expect a zero to occur at point d, but our first version of ranking function g would not lead us to evaluate d. Rather, point a influences our supposed optimum evaluation point to be closer to c. [worked example]
So what we need is some form of shadowing influence so that the decision procedure more closely matches our local intuition. We say that a point b shadows point a from point d if:
b is closer to d than a, and the slope between a and b is greater than the slope between a and d.
So with a shadowed by b, we would then prefer d as the next best point to evaluate. This shadowing is implemented in the current ranking function g.