A way to create a custom timing function is by using the functionWithControlPoints:::: factory method in CAMediaTimingFunction (there is a corresponding initWithControlPoints:::: init method as well). What this does is create a Bézier curve for your timing function. It is not an arbitrary curve, but Bézier curves are very powerful and flexible.
It takes a little practice to get the hang of the control points. A tip: most drawing programs can create Bézier curves. Playing with those will give you a visual feedback on the curve you are representing with the control points.
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