Cut Road polygon where points at intersection

[M_DJohnson]

We have two layers point and polygon. We would like to cut the road polygon where point is available. The road polygon currently single huge polygon. At every point how can find road polygon corner point those will use to build line to cut polygon.

[XanderBakker]

That might be quite a challenge. Probably need to generalize the polygon features and select the remaining vertices based on a distance tolerance from the point and create the lines between vertices (excluding the diagonals) and split the geometry based on those new lines... 

You placed this question in the ArcObjects SDK space, Just to be sure... is Python an option too? That would potentially save a lot of lines of code....