Before revision:  The task at hand is to decide for each point of P if it is in C  . We show that one can solve this problem in two and three dimensions using O( \mathrm{index (P) \log n) queries, where \mathrm{index (P) is the largest subset of points of P in convex position.
After revision:  The task at hand is to decide for each point of P if it is in C . We show that one can solve this problem in two and three dimensions using O( h (P) \log n) queries, where \mathrm{index (P) is the largest subset of points of P in convex position.