determine if a given point is inside the polygon

Question

Given a convex polygon as a counter-clockwise list of n vertices, give O(lgn) algorithm to determine if a given point is inside the polygon. Assume the basic operations take

Answer 1

The condition for a point to be inside a polygon is that the point should be on same side of all line segments. You should check for the sign of the distance of the point in question with each line segments that make up the polygon - if all are same sign the point is inside the polygon. A google search should give you many algorithms.