Before revision:  The preprocessing time is O(n^2\log n +(h+1)n^2+\varepsilon^{-1 can be improved to O(n^2 +\varepsilon^{-1 ) for simple polygons.
After revision:  The preprocessing time is O(n^2\log n +(h+1)n^2+\varepsilon^{-1 can be improved to O(n^2 ) for simple polygons.