## 1 Introduction

One of the most natural and elegant paradigm for designing geometric algorithms is randomized incremental construction or RIC for short. It can be viewed as generalization of Quicksort and evolved over a sequence of papers [Mu88, Cl89] eventually culminating in a very general framework of configuration space by Clarkson and Shor [CS89]. The basic procedure is described in Figure LABEL:fig:ric0.