Network on Chip (NoC) is proposed as a promising intra-chip communication infrastructure. A simple and efficient routing scheme is important for large scale NoC to provide the required communication performance to applications with low area and power overheads. Although mesh is preferred for NoC, virtualization may lead to irregular topologies. In this paper, we propose a Convex-Based DOR (CBDOR) routing scheme for the convex topologies. We demonstrate the connectedness and deadlock-freedom of CBDOR. This routing mechanism relies only on two bits per switch. Simulation results show that the area overhead of CBDOR switch is just 2.2% higher than that of traditional DOR switch, with the added complexity negligible. Therefore, the simplicity in the routing mechanism and switch architecture makes CBDOR more practical and scalable when compared to LBDR and FDOR.