Fast and Memory Efficient Approximated Convex Hull Computation with FPGA

The convex hull is the minimum convex set surrounding a set of points. The process of finding the convex hull has many application fields, including embedded applications on power-limbered and real-time systems. In general, such systems are preferably implemented with FPGAs. In order to compute the convex hull of an unsorted point set, it is necessary to store all the points during the computation, and thus the capacity of a on-chip memory is likely to be a major constraint for efficient FPGA implementation. On the other hand, approximated convex hulls are often sufficient for practical applications. Therefore, in this paper, we proposed an algorithm that computes an approximated convex hull without storing all unsorted points, and presented its FPGA implementation to evaluate the effectiveness. As a result, we achieved 11 to 30 times faster performance compared to the widely-used convex hull computation library Qhull. In addition, quality comparisons revealed that the maximum approximation error normalized to the diameters of point sets was 0.038%, which was reasonably small for practical use cases.