Streaming Certificate-Based Convex Hull Reduction for Planar Point Sets

Convex hull computation is a crucial operation in computational geometry, used in a wide range of fields like robotics, computer graphics, and biology. Before constructing an exact convex hull, it’s common to filter out interior points to streamline the process. But what if we could filter these points in real-time as they arrive, ensuring both efficiency and accuracy?

Researcher Oswaldo Cadenas has developed a groundbreaking streaming, certificate-based reduction method that precisely identifies and discards the interior points in planar point sets. This reduction guarantees the preservation of the exact convex hull by eliminating only the points certified to be inside the hull. It operates efficiently in a single streaming pass, utilizing local geometric operations.

In experiments conducted on synthetic and real-world datasets, remarkable reductions were achieved. On average, the reduction retained between 5% and 11% of input points for synthetic distributions and less than 1% for large real-world data. This innovative approach combines accuracy, efficiency, and streamlining, paving the way for enhanced geometric processing systems in various applications.