The CAD/CAM/CAI Research Laboratory is developing revolutionary geometric computing software technologies to support practical computer-aided design, manufacturing, and inspection applications. In recent years, our research work consistently involves highly flexible and efficient geometric modeling, machining simulation and verification, and 3D laser scanning and scanned point cloud data processing. To date, we have developed many advanced geometric modeling and computing algorithms. Many of these algorithms are fundamental to the emerging digital manufacturing technologies, which are being viewed as the next wave of manufacturing innovation.