To address the challenges of heavy data processing volume and the difficulty in meeting real-time requirements for industrial applications in 3D point cloud–based manipulator grasping, this paper proposes a novel visual grasping method based on negative space analysis of point cloud bird's-eye view (BEV). First, the YOLOv8 network is employed to perform fast and accurate 2D localization of targets in RGB images, and a 3D frustum is constructed to preliminarily filter the scene point cloud, followed by the random sample consensus (RANSAC) algorithm to robustly segment the desktop support plane. The core innovation involves a geometric manifold projection strategy that reduces the dimensionality of sparse 3D point clouds onto a 2D BEV plane. Based on the theory of image moments, the contour of the "negative space" occupied by the object is analytically parsed, thereby solving the target's six-degree-of-freedom (6-DoF) grasping pose with a linear computational complexity of $O(N)$. Experimental results demonstrate that, compared with the baseline method combining single-shot multiBox detector (SSD) and PointNetGPD, the proposed method achieves a 5% improvement in the total system success rate (rising from 65% to 70%). Moreover, the average computation time per grasp is significantly reduced from 550 to 210 ms, exhibiting a speed advantage of more than 2.6 times. This work verifies the feasibility of replacing complex 3D deep-learning models with lightweight geometric analysis in specific structured scenes.