Mandibular reconstruction restores facial continuity and oral function after segmental resection. Patient-specific cutting guides transfer a computed tomography (CT)-based plan to the operating room with three-dimensional information, but printed guides add cost and lead time, cannot adapt after fabrication, and may interrupt surgery if sterility is lost. We investigate a markerless augmented reality (AR) alternative that registers a virtual cutting guide to the exposed mandible from surface geometry. The method extends surface-based registration for the transoral setting, where teeth form the most distinctive visible surface. After camera calibration, a HoloLens 2 time-of-flight camera captures a partial intraoperative point cloud. The user supplies a rough head-based alignment only to crop the region of interest. A teeth-weighted global stage computes correspondences and solves a truncated least-squares rigid alignment. An asymmetric point-to-plane iterative closest point (ICP) stage refines the complete CT mandible against the partial depth cloud target. The guide-to-mandible transform places the guide in the HoloLens world frame, while pose updates and interpolation follow target motion. We define a blinded phantom protocol with 30 target registration error (TRE) points under full, intermediate, and teeth-only exposure, plus a motion-to-display latency test. Our median TRE is 4.05, 6.10, and 7.10 mm respectively, and median latency is 0.805 s. These values support the feasibility of using AR to replace physical prints. The workflow removes mounted fiducials and manual landmark selection and provides a testable path toward transoral cutting guidance.
Partial-to-full registration remains challenging due to varying overlap ratios, fluctuating point densities, and the presence of noise. While transformers have shown strong potential for point cloud processing, prior methods typically confine them to global context aggregation, overlooking fine-grained local geometry crucial for accurate correspondence. We propose \emph{GAPR-Net}, a learning-based point cloud registration framework with a coarse-to-fine architecture that combines convolution and transformer modules, in which local and global information is fused between the partial and full point clouds using a cross-attention mechanism. To achieve this, a transformation-invariant point-wise geometric feature representation is proposed, which can robustly capture relative geometric features for individual points with respect to their neighboring points. To evaluate the effectiveness of the proposed approach, experiments are conducted on four geometrically distinct bones, including the tibia, femur, pelvis, and thoracic cartilage. The overall registration recall reaches 94.2\%, the method results in a low RMSE of 1.992 mm and $R^2$ values of 0.908 and 0.974 for rotation and translation, respectively. The results demonstrate that the proposed method effectively addresses the partial-to-full point cloud registration problem. The proposed method enables highly accurate 3D point cloud registration using partial observation, providing a critical foundation for precise surgical navigation and robotic interventions in computer-assisted surgery. The code will be accessed after the double-blind review process.