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Streaming transmission of 3D data sets is a key technology for remote rendering and visualization of huge geometrical models or complex scenes. We propose an efficient point-based progressive transmission method with gaze-guided control of the level-of-detail (LOD) of the data samples. The efficiency results from a multiresolution simplification scheme based on hierarchical clustering and a compact data structure for organizing the LOD hierarchy. After the data rearrangement, we can transmit the data for rendering with selective LODs by enhancing regions of interest (ROIs) around the gaze point of a viewer. The LOD distribution is continuous over the ROI and the whole scene can be updated dynamically as the gaze moves on the model surfaces. The method is fast and easy to implement, and experimental results demonstrate that it is effective even for some very large models.