Deep neural networks have revolutionized 3D point cloud processing, yet efficiently handling large and irregular point clouds remains challenging. To tackle this problem, we introduce FastPoint, a novel software-based acceleration technique that leverages the predictable distance trend between sampled points during farthest point sampling. By predicting the distance curve, we can efficiently identify subsequent sample points without exhaustively computing all pairwise distances. Our proposal substantially accelerates farthest point sampling and neighbor search operations while preserving sampling quality and model performance. By integrating FastPoint into state-of-the-art 3D point cloud models, we achieve 2.55x end-to-end speedup on NVIDIA RTX 3090 GPU without sacrificing accuracy.