LiDAR sensors provide rich 3D information about surrounding scenes and are becoming increasingly important for autonomous vehicles' tasks, such as semantic segmentation, object detection, and tracking. Being able to simulate a LiDAR sensor will accelerate the testing, validation, and deployment of autonomous vehicles while reducing the cost and eliminating the risks of testing in real-world scenarios. To tackle the issue of simulating LiDAR data with high fidelity, we present a pipeline that leverages real-world point clouds acquired by mobile mapping systems. Point-based geometry representations, more specifically splats, have proven their ability to accurately model the underlying surface in very large point clouds. Showing the limits of basic splatting, we introduce an adaptative splats generation method that accurately models the underlying 3D geometry, especially for thin structures. We have also developed a LiDAR simulation that is 200 times faster-than-real-time by ray casting on GPU while focusing on efficiently handling large point clouds. We test our LiDAR simulation in real-world conditions, showing qualitative and quantitative results against basic splatting and meshing, demonstrating the superiority of our modeling technique.