LAUSR

In this manuscript, we present a novel cutting method that involves using a vertex‐snapping strategy to fit the boundary surface onto the cutting path while avoiding generating new elements. We employ a point cloud with polynomial fitting to generate the cutting path, allowing for operation with unscheduled cuts and potential perturbations. Efficient geometry operations are developed to handle topological changes during progressive cutting. While it is challenging to optimize the mesh quality and accurately align the cut surface with the cutting path, we propose an innovative strategy that converts this geometric problem into a quasi‐static elastic problem. This involves solving a constrained elastic problem within an auxiliary simulation, where the system optimizes the mesh quality when reaching equilibrium. Furthermore, we propose modifications to a GPU‐based matrix‐free solver, enabling efficient updates of the precomputed data stored in the GPU memory and thus ensuring real‐time performance.