Towards Interactive Progressive Cutting of Deformable Bodies via Phyxel-Associated Surface Mesh Approach for Virtual Surgery

Interactive progressive cutting of deformable body is vital for surgical training/planning systems with resection operations. Unfortunately, it is challenging to robustly simulate this phenomenon with faithful reflection of user's motion. The underlying reason is that sophisticated boundary conditions should be considered for the consistency between scalpel motion trajectory and incision during progressive cutting. Meanwhile, both geometrical and physical primitives along cutting trajectory need to be updated for each step induced by topological modifications, which is time-consuming for interactive environment. To tackle the above-mentioned issues, we present a phyxel-associated surface mesh approach for interactive progressive cutting of deformable bodies. Our method is based on a hybrid geometry, including a triangular surface mesh and an internal physical point cloud (phyxels), and we employ the moving least squares shape function to achieve the fast bijective mapping. This structure can well decouple the mechanical modeling from the geometry processing, thus allowing efficient handling of topological modifications, mechanical response, and rendering issues. Furthermore, we propose tailored continuous collision detection and constrained bilateral triangulation methods for fast geometrical modification. Besides, a dynamic adaptation scheme is proposed to avoid material slivers along splitting trajectories and guarantee numerical stability of simulation. Experimental results demonstrate that our method can provide effective progressive cutting simulation with realistic mechanical response, and it has a great potential to be an efficient and versatile computational framework for interactive surgical cutting simulation with high fidelity.