FlowMesher: An automatic unstructured mesh generation algorithm with applications from finite element analysis to medical simulations

Abstract: In this work, we propose an automatic mesh generation algorithm, FlowMesher, which can be used to generate unstructured meshes for mesh domains in any shape with minimum (or even no) user intervention. The approach can generate high-quality simplex meshes directly from scanned images in OBJ format in 2D and 3D or just from a line drawing in 2-D. Mesh grading can be easily controlled also. The FlowMesher is robust and easy to be implemented and is useful for a variety of applications including surgical simulators. The core idea of the FlowMesher is that a mesh domain is considered as an "airtight container" into which fluid particles are "injected" at one or multiple selected interior points. The particles repel each other and occupy the whole domain somewhat like blowing up a balloon. When the container is full of fluid particles and the flow is stopped, a Delaunay triangulation algorithm is employed to link the fluid particles together to generate an unstructured mesh (which is then optimized using a combination of automated mesh smoothing and element removal in 3D). The performance of the FlowMesher is demonstrated by generating meshes for several 2D and 3D mesh domains including a scanned image of a bone.