  A general method is introduced for constructing two-dimensional (2D) surface
meshes embedded in three-dimensional (3D) space time, and 3D hypersurface
meshes embedded in four-dimensional (4D) space time. In particular, we begin by
dividing the space-time domain into time slabs. Each time slab is equipped with
an initial plane (hyperplane), in conjunction with an unstructured simplicial
surface (hypersurface) mesh that covers the initial plane. We then obtain the
vertices of the terminating plane (hyperplane) of the time slab from the
vertices of the initial plane using a space-time trajectory-tracking approach.
Next, these vertices are used to create an unstructured simplicial mesh on the
terminating plane (hyperplane). Thereafter, the initial and terminating
boundary vertices are stitched together to form simplicial meshes on the
intermediate surfaces or sides of the time slab. After describing this new
mesh-generation method in rigorous detail, we provide the results of multiple
numerical experiments which demonstrate its validity and flexibility.
