Tetrahedronization, also known as Delaunay triangulation, is a mathematical technique used to partition space into a set of tetrahedra based on a given set of points. It is commonly used in computational geometry and mesh generation. However, it is not directly applicable to charting routes between two points in space and time.
In the context of spacetime, it's important to note that time is considered a dimension separate from the three spatial dimensions. It is not typically treated as a dimension that can be triangulated or tetrahedronized in the same sense as spatial dimensions.
To chart routes between two points in spacetime, one would typically use the framework of spacetime geometry, specifically the mathematics of general relativity. General relativity describes how matter and energy curve the fabric of spacetime, resulting in the phenomenon of gravity. The paths followed by objects in this curved spacetime are known as geodesics.
When calculating routes in spacetime, factors such as the curvature of spacetime, the distribution of matter and energy, and the dynamics of the objects involved would need to be taken into account. This requires solving the equations of general relativity or using approximation methods, depending on the specific scenario.
In summary, while tetrahedronization is a useful mathematical technique for certain applications, it is not directly applicable to charting routes between points in spacetime. Understanding and navigating through spacetime involve more complex frameworks, such as the principles of general relativity.