A consistent analytical formulation for volume-estimation of geometries enclosed by implicitly defined surfaces
Provides a consistent analytical volume estimation method for implicit surfaces, solving an inconsistency problem in mesh-based approaches.
The authors derived an analytical formulation for volume estimation of geometries enclosed by implicitly defined surfaces, achieving 2nd-order accuracy in 2D and 3D cases while addressing mesh refinement inconsistency.
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all two-dimensional cases, and for elementary three three-dimensional cases by which the volume of general three-dimensional cases can be computed. Second, our method addresses the inconsistency issue due to mesh refinement. It is demonstrated by several two-dimensional and three-dimensional cases that this analytical formulation exhibits 2nd-order accuracy.