# Construct surface mesh

Input: | Output:

This modifier constructs a polyhedral mesh around a set of particles. It can be used to generate a geometric representation of the outer and inner surfaces of an atomistic solid. In addition to visualization purposes, the geometric description of the surface is good for quantitative measurements of the surface area and the solid volume or porosity of an atomistic structure.

After constructing the surface, OVITO computes the total surface area and the solid volume. The modifier also reports derived quantities such as the specific surface area. If you are using this modifier, in particular to perform quantitative analyses, you should cite the following article, which describes the algorithm implemented in OVITO: A. Stukowski, JOM: Vol. 66, Issue 3 (2014), 399-407.

The surface construction algorithm requires considerable memory, typically up to 1 kilobyte per input particle. So make sure your system has enough RAM available when processing a large simulation set, and keep in mind that 32-bit program versions of OVITO cannot access more than 2 GB of memory.

The appearance of the polyhedral mesh generated by this modifier is controlled by the attached surface mesh display object, whose parameters can be changed in the second panel.

## Parameters

Probe sphere radius

  This parameter controls the radius of the probe sphere used in the surface construction algorithm, which determines the level of surface details captured. A larger sphere radius leads to a surface with less details, which reflects only coarser features of the surface topology. A small sphere radius, on the other hand, will resolve finer surface features and small voids inside a solid. However, the sphere radius should not be smaller than half of the typical interatomic distance. Otherwise artificial holes will appear in the constructed surface.

Smoothing level

  After the triangulated surface mesh has been constructed, it is further refined by applying a smoothing and fairing algorithm to remove atomically sharp surface steps. This parameter controls how many iterations of the smoothing algorithm are performed.

Use only selected particles

  By default, the modifier constructs the surface mesh around all input particles. This option restricts the construction to only the selected particles.

## Technical background information

OVITO's surface construction algorithm is based on the mathematical alpha complex concept (Edelsbrunner and Mücke, ACM Trans. Graph. 13:43–72, 1994). First, a Delaunay tessellation of the atomistic input data is generated to subdivide the simulation cell into tetrahedral elements. Each Delaunay element is subsequently classified as either solid or empty by computing the alpha complex. The alpha complex, being a subcomplex of the Delaunay tessellation, includes all Delaunay tetrahedra that have an empty circumscribing sphere with squared radius equal or smaller than a parameter α. Here "empty" means that the open sphere does not include any atoms. The parameter α is the squared radius of an imaginary probe sphere. Space regions that are accessible to the probe without it overlapping any particles are considered empty; and solid otherwise. The surface mesh is then constructed from the dividing surface between solid and empty space regions, which consists of all triangular facets of the Delaunay tessellation that are adjacent to both a solid and an empty tetrahedron. In a final fairing step (Taubin, SIGGRAPH 95 Conf. Proc., pp. 351-358, 1995) the triangulated surface mesh is smoothed to remove atomically sharp steps.

Note: OVITO computes the volume of the solid region before the mesh gets smoothed in the final step. This is valid, because the smoothing method is supposed to be volume preserving.