Figure 4.

Automatic mesh quality operations can convert surfaces and bodies to a vertex. (A) Schematic of a surface demote operation, which converts a surface to a vertex. Beginning with an initial set of connected surfaces (top), a surface is selected for conversion to a vertex (middle, red). A new vertex (green dot) is created at the centroid of the selected surface, and the connectivity of the new vertex (green lines) is determined by replacing the vertices of the converted surface that define surfaces connected to it (relevant edges shown as blue lines). Connected surfaces that are invalidated by the operation are also removed (bottom). (B) Consecutive body demote operations, which convert a body to a vertex, on a mesh of connected cubes. From top to bottom, cubes are selected (white) and made to reduce their volume to zero, resulting in a body demote operation. A body demote operation that does not invalidate any other body only converts its target body to a vertex, but any invalidated body is also converted to the resulting vertex (bottom two rows).