Enum VolumeMethod

Namespace

GeometryHelper.Enums

Assembly

GeometryHelper.dll

How the volume of a body is summed over its faces: each face broken into triangles, or read flat, and every triangle taken as a tetrahedron to the middle of the body's box, as the divergence theorem has it.

public enum VolumeMethod

Fields

Fan = 0

The fan of each face's boundary from its first corner, less the fans of its holes: what GetVolume(Tolerance) sums, and the quickest. Whatever the face's shape, its fan sums to the face read flat through that corner, a third of its area vector against it, so over a face a hair out of flat the volume moves by a third of the face's area times how far its first corner stands off its middle plane. Tekla Structures reports the volume of a part read so.

Surface = 1

The triangles lying in each face, on its own corners, its holes left open: the volume the faces hold as the closed surface of triangles they mesh to, which over a face a hair out of flat is bent along the diagonals the triangulation chose. What GetMassProperties(double, Tolerance) sums.

FlatFaces = 2

Each face read flat: laid onto the plane square to its area that runs through the middle of its corners, as Newell's method fits a plane, which is the face's own plane where it is flat. It rests on no triangulation: over a face of four corners a hair out of flat, it is the middle of the two ways of splitting it.

Remarks

Over flat faces every method gives the same volume, centroid and moments, but for the rounding: the divergence theorem is exact for them. They part only where a face is a hair out of flat, as the planar tolerance lets one be, and there no one surface is the face, so no one volume is the body's: a face of four corners with one of them lifted holds a third of the lift times its area more split along the diagonal through that corner, a sixth more split along the other, and a quarter more read flat. How far the methods part says how far the faces leave the volume open; Compare(GeoSolid3, Tolerance) sets them side by side.