Bend minimization

In graph drawing styles that represent the edges of a graph by polylines (sequences of line segments connected at bends), it is desirable to minimize the number of bends per edge (sometimes called the curve complexity) or the total number of bends in a drawing.Bend minimization is the algorithmic problem of finding a drawing that minimizes these quantities.

Eliminating all bends

The prototypical example of bend minimization is Fáry's theorem, which states that every planar graph can be drawn with no bends, that is, with all its edges drawn as straight line segments.

Drawings of a graph in which the edges are both bendless and axis-aligned are sometimes called rectilinear drawings, and are one way of constructing RAC drawings in which all crossings are at right angles. However, it is NP-complete to determine whether a planar graph has a planar rectilinear drawing, and NP-complete to determine whether an arbitrary graph has a rectilinear drawing that allows crossings.

Bend minimization

Bend

Bend may refer to:

Engineering and construction

Places

Music

Transportation

Other uses

Bend (song)

"Bend" is a song by Australian musician Chet Faker, released as a digital single in Australia on 19 June 2015 through Future Classic.

Faker announced a new Australian tour and premiered the song on the Matt and Alex show on Triple J on June 17. During the interview Faker said the song was intended to be on his debut album Built on Glass, but was ultimately replaced by "To Me". Faker said, "Ever since it got cut from the album it's just been sitting on my iTunes, sitting there looking at me. Usually when I cut a song after a few months I'm like 'yeah cool, that song's dead' but it's been annoying me... [so] it was either never going to be put out, or now, with this tour." "I recorded it in 2013 and kinda wanted to put it out since. It's always felt like a part of Built on Glass and since [the upcoming Australian] tour is the sort of live 'director's cut' of the album it made sense to release this before it lost context."

Track listing

Charts

Release history

References

Bend (heraldry)

In heraldry, a bend is a band or strap running from the upper dexter (the bearer's right side and the viewer's left) corner of the shield to the lower sinister (the bearer's left side, and the viewer's right). Authorities differ as to how much of the field it should cover, ranging from one-fifth (if shown between other charges) up to one-third (if charged alone). The supposed rule that a bend should occupy a maximum of one-third of the field appears to exclude the possibility of two or three bends being shown together, but contrary examples exist.

Modified bends

A bend can be modified by most of the lines of partition, such as the bend engrailed in the ancient arms of Fortescue or in the more modern examples of Cleethorpes Borough Council, England, and the bend wavy in the ancient coat of Wallop, Earls of Portsmouth of the modern Picard, Canada.

Bend sinister and "bar sinister"

The usual bend is occasionally called a bend dexter when it needs to contrast with the bend sinister, which runs in the other direction, like a sash worn diagonally from the left shoulder (Latin sinister means left).