... Trade-off (area vs. angular resolution): ■ [Kant 92] Computing the optimal angular resolution is NP-hard. 1 n ρ O dlog d 3 -- -- - -- - -- - - = A Ω c ρn ()= Graph Drawing 37 Planar Straight-Line ... Graph Drawing 32 Planar Undirected Graphs Graph Drawing 33 Planar Drawings and Embeddings ■ a planar embedding is a class of topologically equivalent planar...
... Graph Drawing 58 General Undirected Graphs Graph Drawing 59 Algorithmic Strategies for Drawing General Undirected Graphs ■ Planarization method ■ if the graph is nonplanar, make it planar! ... of the drawing algorithms for planar graphs e.g., GIOTTO [Tamassia Batini Di Battista 87] ■ Orientation method ■ orient the graph into a digraph ■ use one the drawing algorithms...
... Construct Upward Planar
Drawings
■
Since an upward planar digraph is a
subgraph of a planar st-digraph, we only
need to know how to draw planar st-digraphs
■
If G is a planar st-digraph without ... Lubiw 91]
■
O(n
2
)-time for single-source digraphs
■
[Bertolazzi Di Battista Mannino
Tamassia 93]
■
O(n)-time for single-source digraphs
■
[Garg Tamassia 93]
■
NP-complete
Graph Drawi...
... graphs admit planar drawings.
A
graph which admits
a
planar drawing is called
a
planar graph.
b
d
Fig.
1.3
(a) A planar drawing, and
(b)
a
non -planar drawing of the same graph.
If ... algorithms for drawing planar graphs can be successfully used for
drawing
a
nonplanar graph by transforming the nonplanar graph into
a
similar planar graph. Furthe...
... box inclusion drawings) ■ drawings of series-parallel digraphs (delta drawings) ■ drawings of planar acyclic digraphs (visibility drawings, upward planar polyline drawings) Graph Drawing 91 Tree ... layout graph grammars for which optimal graph drawings can be constructed in polynomial time: ■ H-tree layouts of complete binary trees ■ hv-drawings of binary trees ■ series-parallel...
... symmetries
Graph Drawing
3
orthogonal drawing
bend
Drawing Conventions
■
general constraints on the geometric
representation of vertices and edges
polyline drawing
planar straight-line drawing
Graph Drawing
10
Beyond ... ∆'a
radial drawing ∆ of T
Graph Drawing
0
Graph Drawing Tutorial
Isabel F. Cruz
Worcester Polytechnic Institute
Roberto Tamassia
Brown Univer...
... tích cực (vàkhoá chéo tác động) thìbiểu thức đợc thực hiện.A:=BA:=func(B)A:=B<operator>C -- - ý nghĩaBiểu thứcSự kiệnCác dữ liệu sau đợc phép gán trực tiếp:8 bits: BYTE, CHAR16 bits: WORD, ... bằng nét gạch ngang trên sơ đồĐiều kiện luôn đúngA11T2T1= 1
Thiết bị lập trình5Trong ngôn ngữ S7 -Graph, thì điều kiện đợc lập trình bằng ngôn ngữ LAD (FBD).Các điều kiện có thể xảy ra tại các .....