Layouts versus drawings of wiring diagrams

In Catlab, layout and drawing (rendering) of wiring diagrams are mostly decoupled. This notebook shows how to lay out diagrams using Graphviz's rank-based layout or Catlab's series-parallel layout and then render them using Compose.jl or TikZ.

The morphism we will visualize is:

using Catlab.Theories

X = Ob(FreeSymmetricMonoidalCategory, :X)
f, g, h = (Hom(sym, X, X) for sym in (:f, :g, :h))

expr = otimes(f, compose(f,g), compose(f,g,h))

\[f \otimes \left(f \cdot g\right) \otimes \left(f \cdot g \cdot h\right) : X \otimes X \otimes X \to X \otimes X \otimes X\]

Let's convert this expression into a wiring diagram. This yields a purely combinatorial object, as evidenced by its underlying graph.

using Catlab.WiringDiagrams, Catlab.Graphics

diagram = to_wiring_diagram(expr)
WiringDiagrams.graph(diagram)

ACSet with elements V = 1:8, E = 1:9

V	box
1	1
2	2
3	3
4	4
5	5
6	6
7	-2
8	-1

E	src	tgt	wire
1	2	3	1
2	5	6	2
3	4	5	3
4	7	1	1
5	7	2	2
6	7	4	3
7	1	8	1
8	3	8	2
9	6	8	3

Graphviz layout

Calling to_graphviz both lays out and draws the diagram, entirely within Graphviz.

to_graphviz(diagram, orientation=LeftToRight)

To get just the layout from Graphviz, we call graphviz_layout instead. We can then render this layout using Compose.jl. Note that the Graphviz layout has units in points.

import Compose

layout = graphviz_layout(diagram, orientation=LeftToRight)
layout_to_composejl(layout, base_unit=Compose.pt)

The same layout can be rendered in TikZ:

import TikzPictures

layout_to_tikz(layout, base_unit="1pt")

Series-parallel layout

Catlab has its own layout system based on series-parallel decomposition. In this case, the layout exactly recovers the structure of the morphism expression created at the beginning.

layout = layout_diagram(FreeSymmetricMonoidalCategory, diagram,
                        orientation=LeftToRight)
layout_to_composejl(layout)

layout_to_tikz(layout)