Linear constraint-solving module for diagram layout

[fryguybob]

(Imported from http://code.google.com/p/diagrams/issues/detail?id=12. Original issue from byor...@gmail.com on January 15, 2011, 01:25:26 AM UTC)

There should be a module in the standard library providing an interface for specifying relative positions of subdiagrams via linear constraints (= equations or possibly even inequalities?), which then solves the constraints and takes care of actually positioning the diagrams as necessary.

[fryguybob]

(Imported. Original comment by byor...@gmail.com on May 16, 2011, 03:45:47 PM UTC)

It may be interesting/useful towards this end to be able to construct diagrams over a "free vector space". By the free vector space over v I mean something like

data FreeV v =
Var String
| Con v
| FreeV v :+: FreeV v
| Scalar v :*: FreeV v

[byorgey]

Note that #50 may also be relevant.

[cmears]

An example of the kind of thing we could do, just using the toysolver library:

import Diagrams.Prelude
import Diagrams.Backend.Cairo
import Diagrams.Backend.Cairo.CmdLine
import Algorithm.LPSolverHL
import Data.ArithRel
import qualified Data.IntMap as IM
import Data.LA
import Data.Ratio
import Data.Maybe

-- the layout specification
go = let [x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6] = map var [0..11]
     in solve
        [
          -- x1,x2,x3,x4 evenly spaced
          x2 ^-^ x1 .==. x3 ^-^ x2
        , x3 ^-^ x2 .==. x4 ^-^ x3

          -- spacing is 5
        , x2 ^-^ x1 .==. constant 5
          -- x1,y1 at origin
        , x1 .==. constant 0
        , y1 .==. constant 0

          -- y1,y2,y3,y4 all equal
        , y1 .==. y2
        , y1 .==. y3
        , y1 .==. y4

        -- x5,y5 on NNE-SSW line from x2,y2
        , y5 ^-^ y2 .==. 2*^x5 ^-^ 2*^x2
        -- x5,y5 vertically aligned with x3,y3
        , x5 .==. x3

        -- x6,y6 on NE-SW diagonal from x2,y2
        , y6 ^-^ y2 .==. x6 ^-^ x2
        -- x6,y6 vertically aligned with x1,y1
        , x6 .==. x1
        ]

-- this just draws labeled circles at the points determined by the
-- solver
go2 :: Diagram Cairo R2
go2 = let [x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6] =
              map fromRational (map snd (IM.toList (fromJust go)))
          pairs = [(x1,y1),(x2,y2),(x3,y3),(x4,y4),(x5,y5),(x6,y6)]
      in position [ (p2 pair, f n) | (pair,n) <- zip pairs [1..] ]
  where f n = circle 1 <> text (show n)

main = defaultMain (go2 # centerXY # pad 1.1 # bg white)

[cartazio]

gridstylesheets.org might have some ideas, its focused on js / css minyou)

[jeffreyrosenbluth]

that looks cool, maybe we can do it at hac

On Thu, Mar 20, 2014 at 11:33 PM, Carter Tazio Schonwald <
notifications@github.com> wrote:

gridstylesheets.org might have some ideas, its focused on js / css minyou)

Reply to this email directly or view it on GitHubhttps://github.com//issues/8#issuecomment-38246658
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[byorgey]

I'm now working on this using mfsolve for the constraint solving.

[jeffreyrosenbluth]

Interesting, is there any similarity to Cassowary?
https://en.wikipedia.org/wiki/Cassowary_(software)

On Sat, Sep 12, 2015 at 5:35 PM Brent Yorgey notifications@github.com
wrote:

I'm now working on this using mfsolve for the constraint solving.

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[byorgey]

I am not familiar with Cassowary, but yes, it seems similar. Differences
that I can see: mfsolve deals with equalities only (no inequalities) and
there is no way to specify constraints as being required or
preferred---every constraint is required. On the other hand, mfsolve is
able to work with non-linear constraints, whereas it seems Cassowary does
not. In any case, I think my approach should scale easily if we switch to
a more powerful constraint-solving engine in the future.

On Sun, Sep 13, 2015 at 6:22 AM Jeffrey Rosenbluth notifications@github.com
wrote:

Interesting, is there any similarity to Cassowary?
https://en.wikipedia.org/wiki/Cassowary_(software)

On Sat, Sep 12, 2015 at 5:35 PM Brent Yorgey notifications@github.com
wrote:

I'm now working on this using mfsolve for the constraint solving.

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