silky/penrose

a system to automatically visualize mathematics

Penrose

Note: this README is obsolete!

TODO: redocument the code after the dust settles.

Directories

optimization contains the code I'm currently working on, as well as GIFs. layout.hs contains the cleaned-up and commented code. The rest of the files contain irrelevant code relating to the autodiff library.

constraint-code contains the old code for the set theory DSL and simple constraint satisfaction.

documentation only contains the system diagram in Keynote.

byhand contains diagrams made by hand, e.g. in Keynote.

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More information

I use the [gloss library]( I use the following library for the graphics/animation/input: https://hackage.haskell.org/package/gloss-1.10.2.3/docs/Graphics-Gloss-Interface-Pure-Game.html) to handle graphics, animation, and user input.

Functionality of the current code:

• gradient-descent-based layout
• with backtracking line search
• for sets only
• with very simple objective functions provided (e.g. centering)
• where the layout is animated and interactive (v. useful for debugging)

Pressing limitations:

• need to add autodiff
• need to debug line search and add Wolfe condition
• does not handle arbitrary numbers of objects
• does not handle labels, points, boxes, or maps (labels were handled at one point, but I removed the functionality)
• needs more objective functions to handle other cases
• needs to generalize to sums of objective functions and ones with arbitrary numbers of parameters, including object size
• need a better debugging interface for optimization, e.g. live parameter tuning

Parameters:

• picWidth, picHeight: canvas dimensions
• stepFlag: turns stepping the simulation on and off for debugging (no stepping = objects don't move)
• clampFlag: turns clamping gradient values on and off for debugging
• debug: turns on/off the debug print functions
• constraintFlag: turns constraint satisfaction on/off (currently off because we're doing unconstrained optimization)
• objFn1: objective function to use
• btls: turn on/off the backtracking line search for debugging (off = use a fixed timestep specified in the code)
• alpha and beta: parameters for the backtracking line search (see code for a more detailed description)
• stopEps: stopping condition sensitivity for gradient descent. Stop when magnitude of gradient is less than stopEps.

Debugging:

• Use the flags above.
• I also use ghci, the Haskell REPL. To load the file, do :l filename.hs. To import a library, paste in the normal import statement. To declare something, start with a let statement, e.g. let x = 5.
• For printing internal values, I use the Debug.Trace library.

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Usage for current code

Compile: ghc layout.hs

Install any relevant packages: cabal install $PACKAGE_NAME (though I'm told the Haskell community has moved on to the better stack package manager?)

Run: ./layout.hs

Pressing the R key will resample the configuration. You can also click and drag the objects. The object on top is semi-arbitrary, decided by the order of the objects in the internal list.

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Usage for old code

Compile: ghc settheory.hs

Create SVG: ./settheory -w 500 -h 500 -o set.svg (The parameters are the width and height of the rendered picture.)

Open SVG: chrome set.svg