Created 'MonotonePolygon'

[1ndy]

I'd like to attempt random monotone polygon generation

TODO:

• Generate points in counter-clockwise order. Going counter-clockwise from a minimum point to a maximum point means the 'right-half' should be in between the extremes and the 'left-half' should be after.
• Generalize the function to accept a list of points instead of randomly generating them. All in all, the type signatures should look like this:

randomMonotone :: RandomGen g => Int -> Rand g (SimplePolygon () Rational)
randomMonotoneDirected :: RandomGen g => Int -> Vector 2 Rational -> Rand g (SimplePolygon () Rational)
monotoneFrom :: (Ord r, Num r) => Vector 2 r -> [Point 2 r -> SimplePolygon () r

randomMonotone should generate a random Vector and call randomMonotoneDirected.
randomMonotoneDirected should generate a set of random points and call randomMonotoneFrom. Splitting up the functions like this makes it a lot easier to test them.

[lemmih]

Excellent!

To rehash the algorithm:

1. Create N Point 2 Rational (N >= 3)
2. Create a random Vector 2 Rational
3. Find the extremes (min and max) of the points when sorted in the direction of the vector.
   We already have code for this. See maximumBy (cmpExtreme vector) and minimumBy (cmpExtreme vector).
4. Take out the two extremal points from the set.
5. Partition the remaining points according to whether they're on the left side or right side of the imaginary line between the two extremal points.
6. Sort the two partitioned sets, one in the direction of the vector and one in the opposite direction.
7. Connect the points, starting from the minimal extreme point, going through the set of points that are increasing in the direction of the vector, then to the maximal point, and finally down through the points that are decreasing in the direction of the vector.

I'll add some type-signatures and tests to your branch.

[lemmih]

Could you tick "Allow edits from maintainers" if you haven't already. Here's a guide: https://docs.github.com/en/free-pro-team@latest/github/collaborating-with-issues-and-pull-requests/allowing-changes-to-a-pull-request-branch-created-from-a-fork

[1ndy]

Box is checked. Thanks for giving me a starting point, I'll get started tomorrow

[lemmih]

For random Rational points, see this code:

granularity :: Integer
granularity = 10000000

-- Random point between screenTop/screenBottom.
genPoint :: RandomGen g => Rand g (Point 2 Rational)
genPoint = do
  x <- liftRand $ randomR (0, granularity)
  y <- liftRand $ randomR (0, granularity)
  pure $ Point2
    ((x % granularity) * screenHeight - screenTop)
    ((y % granularity) * screenHeight - screenTop)

It has to be in the Rand monad and cannot just be a Point 2 Rational.

[lemmih]

Also, you can use the ClosedLineSegment constructor to make a line. But the line is actually not needed. It can be imaginary. We just need to partition the points according to which side they're on. We can test this by just using the 'min' and 'max' points you already found.

[lemmih]

Your solution is very close to being correct. It just has to be monadic and use do. Like this:

randomMonotone :: RandomGen g => Int -> Vector 2 Rational -> Rand g (SimplePolygon () Rational)
randomMonotone nVertices direction = do
  -- 1, skip 2 in this function bc `direction` is given
  points <- replicateM nVertices genPoint
  -- 3
  let min = Data.Geometry.Polygon.Core.minimumBy (cmpExtreme direction) points
      max = Data.Geometry.Polygon.Core.maximumBy (cmpExtreme direction) points
  -- rest of your code here.

[lemmih]

Another hint: There's a built-in function for testing which side a point is on.

toTheLeft :: Point 2 r -> Bool
toTheLeft x = ccw min max x == CCW

You can then use Data.List.partition :: (a -> Bool) -> [a] -> ([a], [a]) to split the points in two.

[lemmih]

This code:

        polygon = SimplePolygon $ Data.CircularSeq.fromList (min : leftHalf : max : rightHalf)

Can be written as:

        polygon = fromPoints ([min] ++ leftHalf ++ [max] ++ rightHalf)

Let me know if I'm micro-managing too much and you'd rather want some peace and quiet. :)

[1ndy]

No you're fine, I appreciate the advice. I am pretty new to haskell and very new to this codebase so it is helpful to see these shortcuts. I've got some other responsibilities to tend to to wrap up this work week but I'll get back to this very soon and incorporate your suggestions.

…

On Tue, Jan 12, 2021 at 10:18 PM David Himmelstrup ***@***.***> wrote: This code: polygon = SimplePolygon $ Data.CircularSeq.fromList (min : leftHalf : max : rightHalf) Can be written as: polygon = fromPoints ([min] ++ leftHalf ++ [max] ++ rightHalf) Let me know if I'm micro-managing too much and you'd rather want some peace and quiet. :) — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#95 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AH4DYV7JHIRB5EJNDJ56BXDSZUGJFANCNFSM4V4BPIVQ> .

[1ndy]

Sorry for all the commits. I am getting an error while building hgeometry-ipe so this is the only way I can check my code right now

[noinia]

What error do you get when building hgeometry-ipe?

As a workaround (i.e. so that locally you can at least properly compile stuff), you can probably also remove hgeometry-ipe from the cabal.project file as well as disable tests. Not really an ideal solution though.

[lemmih]

I will push some visualization code to make debugging easier.

[lemmih]

Pushed.
If you go to the hgeometry-showcase folder and run stack repl hgeometry-showcase, it'll give you a GHCi prompt. In GHCi run :main random_monotone and an animation will appear in a browser window. It only works with stack and not cabal.

[lemmih]

Ah, I made a mistake in isMonotone :D Will push a fix.

[lemmih]

I love it! Your code works really well:

random_monotone.mp4

[lemmih]

I added two TODO items to your original post.

[1ndy]

Hey that's pretty cool! I'll work on those changes, I like the idea of a generalized randomMonotoneFrom function, though since it doesn't use the random monad maybe we should just call it monotoneFrom? I'll export it as the former for now

[lemmih]

Hey that's pretty cool! I'll work on those changes, I like the idea of a generalized randomMonotoneFrom function, though since it doesn't use the random monad maybe we should just call it monotoneFrom? I'll export it as the former for now

Oh yeah, monotoneFrom is a much better name.

[lemmih]

I've deleted some of the code I copy&pasted into your module at the start of the PR. It's been replaced by a better and more standard way of generating random points. Your code is unchanged except for a few type signatures.

[1ndy]

Looks good, are we ready to move it to the proper directory and submit the PR?

[lemmih]

Yes, everything looks good. I'll move the module, write a QuickCheck test, and mark the PR as ready.

[lemmih]

Alright, looks like everything is in order:

• Implementation
• Tests
• Documentation
• Showcase animation: https://hgeometry.org/#random-monotone
• Copyright notice to @1ndy (don't know your name so I just wrote 1ndy, feel free to change it)

I'll go ahead and merge this PR. Thank you so much, @1ndy. You've improved HGeometry. I hope we'll see more algorithms from you in the future.

[1ndy]

Thanks for all your help!!