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-- |
-- Module      :  Algorithms.Geometry.PolygonTriangulation.Triangulate
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--------------------------------------------------------------------------------
module Algorithms.Geometry.PolygonTriangulation.Triangulate where


import qualified Algorithms.Geometry.PolygonTriangulation.MakeMonotone as MM
import qualified Algorithms.Geometry.PolygonTriangulation.TriangulateMonotone as TM
import           Algorithms.Geometry.PolygonTriangulation.Types
import           Control.Lens
import           Data.Either (lefts)
import           Data.Ext
import qualified Data.Foldable as F
import           Data.Geometry.LineSegment
import           Data.Geometry.PlanarSubdivision.Basic
import           Data.Geometry.Polygon

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-- | Triangulates a polygon of \(n\) vertices
--
-- running time: \(O(n \log n)\)
triangulate     :: forall s t p r. (Ord r, Fractional r)
                => Polygon t p r -> PlanarSubdivision s p PolygonEdgeType PolygonFaceData r
triangulate pg' = constructSubdivision e es diags
  where
    (pg, diags)   = computeDiagonals' pg'
    (e:es)        = listEdges pg


-- | Triangulates a polygon of \(n\) vertices
--
-- running time: \(O(n \log n)\)
triangulate'     :: forall s t p r. (Ord r, Fractional r)
                 => Polygon t p r -> PlaneGraph s p PolygonEdgeType PolygonFaceData r
triangulate' pg' = constructGraph e es diags
  where
    (pg, diags)   = computeDiagonals' pg'
    (e:es)        = listEdges pg


-- | Computes a set of diagaonals that together triangulate the input polygon
-- of \(n\) vertices.
--
-- running time: \(O(n \log n)\)
computeDiagonals :: (Ord r, Fractional r) => Polygon t p r -> [LineSegment 2 p r]
computeDiagonals = snd . computeDiagonals'

-- | Computes a set of diagaonals that together triangulate the input polygon
-- of \(n\) vertices. Returns a copy of the input polygon, whose boundaries are
-- oriented in counter clockwise order, as well.
--
-- running time: \(O(n \log n)\)
computeDiagonals'     :: (Ord r, Fractional r)
                      => Polygon t p r -> (Polygon t p r, [LineSegment 2 p r])
computeDiagonals' pg' = (pg, monotoneDiags <> extraDiags)
  where
    pg            = toCounterClockWiseOrder pg'
    monotoneP     = MM.makeMonotone @() pg -- use some arbitrary proxy type
    -- outerFaceId'  = outerFaceId monotoneP

    monotoneDiags = map (^._2.core) . filter (\e' -> e'^._2.extra == Diagonal)
                  . F.toList . edgeSegments $ monotoneP
    extraDiags    = concatMap (TM.computeDiagonals . toCounterClockWiseOrder')
                  . lefts . map (^._2.core)
                  . filter (\mp -> mp^._2.extra == Inside) -- triangulate only the insides
                  -- . filter (\f -> f^._1 /= outerFaceId')
                  . F.toList . internalFacePolygons $ monotoneP
    -- FIXME: we should already get all polygons in CCW order, so no
    -- need for the toClockwiseOrder' call