```{-# LANGUAGE TypeFamilies               #-}
{-# OPTIONS -Wall #-}

--------------------------------------------------------------------------------
-- |
-- Module      :  Wumpus.Drawing.Basic.Paths
-- Copyright   :  (c) Stephen Tetley 2010-2011
--
-- Maintainer  :  Stephen Tetley <stephen.tetley@gmail.com>
-- Stability   :  highly unstable
-- Portability :  GHC
--
-- Paths for /elementary/ shapes - rectangles...
--
-- \*\* - WARNING \*\* - half baked.
--
--------------------------------------------------------------------------------

module Wumpus.Basic.Geometry.Paths
(

PathAlg
, runPathAlgPoint
, runPathAlgVec
, pathStartIsStart
, pathStartIsLocus
, pathIterateLocus

, rectanglePathAlg
, blRectanglePathAlg

, diamondPathAlg
, polygonPathAlg

, arcPathAlg
, circlePathAlg

, LocCoordPath
, coordinatePrimPath

, rectangleCoordPath
, diamondCoordPath
, polygonCoordPath
, isoscelesTriangleCoordPath
, isoscelesTrianglePoints
, equilateralTriangleCoordPath
, equilateralTrianglePoints
)
where

import Wumpus.Basic.Geometry.Base
import Wumpus.Basic.Kernel

import Wumpus.Core                              -- package: wumpus-core

import Data.AffineSpace                         -- package: vector-space
import Data.VectorSpace

import Data.List ( unfoldr )

data PathAlgScheme = START_IS_START | START_IS_LOCUS
deriving (Enum,Eq,Ord,Show)

-- | A vector chain building a path.
--
-- The vectors are relative to the predecessor, so the
-- rendering of a 'PathAlg' iterates the start point.
--
-- A polygon PathAlg should have steps for all sides of the
-- polygon with the end point generated by the last vector
-- coinciding with thet start point.
--
data PathAlg u = PathAlg { path_alg_scheme  :: PathAlgScheme
, path_alg_steps   :: [Vec2 u]
}

type instance DUnit (PathAlg u) = u

runPathAlgPoint :: Num u => Point2 u -> PathAlg u -> [Point2 u]
runPathAlgPoint _  (PathAlg _   [])       = []
runPathAlgPoint p0 (PathAlg scm (v0:xs))
| scm == START_IS_START = p0 : step (p0 .+^ v0) xs
| otherwise             = step (p0 .+^ v0) xs
where
step pt []      = [pt]
step pt (v:vs)  = pt : step (pt .+^ v) vs

runPathAlgVec :: PathAlg u -> (Maybe (Vec2 u), [Vec2 u])
runPathAlgVec (PathAlg START_IS_LOCUS (v:vs)) = (Just v, vs)
runPathAlgVec (PathAlg _ vs)                  = (Nothing, vs)

-- TO CLARIFY - should all four side paths of a rectangle be
-- generated, or three sides with the implication that close forms
-- the fourth?
--

pathStartIsStart :: [Vec2 u] -> PathAlg u
pathStartIsStart vs = PathAlg { path_alg_scheme = START_IS_START
, path_alg_steps  = vs }

pathStartIsLocus :: [Vec2 u] -> PathAlg u
pathStartIsLocus vs = PathAlg { path_alg_scheme = START_IS_LOCUS
, path_alg_steps  = vs }

-- | Note this creates a path very the first vector represents a
-- @moveto@, then the subsequence vectors represent @linetos@.
--
pathIterateLocus :: Num u => [Vec2 u] -> PathAlg u
pathIterateLocus []      = pathStartIsLocus []
pathIterateLocus (v0:xs) = pathStartIsLocus \$ v0 : step v0 xs
where
step v1 []      = [v0 ^-^ v1]
step v1 (v2:vs) = (v2 ^-^ v1) : step v2 vs

-- | Supplied point is /center/, the genearated points are
-- counter-clockwise so [ bl, br, tr, tl ] .
--
rectanglePathAlg :: Fractional u => u -> u -> PathAlg u
rectanglePathAlg w h = pathStartIsLocus [ vbl, vbr, vtr, vtl ]
where
vbl = vec (negate \$ 0.5*w) (negate \$ 0.5*h)
vbr = hvec w
vtr = vvec h
vtl = hvec (-w)

-- | Supplied point is /bottom-left/, subsequent points are
-- counter-clockwise so [ bl, br, tr, tl ] .
--
blRectanglePathAlg :: Num u => u -> u -> PathAlg u
blRectanglePathAlg w h = pathStartIsStart [ vbr, vtr, vtl, vbl ]
where
vbr = hvec w
vtr = vvec h
vtl = hvec (-w)
vbl = vvec (-h)

-- | 'diamondPathAlg' : @ half_width * half_height -> PathAlg @
--
diamondPathAlg :: Num u => u -> u -> PathAlg u
diamondPathAlg hw hh = pathIterateLocus [ vs,ve,vn,vw ]
where
vs = vvec (-hh)
ve = hvec hw
vn = vvec hh
vw = hvec (-hw)

-- | 'polygonPathAlg' : @ num_points * radius -> PathAlg @
--
polygonPathAlg :: Floating u => Int -> u -> PathAlg u
polygonPathAlg n radius = pathIterateLocus \$ unfoldr phi (0,top)
where
top                     = 0.5*pi
theta                   = (2*pi) / fromIntegral n

phi (i,ang) | i < n     = Just (avec ang radius, (i+1,ang+theta))
| otherwise = Nothing

arcPathAlg :: Floating u => u -> Radian -> Radian -> PathAlg u
arcPathAlg r ang1 ang2 = pathStartIsLocus \$ step1 \$ arcdiv ang1 ang2
where
step1 []         = []
step1 ((a,b):xs) = let (v0,v1,v2,v3) = minorArcQuadVec r a b
in v0 : v1: v2: v3 : step xs

step []         = []
step ((a,b):xs)  = let (_,v1,v2,v3) = minorArcQuadVec r a b
in v1: v2: v3 : step xs

-- | Helper - generate four vectors building a minor (<90 deg)
-- arc.
--
-- The first vec is from center - for cumulative arcs this should
-- only taken once.
--
=> u -> Radian -> Radian -> (Vec2 u, Vec2 u, Vec2 u, Vec2 u)
minorArcQuadVec r ang1 ang2 = (v0, v1, v2, v3)
where
(p1,p2,p3,p4) = bezierArc r ang1 ang2 zeroPt
v0            = pvec zeroPt p1
v1            = pvec p1 p2
v2            = pvec p2 p3
v3            = pvec p3 p4

circlePathAlg :: (Fractional u, Floating u)
=> u -> PathAlg u
circlePathAlg r = pathStartIsLocus vs
where
vs = hvec r : diff (flip pvec) (bezierCircle r zeroPt)

-- | Helper - diff
--
-- Note diff relies on the pointlist cycling the endpoint
--
-- > [p0, ..., p0]
--
-- This is how Wumpus-Core generates Bezier circles.
--
diff :: (a -> a -> b) -> [a] -> [b]
diff _  [] = []
diff op (x:xs) = step x xs
where
step _ []     = []
step a (b:bs) = b `op` a : step b bs

-- | Helper - divide an arc into quadrants plus remainder.
--
arcdiv ang1 ang2 | ang1 >  ang2 = step ang1 (ang2 + 2 * pi)
| otherwise    = step ang1 ang2
where
step a1 a2 | a1 == a2 = []
step a1 a2 | a2 - a1 > half_pi = norm (a1,a1+half_pi) : step (a1+half_pi) a2
| otherwise         = [(a1,a2)]

norm (a,b) = (circularModulo a, circularModulo b)

-- arcs - wedges - circles...

---------------------------------------------------------------------------
-- OLD ...

-- | A functional type from /initial point/ to point list.
--
type LocCoordPath u = Point2 u -> [Point2 u]

-- Note - extraction needs a naming scheme - extractFROM or
-- extractTO? - in either case this might be queuing up
-- name-clash problems.
--
-- The Path data type will also need a similar function...
--

-- | Relative unit version of 'coordinatePrimPathAU'.
--
coordinatePrimPath :: InterpretUnit u
=> LocCoordPath u -> Point2 u -> Query PrimPath
coordinatePrimPath fn pt = vertexPP \$ fn pt

-- | Supplied point is /bottom-left/, subsequenct points are
-- counter-clockwise so [ bl, br, tr, tl ] .
--
rectangleCoordPath :: Num u => u -> u -> LocCoordPath u
rectangleCoordPath w h bl = [ bl, br, tr, tl ]
where
br = bl .+^ hvec w
tr = br .+^ vvec h
tl = bl .+^ vvec h

-- | 'diamondPath' : @ half_width * half_height * center_point -> PrimPath @
--
diamondCoordPath :: Num u => u -> u -> LocCoordPath u
diamondCoordPath hw hh ctr = [ s,e,n,w ]
where
s     = ctr .+^ vvec (-hh)
e     = ctr .+^ hvec hw
n     = ctr .+^ vvec hh
w     = ctr .+^ hvec (-hw)

-- | 'polygonCoordPath' : @ num_points * radius * center -> [point] @
--
polygonCoordPath :: Floating u => Int -> u -> LocCoordPath u
polygonCoordPath n radius ctr = unfoldr phi (0,(pi*0.5))
where
theta = (pi*2) / fromIntegral n

phi (i,ang) | i < n     = Just (ctr .+^ avec ang radius, (i+1,ang+theta))
| otherwise = Nothing

-- | @isocelesTriangle bw h pt@
--
-- Supplied point is the centriod of the triangle. This has a
-- nicer visual balance than using half-height.
--
isoscelesTriangleCoordPath :: Floating u => u -> u -> LocCoordPath u
isoscelesTriangleCoordPath bw h ctr = [bl,br,top]
where
(bl,br,top) = isoscelesTrianglePoints bw h ctr

-- | @isocelesTriangle bw h pt@
--
-- Supplied point is the centriod of the triangle. This has a
-- nicer visual balance than using half-height.
--
isoscelesTrianglePoints :: Floating u
=> u -> u -> Point2 u -> (Point2 u, Point2 u, Point2 u)
isoscelesTrianglePoints bw h ctr = (bl, br, top)
where
hw         = 0.5*bw
theta      = atan \$ h / hw
centroid_h = hw * tan (0.5*theta)
top        = ctr .+^ vvec (h - centroid_h)
br         = ctr .+^ V2   hw  (-centroid_h)
bl         = ctr .+^ V2 (-hw) (-centroid_h)

-- | @ side_length * ctr -> [Points] @
--
equilateralTriangleCoordPath :: Floating u => u -> LocCoordPath u
equilateralTriangleCoordPath sl ctr = [bl, br, top]
where
(bl,br,top) = equilateralTrianglePoints sl ctr

equilateralTrianglePoints :: Floating u
=> u -> Point2 u -> (Point2 u, Point2 u, Point2 u)
equilateralTrianglePoints sl = isoscelesTrianglePoints sl h
where
h = sl * sin (pi/3)

```