RefineSegs.hs

-- Implicit CAD. Copyright (C) 2011, Christopher Olah (chris@colah.ca)
-- Released under the GNU GPL, see LICENSE

module Graphics.Implicit.Export.Render.RefineSegs where

import Graphics.Implicit.Definitions
import qualified Graphics.Implicit.SaneOperators as S
import Graphics.Implicit.SaneOperators ((⋅), (⨯), norm, normalized)

refine :: ℝ -> Obj2 -> [ℝ2] -> [ℝ2]
refine res obj = simplify res . detail' res obj


detail' res obj [p1@(x1,y1), p2@(x2,y2)] | (x2-x1)^2 + (y2-y1)^2 > res^2/200 = 
		detail 0 res obj [p1,p2]
detail' _ _ a = a

detail :: Int -> ℝ -> (ℝ2 -> ℝ) -> [ℝ2] -> [ℝ2]
detail n res obj [p1@(x1,y1), p2@(x2,y2)] | n < 2 =
	let
		mid@(midX, midY) = (p1 S.+ p2) S./ (2 :: ℝ)
		midval = obj mid 
	in if abs midval < res / 40
	then [(x1,y1), (x2,y2)]
	else let
		normal = (\(a,b) -> (b, -a)) $ normalized (p2 S.- p1) 
		derivN = -(obj (mid S.- (normal S.* (midval/2))) - midval) S.* (2/midval)
	in if abs derivN > 0.5 && abs derivN < 2
	then let
		mid' = mid S.- (normal S.* (midval / derivN))
	in detail (n+1) res obj [(x1,y1), mid'] 
	   ++ tail (detail (n+1) res obj [mid', (x2,y2)] )
	else let
		derivX = (obj (midX + res/100, midY) - midval)*100/res
		derivY = (obj (midX, midY + res/100) - midval)*100/res
		derivNormSq = derivX^2+derivY^2
	in if abs derivNormSq > 0.09 && abs derivNormSq < 4
	then let
		(dX, dY) = (- derivX*midval/derivNormSq, - derivY*midval/derivNormSq)
		mid'@(midX', midY') = 
			(midX + dX, midY + dY)
		midval' = obj mid'
		posRatio = midval/(midval - midval')
		mid''@(midX'', midY'') = (midX + dX*posRatio, midY + dY*posRatio)
	in 
		detail (n+1) res obj [(x1,y1), mid''] ++ tail (detail (n+1) res obj [mid'', (x2,y2)] )
	else [(x1,y1), (x2,y2)]


detail _ _ _ x = x

simplify res = {-simplify3 . simplify2 res . -} simplify1

simplify1 :: [ℝ2] -> [ℝ2]
simplify1 (a:b:c:xs) =
	if abs ( ((b S.- a) ⋅ (c S.- a)) - norm (b S.- a) * norm (c S.- a) ) < 0.0001
	then simplify1 (a:c:xs)
	else a : simplify1 (b:c:xs)
simplify1 a = a

{-
simplify2 :: ℝ -> [ℝ2] -> [ℝ2]
simplify2 res [a,b,c,d] = 
	if norm (b S.- c) < res/10
	then [a, ((b S.+ c) S./ (2::ℝ)), d]
	else [a,b,c,d]
simplify2 _ a = a

simplify3 (a:as) | length as > 5 = simplify3 $ a : half (init as) ++ [last as]
	where
		half (a:b:xs) = a : half xs
		half a = a
simplify3 a = a

-}