[Lib2geom-devel] Curve/Path2 in Haskell

[MenTaLguY <me...@ry...>]

I've been thinking about Curve more since last night and I think Mike is correct that the Curve implementations and the various function types ought to be unified.  As usual, formulating the problem in Haskell has been helpful:

module Geom2.Curve (
  Curve (Curve), ICurve (..)
) where

import Control.Monad
import Data.Maybe
import Data.Typeable
import Data.Dynamic

import Geom2.D2
import Geom2.Point -- type Point = D2 Double
import Geom2.Rect  -- type Rect = D2 Range
import Geom2.Function

class ICurve c where
  initialPoint :: c -> Point
  finalPoint :: c -> Point
  fastBounds :: c -> Rect
  exactBounds :: c -> Rect
  winding :: Point -> c -> Maybe Int
  subdivide :: Double -> c -> (Curve, Curve)
  pointAt :: Double -> c -> Point
  pointAndDerivativesAt :: Double -> Int -> c -> [Point]
  toSBasis :: c -> D2 SBasis

data Curve = forall c. (ICurve c, Typeable c) => Curve c

fromCurve :: (ICurve c, Typeable c) => Curve -> c
fromCurve (Curve c) = fromDynamic $ toDyn c

instance ICurve Curve where
  initialPoint (Curve c) = initialPoint c
  finalPoint (Curve c) = finalPoint c
  fastBounds (Curve c) = fastBounds c
  exactBounds (Curve c) = exactBounds c
  winding p (Curve c) = winding p c
  subdivide t (Curve c) = subdivide t c
  pointAt t (Curve c) = pointAt t c
  pointAndDerivativesAt t n (Curve c) = pointAndDerivativesAt t n c
  toSBasis (Curve c) = toSBasis c

-- and then we should be able to define for all D2'ed functions...
instance (Function f) => ICurve (D2 f) where
  -- etc...

In C++, I don't know whether it would work best for e.g. D2<SBasis> to derive from Curve, or whether we keep SBasisCurve, which derives from Curve and D2<SBasis> both.