{-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE TypeFamilies #-} {-# OPTIONS_GHC -fno-warn-incomplete-patterns #-} ----------------------------------------------------------------------------- -- | -- Module : Diagrams.CubicSpline -- Copyright : (c) 2011 diagrams-lib team (see LICENSE) -- License : BSD-style (see LICENSE) -- Maintainer : diagrams-discuss@googlegroups.com -- -- A /cubic spline/ is a smooth, connected sequence of cubic curves -- passing through a given sequence of points. This module provides -- the 'cubicSpline' method, which can be used to create closed or -- open cubic splines from a list of points. For access to the -- internals of the spline generation algorithm (including in -- particular a solver for cyclic tridiagonal systems of linear -- equations), see "Diagrams.CubicSpline.Internal". -- ----------------------------------------------------------------------------- module Diagrams.CubicSpline ( -- * Constructing paths from cubic splines cubicSpline ) where import Control.Lens (view) import Diagrams.Core import Diagrams.CubicSpline.Internal import Diagrams.Located (Located, at, mapLoc) import Diagrams.Segment import Diagrams.Trail import Diagrams.TrailLike (TrailLike (..)) import Linear.Affine import Linear.Metric -- | Construct a spline path-like thing of cubic segments from a list of -- vertices, with the first vertex as the starting point. The first -- argument specifies whether the path should be closed. -- -- <> -- -- > pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)] -- > spot = circle 0.2 # fc blue # lw none -- > mkPath closed = position (zip pts (repeat spot)) -- > <> cubicSpline closed pts -- > cubicSplineEx = (mkPath False ||| strutX 2 ||| mkPath True) -- > # centerXY # pad 1.1 -- -- For more information, see . cubicSpline :: (V t ~ v, N t ~ n, TrailLike t, Fractional (v n)) => Bool -> [Point v n] -> t cubicSpline closed [] = trailLike . closeIf closed \$ emptyLine `at` origin cubicSpline closed [p] = trailLike . closeIf closed \$ emptyLine `at` p cubicSpline closed ps = flattenBeziers . map f . solveCubicSplineCoefficients closed . map (view lensP) \$ ps where f [a,b,c,d] = [a, (3*a+b)/3, (3*a+2*b+c)/3, a+b+c+d] flattenBeziers bs@((b:_):_) = trailLike . closeIf closed \$ lineFromSegments (map bez bs) `at` P b bez [a,b,c,d] = bezier3 (b - a) (c - a) (d - a) closeIf :: (Metric v, OrderedField n) => Bool -> Located (Trail' Line v n) -> Located (Trail v n) closeIf c = mapLoc (if c then wrapLoop . glueLine else wrapLine)