1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
|
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
-----------------------------------------------------------------------------
-- |
-- Module : Diagrams.TwoD.Types
-- Copyright : (c) 2011 diagrams-lib team (see LICENSE)
-- License : BSD-style (see LICENSE)
-- Maintainer : diagrams-discuss@googlegroups.com
--
-- Basic types for two-dimensional Euclidean space.
--
-----------------------------------------------------------------------------
module Diagrams.TwoD.Types
( -- * 2D Euclidean space
V2 (..), R1 (..), R2 (..)
, P2, T2
, r2, unr2, mkR2, r2Iso
, p2, mkP2, unp2, p2Iso
, r2PolarIso
, HasR (..)
) where
import Control.Lens (Iso', Lens', iso, _1, _2)
import Diagrams.Angle
import Diagrams.Points
import Diagrams.Core.Transform
import Diagrams.Core.V
import Linear.Metric
import Linear.V2
type P2 = Point V2
type T2 = Transformation V2
type instance V (V2 n) = V2
type instance N (V2 n) = n
-- | Construct a 2D vector from a pair of components. See also '&'.
r2 :: (n, n) -> V2 n
r2 = uncurry V2
-- | Convert a 2D vector back into a pair of components. See also 'coords'.
unr2 :: V2 n -> (n, n)
unr2 (V2 x y) = (x, y)
-- | Curried form of `r2`.
mkR2 :: n -> n -> V2 n
mkR2 = V2
r2Iso :: Iso' (V2 n) (n, n)
r2Iso = iso unr2 r2
-- | Construct a 2D point from a pair of coordinates. See also '^&'.
p2 :: (n, n) -> P2 n
p2 = P . uncurry V2
-- | Convert a 2D point back into a pair of coordinates. See also 'coords'.
unp2 :: P2 n -> (n,n)
unp2 (P (V2 x y)) = (x,y)
-- | Curried form of `p2`.
mkP2 :: n -> n -> P2 n
mkP2 x y = P (V2 x y)
p2Iso :: Iso' (Point V2 n) (n, n)
p2Iso = iso unp2 p2
instance Transformable (V2 n) where
transform = apply
r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n)
r2PolarIso = iso (\v@(V2 x y) -> (norm v, atan2A y x))
(\(r,θ) -> V2 (r * cosA θ) (r * sinA θ))
{-# INLINE r2PolarIso #-}
-- | A space which has magnitude '_r' that can be calculated numerically.
class HasR t where
_r :: RealFloat n => Lens' (t n) n
instance HasR v => HasR (Point v) where
_r = lensP . _r
{-# INLINE _r #-}
instance HasR V2 where
_r = r2PolarIso . _1
{-# INLINE _r #-}
instance HasTheta V2 where
_theta = r2PolarIso . _2
{-# INLINE _theta #-}
|
