hcg-minus 0.12 → 0.14
raw patch · 7 files changed
+685/−624 lines, 7 filesdep −SG
Dependencies removed: SG
Files
- Data/CG/Minus.hs +508/−449
- Data/CG/Minus/Arrow.hs +2/−2
- Data/CG/Minus/Bearing.hs +2/−2
- Data/CG/Minus/Colour.hs +166/−163
- Data/CG/Minus/Colour/Planck.hs +3/−4
- README +1/−1
- hcg-minus.cabal +3/−3
Data/CG/Minus.hs view
@@ -1,37 +1,67 @@ -- | CG library (minus). module Data.CG.Minus where -import Control.Applicative-import Data.Complex-import Data.Maybe-import qualified Data.SG as G {- SG -}-import Text.Printf+import Data.Complex {- base -}+import Data.Maybe {- base -}+import Text.Printf {- base -} -- * Types -- | Two-dimensional point.-type Pt = G.Point2'--- type Pt a = Pt {pt_x :: a, pt_y :: a}+--+-- Pt are 'Num', pointwise, ie:+--+-- > Pt 1 2 + Pt 3 4 == Pt 4 6+-- > Pt 1 2 * Pt 3 4 == Pt 3 8+-- > negate (Pt 0 1) == Pt 0 (-1)+-- > abs (Pt (-1) 1) == Pt 1 1+-- > signum (Pt (-1/2) (1/2)) == Pt (-1) 1+data Pt a = Pt {pt_x :: a,pt_y :: a} deriving (Eq,Ord,Show) --- | Two-dimensional vector.-type Vc = G.Rel2'--- type Vc a = Vc {vc_x :: a, vc_y :: a}+instance Num a => Num (Pt a) where+ (+) = pt_binop (+)+ (-) = pt_binop (-)+ (*) = pt_binop (*)+ negate = pt_uop negate+ abs = pt_uop abs+ signum = pt_uop signum+ fromInteger n = let n' = fromInteger n in Pt n' n' +-- | Two-dimensional vector. Vector are 'Num' in the same manner as+-- 'Pt'.+data Vc a = Vc {vc_x :: a,vc_y :: a} deriving (Eq,Ord,Show)++instance Num a => Num (Vc a) where+ (+) = vc_binop (+)+ (-) = vc_binop (-)+ (*) = vc_binop (*)+ negate = vc_uop negate+ abs = vc_uop abs+ signum = vc_uop signum+ fromInteger n = let n' = fromInteger n in Vc n' n'+ -- | Two-dimensional line.-type Ln = G.Line2'--- type Ln a = Ln (Pt a) (Pt a)+data Ln a = Ln {ln_start :: Pt a,ln_end :: Pt a} deriving (Eq,Ord,Show) -- | Line segments. type Ls a = [Pt a] -- | Window, given by a /lower left/ 'Pt' and an /extent/ 'Vc'.-type Wn a = (Pt a,Vc a)+data Wn a = Wn {wn_ll :: Pt a,wn_ex :: Vc a} deriving (Eq,Show) -- | Real number, synonym for 'Double'. type R = Double -- * R(eal) functions +-- | Epsilon.+epsilon :: Floating n => n+epsilon = 0.000001++-- | Is absolute difference less than 'epsilon'.+(~=) :: (Floating a, Ord a) => a -> a -> Bool+p ~= q = abs (p - q) < epsilon+ -- | Degrees to radians. -- -- > map r_to_radians [-180,-90,0,90,180] == [-pi,-pi/2,0,pi/2,pi]@@ -54,190 +84,118 @@ both n i j x = up n i (down n j x) in both (r - l) l r --- * Pt functions---- | 'Pt' constructor.------ > pt_xy (pt 0 pi) == (0,pi)-pt :: a -> a -> Pt a-pt = curry G.Point2--- pt = Pt+-- | Sum of squares.+mag_sq :: Num a => a -> a -> a+mag_sq x y = x * x + y * y --- | Variant 'Pt' constructor, ie. 'uncurry' 'pt'.------ > pt_xy (pt' (0,pi)) == (0,pi)-pt' :: (a,a) -> Pt a-pt' = G.Point2---pt' = uncurry pt+-- | 'sqrt' of 'mag_sq'.+mag :: Floating c => c -> c -> c+mag x = sqrt . mag_sq x --- | /x/ field of 'Pt'.------ > pt_x (pt 0 pi) == 0-pt_x :: Pt t -> t-pt_x = G.getX+-- * Pt functions --- | /y/ field of 'Pt'.------ > pt_y (pt 0 pi) == pi-pt_y :: Pt t -> t-pt_y = G.getY+-- | Tuple constructor.+pt' :: (a,a) -> Pt a+pt' (x,y) = Pt x y --- | /x/ and /y/ fields of 'Pt'.------ > pt_xy (pt 0 pi) == (0,pi)-pt_xy :: Pt a -> (a,a)-pt_xy p = (pt_x p,pt_y p)+-- | Tuple accessor.+pt_xy :: Pt t -> (t, t)+pt_xy (Pt x y) = (x,y) -- | 'Pt' of (0,0). ----- > pt_origin == pt 0 0+-- > pt_origin == Pt 0 0 pt_origin :: Num a => Pt a-pt_origin = pt 0 0---- | Binary operator at 'Pt'. Given the 'Applicative' instance for--- 'Pt' this is a synonym for 'liftA2'.------ > pt_binary_op (+) (pt 1 1) (pt 2 2) == pt 3 3-pt_binary_op_ :: (a -> b -> c) -> Pt a -> Pt b -> Pt c-pt_binary_op_ f p1 p2 = pt (pt_x p1 `f` pt_x p2) (pt_y p1 `f` pt_y p2)---- | Variant applicative definition as 'liftA2'-pt_binary_op :: (a -> b -> c) -> Pt a -> Pt b -> Pt c-pt_binary_op = liftA2---- | Pointwise '+'.------ > pt_add (pt 1 2) (pt 3 4) == pt 4 6-pt_add :: (Num a) => Pt a -> Pt a -> Pt a-pt_add = pt_binary_op (+)---- | Pointwise '+' (applicative definition).------ > pt_add_ (pt 1 2) (pt 3 4) == pt 4 6--- > (liftA2 (+)) (pt 1 2) (pt 3 4) == pt 4 6--- > (pure (+) <*> pt 1 2 <*> pt 3 4) == pt 4 6-pt_add_ :: (Num a) => Pt a -> Pt a -> Pt a-pt_add_ = pt_binary_op_ (+)---- | Pointwise '-'.-pt_sub :: (Num a) => Pt a -> Pt a -> Pt a-pt_sub = pt_binary_op (-)---- | Pointwise '*'.-pt_mul :: (Num a) => Pt a -> Pt a -> Pt a-pt_mul = pt_binary_op (*)---- | Unary operator at 'Pt'. Given 'Applicative' instance for 'Pt'--- this is a synonym for 'liftA'.------ > pt_unary_op negate (pt 0 1) == pt 0 (-1)--- > pt_unary_op_ negate (pt 0 1) == pt 0 (-1)--- > (liftA negate) (pt 0 1) == pt 0 (-1)--- > (pure negate <*> pt 0 1) == pt 0 (-1)-pt_unary_op_ :: (a -> b) -> Pt a -> Pt b-pt_unary_op_ f p = pt (f (pt_x p)) (f (pt_y p))---- | Variant applicative definition as 'liftA'.-pt_unary_op :: (a -> b) -> Pt a -> Pt b-pt_unary_op = liftA---- | Pointwise 'negate'.------ > pt_negate (pt 0 1) == pt 0 (-1)-pt_negate :: (Num a) => Pt a -> Pt a-pt_negate = pt_unary_op negate+pt_origin = Pt 0 0 --- | Pointwise 'abs'.------ > pt_abs (pt (-1) 1) == pt 1 1-pt_abs :: (Num a) => Pt a -> Pt a-pt_abs = pt_unary_op abs+-- | Unary operator at 'Pt', ie. basis for 'Num' instances.+pt_uop :: (a -> b) -> Pt a -> Pt b+pt_uop f (Pt x y) = Pt (f x) (f y) --- | Pointwise 'signum'.------ > pt_signum (pt (-1/2) (1/2)) == pt (-1) 1-pt_signum :: (Num a) => Pt a -> Pt a-pt_signum = pt_unary_op signum+-- | Binary operator at 'Pt', ie. basis for 'Num' instances.+pt_binop :: (a -> b -> c) -> Pt a -> Pt b -> Pt c+pt_binop f (Pt x1 y1) (Pt x2 y2) = Pt (x1 `f` x2) (y1 `f` y2) -- | 'Pt' at /(n,n)/. ----- > pt_from_scalar 1 == pt 1 1+-- > pt_from_scalar 1 == Pt 1 1 pt_from_scalar :: (Num a) => a -> Pt a-pt_from_scalar a = pt a a+pt_from_scalar a = Pt a a -- | Clip /x/ and /y/ to lie in /(0,n)/. ----- > pt_clipu 1 (pt 0.5 1.5) == pt 0.5 1+-- > pt_clipu 1 (Pt 0.5 1.5) == Pt 0.5 1 pt_clipu :: (Ord a,Num a) => a -> Pt a -> Pt a pt_clipu u = let f n = if n < 0 then 0 else if n > u then u else n- in pt_unary_op f+ in pt_uop f -- | Swap /x/ and /y/ coordinates at 'Pt'. ----- > pt_swap (pt 1 2) == pt 2 1+-- > pt_swap (Pt 1 2) == Pt 2 1 pt_swap :: Pt a -> Pt a-pt_swap p = pt (pt_y p) (pt_x p)+pt_swap (Pt x y) = Pt y x -- | Negate /y/ element of 'Pt'. ----- > pt_negate_y (pt 1 1) == pt 1 (-1)+-- > pt_negate_y (Pt 1 1) == Pt 1 (-1) pt_negate_y :: (Num a) => Pt a -> Pt a-pt_negate_y p = pt (pt_x p) (negate (pt_y p))+pt_negate_y (Pt x y) = Pt x (negate y) -- | 'Pt' variant of 'r_to_radians'. ----- > pt_to_radians (pt 90 270) == pt (pi/2) (pi*(3/2))+-- > pt_to_radians (Pt 90 270) == Pt (pi/2) (pi*(3/2)) pt_to_radians :: Pt R -> Pt R-pt_to_radians = pt_unary_op r_to_radians+pt_to_radians = pt_uop r_to_radians -- | Cartesian to polar. ----- > pt_to_polar (pt 0 pi) == pt pi (pi/2)+-- > pt_to_polar (Pt 0 pi) == Pt pi (pi/2) pt_to_polar :: Pt R -> Pt R-pt_to_polar p = pt' (polar (pt_x p :+ pt_y p))+pt_to_polar (Pt x y) =+ let (x',y') = polar (x :+ y)+ in Pt x' y' -- | Polar to cartesian, inverse of 'pt_to_polar'. ----- > pt_from_polar (pt pi (pi/2)) ~= pt 0 pi+-- > pt_from_polar (Pt pi (pi/2)) ~= Pt 0 pi pt_from_polar :: Pt R -> Pt R-pt_from_polar p =- let (mg,ph) = pt_xy p- c = mkPolar mg ph- x = realPart c- y = imagPart c- in pt x y+pt_from_polar (Pt mg ph) =+ let c = mkPolar mg ph+ in Pt (realPart c) (imagPart c) -- | Scalar 'Pt' '+'. ----- > pt_offset 1 pt_origin == pt 1 1+-- > pt_offset 1 pt_origin == Pt 1 1 pt_offset :: Num a => a -> Pt a -> Pt a-pt_offset = pt_unary_op . (+)+pt_offset = pt_uop . (+) +-- | Scalar 'Pt' '*'.+--+-- > pt_scale 2 (Pt 1 2) == Pt 2 4+pt_scale :: Num a => a -> Pt a -> Pt a+pt_scale = pt_uop . (*)+ -- | Pointwise 'min'. pt_min :: (Ord a) => Pt a -> Pt a -> Pt a-pt_min = pt_binary_op min+pt_min = pt_binop min -- | Pointwise 'max'. pt_max :: (Ord a) => Pt a -> Pt a -> Pt a-pt_max = pt_binary_op max+pt_max = pt_binop max -- | Apply function to /x/ and /y/ fields of three 'Pt'. pt_ternary_f :: (a->a->b->b->c->c->d) -> Pt a -> Pt b -> Pt c -> d-pt_ternary_f f p0 p1 p2 =- let (x0,y0) = pt_xy p0- (x1,y1) = pt_xy p1- (x2,y2) = pt_xy p2- in f x0 y0 x1 y1 x2 y2+pt_ternary_f f (Pt x0 y0) (Pt x1 y1) (Pt x2 y2) = f x0 y0 x1 y1 x2 y2 -- | Given a /(minima,maxima)/ pair, expand so as to include /p/. ----- > pt_minmax (pt 0 0,pt 1 1) (pt (-1) 2) == (pt (-1) 0,pt 1 2)+-- > pt_minmax (Pt 0 0,Pt 1 1) (Pt (-1) 2) == (Pt (-1) 0,Pt 1 2) pt_minmax :: Ord a => (Pt a,Pt a) -> Pt a -> (Pt a,Pt a) pt_minmax (p0,p1) p = let f x0 y0 x1 y1 x y =- (pt (min x x0) (min y y0)- ,pt (max x x1) (max y y1))+ (Pt (min x x0) (min y y0)+ ,Pt (max x x1) (max y y1)) in pt_ternary_f f p0 p1 p -- | 'Pt' variant of 'constrain'.@@ -246,172 +204,137 @@ let f x0 y0 x1 y1 x y = let x' = r_constrain (x0,x1) x y' = r_constrain (y0,y1) y- in pt x' y'+ in Pt x' y' in pt_ternary_f f p0 p1 p -- | Angle to origin. ----- > pt_angle_o (pt 0 1) == pi / 2+-- > pt_angle_o (Pt 0 1) == pi / 2 pt_angle_o :: Pt R -> R-pt_angle_o p = atan2 (pt_y p) (pt_x p)+pt_angle_o (Pt x y) = atan2 y x -- | Angle from /p/ to /q/. ----- > pt_angle (pt 0 (-1)) (pt 0 1) == pi/2--- > pt_angle (pt 1 0) (pt 0 1) == pi * 3/4--- > pt_angle (pt 0 1) (pt 0 1) == 0+-- > pt_angle (Pt 0 (-1)) (Pt 0 1) == pi/2+-- > pt_angle (Pt 1 0) (Pt 0 1) == pi * 3/4+-- > pt_angle (Pt 0 1) (Pt 0 1) == 0 pt_angle :: Pt R -> Pt R -> R-pt_angle p q = pt_angle_o (q `pt_sub` p)+pt_angle p q = pt_angle_o (q - p) -- | Pointwise '+'.+--+-- pt_translate (Pt 0 0) (vc 1 1) == pt 1 1 pt_translate :: (Num a,Eq a) => Pt a -> Vc a -> Pt a-pt_translate = G.plusDir--- pt_translate p v = pt (pt_x p + vc_x v) (pt_y p + vc_y v)--- pt_translate (Pt x y) (Vc dx dy) = Pt (x + dx) (y + dy)---- | Alternate implementation of 'pt_translate'.-pt_translate_ :: Num a => Pt a -> Vc a -> Pt a-pt_translate_ p v =- let (dx,dy) = vc_xy v- (x,y) = pt_xy p- in pt (x+dx) (y+dy)+pt_translate (Pt x y) (Vc dx dy) = Pt (x + dx) (y + dy) --- | 'pt_unary_op' 'fromIntegral'.+-- | 'pt_uop' 'fromIntegral'. pt_from_i :: (Integral i,Num a) => Pt i -> Pt a-pt_from_i = pt_unary_op fromIntegral+pt_from_i = pt_uop fromIntegral +-- | 'mag_sq' of /x/ /y/ of 'Pt'.+pt_mag_sq :: Num a => Pt a -> a+pt_mag_sq (Pt x y) = mag_sq x y++-- | 'mag' of /x/ /y/ of 'Pt'.+pt_mag :: Floating a => Pt a -> a+pt_mag (Pt x y) = mag x y+ -- | Distance from 'Pt' /p/ to 'Pt' /q/. ----- > pt_distance (pt 0 0) (pt 0 1) == 1--- > pt_distance (pt 0 0) (pt 1 1) == sqrt 2+-- > pt_distance (Pt 0 0) (Pt 0 1) == 1+-- > pt_distance (Pt 0 0) (Pt 1 1) == sqrt 2 pt_distance :: (Floating a,Eq a) => Pt a -> Pt a -> a-pt_distance = G.distFrom+pt_distance (Pt x1 y1) (Pt x2 y2) = pt_mag (Pt (x2 - x1) (y2 - y1)) -- | Are /x/ and /y/ of 'Pt' /p/ in range (0,1). ----- > map pt_is_normal [pt 0 0,pt 1 1,pt 2 2] == [True,True,False]+-- > map pt_is_normal [Pt 0 0,Pt 1 1,Pt 2 2] == [True,True,False] pt_is_normal :: (Ord a,Num a) => Pt a -> Bool-pt_is_normal p =- let (x,y) = pt_xy p- in x >= 0 && x <= 1 && y >= 0 && y <= 1+pt_is_normal (Pt x y) = x >= 0 && x <= 1 && y >= 0 && y <= 1 -- | Rotate 'Pt' /n/ radians. ----- > pt_rotate pi (pt 1 0) ~= pt (-1) 0+-- > pt_rotate pi (Pt 1 0) ~= Pt (-1) 0 pt_rotate :: Floating a => a -> Pt a -> Pt a-pt_rotate a p =- let (x,y) = pt_xy p- s = sin a+pt_rotate a (Pt x y) =+ let s = sin a c = cos a- in pt (x * c - y * s) (y * c + x * s)+ in Pt (x * c - y * s) (y * c + x * s) -- * Vc functions --- | Construct 'Vc'.-vc :: Num a => a -> a -> Vc a-vc = curry G.makeRel2--- vc = Vc---- | Alernate constructor for 'Vc'.------ > (vc 0 0 == vc' (0,0)) == True-vc' :: Num a => (a,a) -> Vc a-vc' = G.makeRel2--- vc' = uncurry vc+-- | Unary operator at 'Vc', ie. basis for 'Num' instances.+vc_uop :: (a -> b) -> Vc a -> Vc b+vc_uop f (Vc x y) = Vc (f x) (f y) --- | 'Vc' /x/ field.-vc_x :: Vc t -> t-vc_x = G.getX+-- | Binary operator at 'Vc', ie. basis for 'Num' instances.+vc_binop :: (a -> b -> c) -> Vc a -> Vc b -> Vc c+vc_binop f (Vc x1 y1) (Vc x2 y2) = Vc (x1 `f` x2) (y1 `f` y2) --- | 'Vc' /y/ field.-vc_y :: Vc t -> t-vc_y = G.getY+-- | 'mag_sq' of 'Vc'.+vc_mag_sq :: Floating c => Vc c -> c+vc_mag_sq (Vc dx dy) = mag_sq dx dy --- | 'Vc' /x/ and /y/ fields.-vc_xy :: Vc a -> (a,a)-vc_xy v = (vc_x v,vc_y v)+-- | 'mag' of 'Vc'.+vc_mag :: Floating c => Vc c -> c+vc_mag (Vc dx dy) = mag dx dy -- | Multiply 'Vc' pointwise by scalar. ----- > vc_scale 2 (vc 3 4) == vc 6 8+-- > vc_scale 2 (Vc 3 4) == Vc 6 8 vc_scale :: Num a => a -> Vc a -> Vc a-vc_scale = G.scaleRel--- vc_scale n v = vc (vc_x v * n) (vc_y v * n)+vc_scale n (Vc x y) = Vc (x * n) (y * n) -- | 'Vc' dot product. ----- > vc_dot (vc 1 2) (vc 3 4) == 11+-- > vc_dot (Vc 1 2) (Vc 3 4) == 11 vc_dot :: Num a => Vc a -> Vc a -> a-vc_dot = G.dotProduct--- vc_dot p q = (vc_x p * vc_x q) + (vc_y p * vc_y q)+vc_dot (Vc x y) (Vc x' y') = (x * x') + (y * y') -- | Scale 'Vc' to have unit magnitude (to within tolerance). ----- > vc_unit (vc 1 1) ~= let x = (sqrt 2) / 2 in vc x x+-- > vc_unit (Vc 1 1) ~= let x = (sqrt 2) / 2 in Vc x x vc_unit :: (Ord a, Floating a) => Vc a -> Vc a-vc_unit = G.unitVector+vc_unit v+ | abs (vc_mag_sq v - 1) < epsilon = v+ | vc_mag_sq v == 0 = v+ | otherwise = let Vc x y = v+ m = mag x y+ in Vc (x / m) (y / m) -- | The angle between two vectors on a plane. The angle is from v1 to -- v2, positive anticlockwise. The result is in (-pi,pi) vc_angle :: Vc R -> Vc R -> R-vc_angle v1 v2 =- let (x1,y1) = vc_xy v1- (x2,y2) = vc_xy v2- t1 = atan2 y1 x1+vc_angle (Vc x1 y1) (Vc x2 y2) =+ let t1 = atan2 y1 x1 t2 = atan2 y2 x2 in r_constrain (-pi,pi) (t2 - t1) -- * Line functions --- | 'Ln' constructor.------ > ln_start (ln (pt 0 0) (pt 1 1)) == pt 0 0-ln :: (Num a,Eq a) => Pt a -> Pt a -> Ln a-ln = G.lineTo---- | Variant constructor.------ > ln_start (ln_ (pt 1 1) (pt 0 0)) == pt 1 1-ln_ :: (Num a,Eq a) => Pt a -> Pt a -> Ln a-ln_ p q = G.Line2 p (G.fromPt q p)---- | Variant on 'ln' which takes 'Pt' co-ordinates as duples.+-- | Variant on 'Ln' which takes 'Pt' co-ordinates as duples. ----- > ln' (0,0) (1,1) == ln (pt 0 0) (pt 1 1)+-- > ln' (0,0) (1,1) == Ln (Pt 0 0) (Pt 1 1)+-- > ln_start (Ln (Pt 0 0) (Pt 1 1)) == Pt 0 0+-- > ln_end (Ln (Pt 0 0) (Pt 1 1)) == Pt 1 1 ln' :: (Num a,Eq a) => (a,a) -> (a,a) -> Ln a-ln' (x1,y1) (x2,y2) = ln (pt x1 y1) (pt x2 y2)---- | Initial 'Pt' of 'Ln'.------ > ln_start (ln (pt 0 0) (pt 1 1)) == pt 0 0-ln_start :: (Num a,Eq a) => Ln a -> Pt a-ln_start = G.getLineStart---- | Alternate implementation of 'ln_start' (without 'Num' constraint).-ln_start_ :: Ln a -> Pt a-ln_start_ (G.Line2 p _) = p---- | End 'Pt' of 'Ln'.------ > ln_end (ln (pt 0 0) (pt 1 1)) == pt 1 1-ln_end :: (Num a,Eq a) => Ln a -> Pt a-ln_end = G.getLineEnd---- | Alternate implementation of 'ln_end'.-ln_end_ :: (Num a,Eq a) => Ln a -> Pt a-ln_end_ (G.Line2 p v) = p `pt_translate` v+ln' (x1,y1) (x2,y2) = Ln (Pt x1 y1) (Pt x2 y2) -- | 'Vc' that 'pt_translate's start 'Pt' to end 'Pt' of 'Ln'. ----- > let l = ln (pt 0 0) (pt 1 1)--- > in ln_start l `pt_translate` ln_vc l == pt 1 1+-- > let l = Ln (Pt 0 0) (Pt 1 1)+-- > in ln_start l `pt_translate` ln_vc l == Pt 1 1 ln_vc :: (Num a,Eq a) => Ln a -> Vc a-ln_vc = G.getLineDir+ln_vc (Ln p q) = let Pt x y = q - p in Vc x y --- | Alternate implementation of 'ln_vc', without 'Num' constraint.-ln_vc_ :: Ln a -> Vc a-ln_vc_ (G.Line2 _ v) = v+-- | 'Pt' UOp at 'Ln'.+ln_uop :: (Pt a -> Pt b) -> Ln a -> Ln b+ln_uop f (Ln l r) = Ln (f l) (f r) +-- | 'pt_scale' at 'Ln'.+ln_scale :: Num b => b -> Ln b -> Ln b+ln_scale m = ln_uop (pt_scale m)+ -- | The angle, in /radians/, anti-clockwise from the /x/-axis. -- -- > ln_angle (ln' (0,0) (0,0)) == 0@@ -419,151 +342,149 @@ -- > ln_angle (ln' (0,0) (0,1)) == pi/2 -- > ln_angle (ln' (0,0) (-1,1)) == pi * 3/4 ln_angle :: Ln R -> R-ln_angle = G.toAngle . ln_vc+ln_angle ln =+ let Vc dx dy = ln_vc ln+ in if dx == 0 && dy == 0 then 0 else atan2 dy dx -- | Start and end points of 'Ln'. ----- > ln_pt (ln (pt 1 0) (pt 0 0)) == (pt 1 0,pt 0 0)-ln_pt :: (Num a,Eq a) => Ln a -> (Pt a, Pt a)-ln_pt l = (ln_start l,ln_end l)+-- > ln_pt (Ln (Pt 1 0) (Pt 0 0)) == (Pt 1 0,Pt 0 0)+ln_pt :: (Num a,Eq a) => Ln a -> (Pt a,Pt a)+ln_pt (Ln s e) = (s,e) -- | Variant of 'ln_pt' giving co-ordinates as duples. ----- > ln_pt' (ln (pt 1 0) (pt 0 0)) == ((1,0),(0,0))+-- > ln_pt' (Ln (Pt 1 0) (Pt 0 0)) == ((1,0),(0,0)) ln_pt' :: (Num a,Eq a) => Ln a -> ((a,a),(a,a))-ln_pt' l =- let (p1,p2) = ln_pt l- in (pt_xy p1,pt_xy p2)+ln_pt' (Ln (Pt x1 y1) (Pt x2 y2)) = ((x1,y1),(x2,y2)) -- | Midpoint of a 'Ln'. ----- > ln_midpoint (ln (pt 0 0) (pt 2 1)) == pt 1 (1/2)+-- > ln_midpoint (Ln (Pt 0 0) (Pt 2 1)) == Pt 1 (1/2) ln_midpoint :: (Fractional a,Eq a) => Ln a -> Pt a-ln_midpoint l =- let (p1,p2) = ln_pt l- x = (pt_x p1 + pt_x p2) / 2- y = (pt_y p1 + pt_y p2) / 2- in pt x y+ln_midpoint (Ln (Pt x1 y1) (Pt x2 y2)) =+ let x = (x1 + x2) / 2+ y = (y1 + y2) / 2+ in Pt x y -- | Variant on 'ln_midpoint'. ----- > cc_midpoint (Just (pt 0 0),Nothing) == pt 0 0--- > cc_midpoint (Nothing,Just (pt 2 1)) == pt 2 1--- > cc_midpoint (Just (pt 0 0),Just (pt 2 1)) == pt 1 (1/2)+-- > cc_midpoint (Just (Pt 0 0),Nothing) == Pt 0 0+-- > cc_midpoint (Nothing,Just (Pt 2 1)) == Pt 2 1+-- > cc_midpoint (Just (Pt 0 0),Just (Pt 2 1)) == Pt 1 (1/2) cc_midpoint :: (Maybe (Pt R), Maybe (Pt R)) -> Pt R cc_midpoint cc = case cc of- (Nothing,Nothing) -> pt 0 0+ (Nothing,Nothing) -> Pt 0 0 (Just p,Nothing) -> p (Nothing, Just q) -> q- (Just p, Just q) -> ln_midpoint (ln p q)+ (Just p, Just q) -> ln_midpoint (Ln p q) -- | Magnitude of 'Ln', ie. length of line. ----- > ln_magnitude (ln (pt 0 0) (pt 1 1)) == sqrt 2--- > pt_x (pt_to_polar (pt 1 1)) == sqrt 2+-- > ln_magnitude (Ln (Pt 0 0) (Pt 1 1)) == sqrt 2+-- > pt_x (pt_to_polar (Pt 1 1)) == sqrt 2 ln_magnitude :: Ln R -> R-ln_magnitude = G.mag . ln_vc---- | Variant definition of 'ln_magnitude'.-ln_magnitude_ :: Ln R -> R-ln_magnitude_ l =- let ((x1,y1),(x2,y2)) = ln_pt' l- x = x2 - x1- y = y2 - y1- in sqrt (x * x + y * y)+ln_magnitude = vc_mag . ln_vc -- | Order 'Pt' at 'Ln' so that /p/ is to the left of /q/. If /x/ -- fields are equal, sort on /y/. ----- > ln_sort (ln (pt 1 0) (pt 0 0)) == ln (pt 0 0) (pt 1 0)--- > ln_sort (ln (pt 0 1) (pt 0 0)) == ln (pt 0 0) (pt 0 1)+-- > ln_sort (Ln (Pt 1 0) (Pt 0 0)) == Ln (Pt 0 0) (Pt 1 0)+-- > ln_sort (Ln (Pt 0 1) (Pt 0 0)) == Ln (Pt 0 0) (Pt 0 1) ln_sort :: (Num a,Ord a) => Ln a -> Ln a-ln_sort l =- let (p,q) = ln_pt l- in case compare (pt_x p) (pt_x q) of- LT -> l- EQ -> if pt_y p <= pt_y q then l else ln q p- GT -> ln q p+ln_sort ln =+ let Ln p q = ln+ Pt x1 y1 = p+ Pt x2 y2 = q+ in case compare x1 x2 of+ LT -> ln+ EQ -> if y1 <= y2 then ln else Ln q p+ GT -> Ln q p -- | Adjust 'Ln' to have equal starting 'Pt' but magnitude 'R'. ----- > ln_adjust (sqrt 2) (ln (pt 0 0) (pt 2 2)) == ln (pt 0 0) (pt 1 1)+-- > ln_adjust (sqrt 2) (Ln (Pt 0 0) (Pt 2 2)) == Ln (Pt 0 0) (Pt 1 1) ln_adjust :: (Floating a, Ord a) => a -> Ln a -> Ln a-ln_adjust = G.makeLength+ln_adjust z ln =+ let Ln p _ = ln+ v = vc_scale z (vc_unit (ln_vc ln))+ in Ln p (pt_translate p v) -- | Extend 'Ln' by 'R', ie. 'ln_adjust' with /n/ added to -- 'ln_magnitude'. ----- > ln_extend (sqrt 2) (ln (pt 0 0) (pt 1 1)) ~= ln (pt 0 0) (pt 2 2)+-- > ln_extend (sqrt 2) (Ln (Pt 0 0) (Pt 1 1)) ~= Ln (Pt 0 0) (Pt 2 2) ln_extend :: R -> Ln R -> Ln R-ln_extend n l = ln (ln_start l) (pt_linear_extension n l)+ln_extend n l = Ln (ln_start l) (pt_linear_extension n l) -- | Variant definition of 'ln_extend'. ----- > ln_extend_ (sqrt 2) (ln (pt 0 0) (pt 1 1)) == ln (pt 0 0) (pt 2 2)+-- > ln_extend_ (sqrt 2) (Ln (Pt 0 0) (Pt 1 1)) == Ln (Pt 0 0) (Pt 2 2) ln_extend_ :: R -> Ln R -> Ln R ln_extend_ n l = ln_adjust (n + ln_magnitude l) l +-- | Calculate the point that extends a line by length 'n'.+--+-- > pt_linear_extension (sqrt 2) (Ln (Pt 1 1) (Pt 2 2)) ~= Pt 3 3+-- > pt_linear_extension 1 (Ln (Pt 1 1) (Pt 1 2)) ~= Pt 1 3+pt_linear_extension :: R -> Ln R -> Pt R+pt_linear_extension n (Ln p q) =+ let Pt mg ph = pt_to_polar (q - p)+ in pt_from_polar (Pt (mg + n) ph) + p+ -- | Does 'Pt' /p/ lie on 'Ln' (inclusive). ----- > let f = pt_on_line (ln (pt 0 0) (pt 1 1))--- > in map f [pt 0.5 0.5,pt 2 2,pt (-1) (-1),pt 0 0] == [True,False,False,True]+-- > let {f = pt_on_line (Ln (Pt 0 0) (Pt 1 1))+-- > ;r = [True,False,False,True]}+-- > in map f [Pt 0.5 0.5,Pt 2 2,Pt (-1) (-1),Pt 0 0] == r pt_on_line :: Ln R -> Pt R -> Bool pt_on_line l r = let (p,q) = ln_pt l- (i,j) = pt_xy (pt_to_polar (q `pt_sub` p))- (i',j') = pt_xy (pt_to_polar (r `pt_sub` p))+ Pt i j = pt_to_polar (q - p)+ Pt i' j' = pt_to_polar (r - p) in r == p || r == q || (j == j' && i' <= i) --- | Variant definition of 'pt_on_line', exclusive of starting point.------ > let f = pt_on_line_ (ln (pt 0 0) (pt 1 1))--- > in map f [pt 0.5 0.5,pt 2 2,pt (-1) (-1),pt 0 0] == [True,False,False,False]-pt_on_line_ :: Ln R -> Pt R -> Bool-pt_on_line_ l p =- case G.distAlongLine p l of- Nothing -> False- Just d -> d >= 0 && d <= 1---- | Calculate the point that extends a line by length 'n'.------ > pt_linear_extension (sqrt 2) (ln (pt 0 0) (pt 1 1)) ~= pt 2 2-pt_linear_extension :: R -> Ln R -> Pt R-pt_linear_extension n l =- let (p0,p1) = ln_pt l- (mg,ph) = pt_xy (pt_to_polar (p1 `pt_sub` p0))- in pt_from_polar (pt (mg+n) ph) `pt_add` p0- -- * Intersection --- | Given /left/ and /right/, is /x/ in range (inclusive).------ > map (in_range 0 1) [-1,0,1,2] == [False,True,True,False]-in_range :: Ord a => a -> a -> a -> Bool-in_range l r x = l <= x && x <= r+ln_intersect :: (Eq t, Fractional t) => Ln t -> Ln t -> Maybe (t,t)+ln_intersect l1 l2 =+ let Ln (Pt x1 y1) _ = l1+ Vc dx1 dy1 = ln_vc l1+ Ln (Pt x2 y2) _ = l2+ Vc dx2 dy2 = ln_vc l2+ a = (dx2 * dy1) - (dx1 * dy2)+ t' = ((dx1 * (y2 - y1)) - (dy1 * (x2 - x1))) / a+ t = ((dx2 * (y1 - y2)) - (dy2 * (x1 - x2))) / (negate a)+ in if a == 0 then Nothing else Just (t,t') +ln_pt_along :: (Eq a, Num a) => a -> Ln a -> Pt a+ln_pt_along z ln =+ let v = vc_scale z (ln_vc ln)+ Ln p _ = ln+ in pt_translate p v+ -- | Do two 'Ln's intersect, and if so at which 'Pt'. ----- > ln_intersection (ln' (0,0) (5,5)) (ln' (5,0) (0,5)) == Just (pt 2.5 2.5)+-- > ln_intersection (ln' (0,0) (5,5)) (ln' (5,0) (0,5)) == Just (Pt 2.5 2.5) -- > ln_intersection (ln' (1,3) (9,3)) (ln' (0,1) (2,1)) == Nothing -- > ln_intersection (ln' (1,5) (6,8)) (ln' (0.5,3) (6,4)) == Nothing -- > ln_intersection (ln' (1,2) (3,6)) (ln' (2,4) (4,8)) == Nothing -- > ln_intersection (ln' (2,3) (7,9)) (ln' (1,2) (5,7)) == Nothing--- > ln_intersection (ln' (0,0) (1,1)) (ln' (0,0) (1,0)) == Just (pt 0 0)+-- > ln_intersection (ln' (0,0) (1,1)) (ln' (0,0) (1,0)) == Just (Pt 0 0) ln_intersection :: (Ord a,Fractional a) => Ln a -> Ln a -> Maybe (Pt a) ln_intersection l0 l1 =- case G.intersectLines2 l0 l1 of+ case ln_intersect l0 l1 of Nothing -> Nothing Just (i,j) -> if i >= 0 && i <= 1 && j >= 0 && j <= 1- then Just (G.alongLine i l0)+ then Just (ln_pt_along i l0) else Nothing -- | Variant definition of 'ln_intersection', using algorithm at -- <http://paulbourke.net/geometry/lineline2d/>. -- -- > ln_intersection_ (ln' (1,2) (3,6)) (ln' (2,4) (4,8)) == Nothing--- > ln_intersection_ (ln' (0,0) (1,1)) (ln' (0,0) (1,0)) == Just (pt 0 0)+-- > ln_intersection_ (ln' (0,0) (1,1)) (ln' (0,0) (1,0)) == Just (Pt 0 0) ln_intersection_ :: (Ord a,Fractional a) => Ln a -> Ln a -> Maybe (Pt a) ln_intersection_ l0 l1 = let ((x1,y1),(x2,y2)) = ln_pt' l0@@ -574,21 +495,21 @@ in if d == 0 then Nothing else if ua' == 0 && ub' == 0- then Just (pt x1 y1)+ then Just (Pt x1 y1) else let ua = ua' / d ub = ub' / d in if in_range 0 1 ua && in_range 0 1 ub then let x = x1 + ua * (x2 - x1) y = y1 + ua * (y2 - y1)- in Just (pt x y)+ in Just (Pt x y) else Nothing -- | Predicate variant of 'ln_intersection'. ----- > ln_intersect (ln' (1,1) (3,8)) (ln' (0.5,2) (4,7)) == True--- > ln_intersect (ln' (3.5,9) (3.5,0.5)) (ln' (3,1) (9,1)) == True-ln_intersect :: (Ord a, Fractional a) => Ln a -> Ln a -> Bool-ln_intersect l = isJust . ln_intersection l+-- > ln_intersect_p (ln' (1,1) (3,8)) (ln' (0.5,2) (4,7)) == True+-- > ln_intersect_p (ln' (3.5,9) (3.5,0.5)) (ln' (3,1) (9,1)) == True+ln_intersect_p :: (Ord a, Fractional a) => Ln a -> Ln a -> Bool+ln_intersect_p l = isJust . ln_intersection l -- * Line slope @@ -620,18 +541,26 @@ ln_parallel_ :: Ln R -> Ln R -> Bool ln_parallel_ p q = ln_angle (ln_sort p) == ln_angle (ln_sort q) +-- | Are two vectors are in the same direction (to within a small+-- tolerance).+vc_same_direction :: (Ord a, Floating a) => Vc a -> Vc a -> Bool+vc_same_direction v w =+ let Vc dx1 dy1 = vc_unit v+ Vc dx2 dy2 = vc_unit w+ in abs (dx2 - dx1) < epsilon && abs (dy2 - dy1) < epsilon+ -- | Do 'Ln's have same direction (within tolerance). -- -- > ln_same_direction (ln' (0,0) (1,1)) (ln' (0,0) (2,2)) == True -- > ln_same_direction (ln' (0,0) (1,1)) (ln' (2,2) (0,0)) == False ln_same_direction :: (Ord a, Floating a) => Ln a -> Ln a -> Bool-ln_same_direction p q = ln_vc p `G.sameDirection` ln_vc q+ln_same_direction p q = ln_vc p `vc_same_direction` ln_vc q -- | Are 'Ln's parallel, ie. does 'ln_vc' of each equal 'ln_same_direction'. -- -- > ln_parallel__ (ln' (0,0) (1,1)) (ln' (2,2) (1,1)) == True ln_parallel__ :: Ln R -> Ln R -> Bool-ln_parallel__ p q = ln_vc (ln_sort p) `G.sameDirection` ln_vc (ln_sort q)+ln_parallel__ p q = ln_vc (ln_sort p) `vc_same_direction` ln_vc (ln_sort q) -- | Is 'Ln' horizontal, ie. is 'ln_slope' zero. --@@ -646,6 +575,18 @@ ln_vertical :: (Fractional a,Eq a) => Ln a -> Bool ln_vertical = (== Nothing) . ln_slope +-- * Ln sets++-- | 'pt_minmax' for set of 'Ln'.+lns_minmax :: [Ln R] -> (Pt R,Pt R)+lns_minmax = ls_minmax . concatMap (\(Ln l r) -> [l,r])++-- | Normalise to (0,m).+lns_normalise :: R -> [Ln R] -> [Ln R]+lns_normalise m l =+ let w = wn_from_extent (lns_minmax l)+ in map (ln_scale m . ln_normalise_w w) l+ -- * L(ine) s(egment) functions -- | 'Ls' constructor.@@ -654,7 +595,7 @@ -- | Variant 'Ls' constructor from 'Pt' co-ordinates as duples. ls' :: [(a,a)] -> Ls a-ls' = map pt'+ls' = map (uncurry Pt) -- | Negate /y/ elements. ls_negate_y :: (Num a) => Ls a -> Ls a@@ -667,64 +608,22 @@ [] -> undefined p:ps -> foldl pt_minmax (p,p) ps --- | Split list at element where predicate /f/ over adjacent elements--- first holds.------ > split_f (\p q -> q - p < 3) [1,2,4,7,11] == ([1,2,4],[7,11])-split_f :: (a -> a -> Bool) -> [a] -> ([a],[a])-split_f f =- let go i [] = (reverse i,[])- go i [p] = (reverse (p:i), [])- go i (p:q:r) =- if f p q- then go (p:i) (q:r)- else (reverse (p:i),q:r)- in go []---- | Variant on 'split_f' that segments input.------ > segment_f (\p q -> abs (q - p) < 3) [1,3,7,9,15] == [[1,3],[7,9],[15]]-segment_f :: (a -> a -> Bool) -> [a] -> [[a]]-segment_f f xs =- let (p,q) = split_f f xs- in if null q- then [p]- else p : segment_f f q- -- | Separate 'Ls' at points where the 'Vc' from one element to the -- next exceeds the indicated distance. ----- > map length (ls_separate (vc 2 2) (map pt' [(0,0),(1,1),(3,3)])) == [2,1]+-- > map length (ls_separate (Vc 2 2) (map (uncurry Pt) [(0,0),(1,1),(3,3)])) == [2,1] ls_separate :: (Ord a,Num a) => Vc a -> Ls a -> [Ls a]-ls_separate v =- let (dx,dy) = vc_xy v- f p0 p1 = let (x0,y0) = pt_xy p0- (x1,y1) = pt_xy p1- in abs (x1 - x0) < dx &&- abs (y1 - y0) < dy+ls_separate (Vc dx dy) =+ let f (Pt x0 y0) (Pt x1 y1) = abs (x1 - x0) < dx &&+ abs (y1 - y0) < dy in segment_f f --- | Delete elements of a list using a predicate over the--- previous and current elements.-delete_f :: (a -> a -> Bool) -> [a] -> [a]-delete_f f =- let go [] = []- go [p] = [p]- go (p:q:r) =- if f p q- then go (p:r)- else p : go (q:r)- in go- -- | Delete 'Pt' from 'Ls' so that no two 'Pt' are within a tolerance -- given by 'Vc'. ls_tolerate :: (Ord a,Num a) => Vc a -> Ls a -> Ls a-ls_tolerate v =- let (x,y) = vc_xy v- too_close p0 p1 =- let (x0,y0) = pt_xy p0- (x1,y1) = pt_xy p1- dx = abs (x1 - x0)+ls_tolerate (Vc x y) =+ let too_close (Pt x0 y0) (Pt x1 y1) =+ let dx = abs (x1 - x0) dy = abs (y1 - y0) in dx < x && dy < y in delete_f too_close@@ -736,38 +635,26 @@ Nothing -> id Just i' -> ls_tolerate i' --- | All adjacent pairs of a list.------ > pairs [1..5] == [(1,2),(2,3),(3,4),(4,5)]-pairs :: [x] -> [(x,x)]-pairs l =- case l of- x:y:z -> (x,y) : pairs (y:z)- _ -> []- -- | Test if point 'Pt' lies inside polygon 'Ls'. ----- > ls_pt_inside (ls' [(0,0),(1,0),(1,1),(0,1)]) (pt 0.5 0.5) == True+-- > ls_pt_inside (ls' [(0,0),(1,0),(1,1),(0,1)]) (Pt 0.5 0.5) == True ls_pt_inside :: Ls R -> Pt R -> Bool-ls_pt_inside s p =- let (x,y) = pt_xy p- in case s of- [] -> undefined- l0:l -> let xs = pairs ((l0:l)++[l0])- f (p1,p2) =- let (x1,y1) = pt_xy p1- (x2,y2) = pt_xy p2- in and [y > min y1 y2- ,y <= max y1 y2- ,x <= max x1 x2- ,y1 /= y2- ,x1 == x2 ||- x <= (y-y1)*(x2-x1)/(y2-y1)+x1]- in odd (length (filter id (map f xs)))+ls_pt_inside s (Pt x y) =+ case s of+ [] -> undefined+ l0:l -> let xs = pairs ((l0:l)++[l0])+ f (Pt x1 y1,Pt x2 y2) =+ and [y > min y1 y2+ ,y <= max y1 y2+ ,x <= max x1 x2+ ,y1 /= y2+ ,x1 == x2 ||+ x <= (y-y1)*(x2-x1)/(y2-y1)+x1]+ in odd (length (filter id (map f xs))) -- | Variant that counts points at vertices as inside. ----- > ls_pt_inside' (ls' [(0,0),(1,0),(1,1),(0,1)]) (pt 0 1) == True+-- > ls_pt_inside' (ls' [(0,0),(1,0),(1,1),(0,1)]) (Pt 0 1) == True ls_pt_inside' :: Ls R -> Pt R -> Bool ls_pt_inside' l p = p `elem` l || ls_pt_inside l p @@ -778,75 +665,64 @@ [] -> True p:z -> pt_is_normal p && ls_check_normalised z --- * Window+-- | Line co-ordinates as /x/,/y/ list.+--+-- > ls_xy [Pt 0 0,Pt 1 1] == [0,0,1,1]+ls_xy :: Ls a -> [a]+ls_xy = concatMap (\(Pt x y) -> [x,y]) --- | 'Wn' constructor.-wn :: Pt a -> Vc a -> Wn a-wn p v = (p,v)+-- * Window -- | Variant 'Wn' constructor. wn' :: Num a => (a,a) -> (a,a) -> Wn a-wn' (x,y) (i,j) = (pt x y,vc i j)---- | Lower-left 'Pt' of 'Wn'.-wn_ll :: Wn a -> Pt a-wn_ll (p,_) = p---- | Extent 'Vc' of 'Wn'.-wn_ex :: Wn a -> Vc a-wn_ex (_,v) = v+wn' (x,y) (i,j) = Wn (Pt x y) (Vc i j) -- | Extract /(x,y)/ and /(dx,dy)/ pairs. ----- > wn_extract (wn (pt 0 0) (vc 1 1)) == ((0,0),(1,1))+-- > wn_extract (Wn (Pt 0 0) (Vc 1 1)) == ((0,0),(1,1)) wn_extract :: Wn a -> ((a,a),(a,a))-wn_extract (p,v) = (pt_xy p,vc_xy v)+wn_extract (Wn (Pt x y) (Vc dx dy)) = ((x,y),(dx,dy)) -- | Show function for window with fixed precision of 'n'. ----- > wn_show 1 (wn (pt 0 0) (vc 1 1)) == "((0.0,0.0),(1.0,1.0))"+-- > wn_show 1 (Wn (Pt 0 0) (Vc 1 1)) == "((0.0,0.0),(1.0,1.0))" wn_show :: Int -> Wn R -> String-wn_show n w =- let ((x0,y0),(dx,dy)) = wn_extract w- fs = printf "((%%.%df,%%.%df),(%%.%df,%%.%df))" n n n n+wn_show n (Wn (Pt x0 y0) (Vc dx dy)) =+ let fs = printf "((%%.%df,%%.%df),(%%.%df,%%.%df))" n n n n in printf fs x0 y0 dx dy -- | Is 'Pt' within 'Wn' exclusive of edge. ----- > map (pt_in_window (wn' (0,0) (1,1))) [pt' (0.5,0.5),pt' (1,1)] == [True,False]+-- > map (pt_in_window (wn' (0,0) (1,1))) [Pt 0.5 0.5,Pt 1 1] == [True,False] pt_in_window :: (Ord a,Num a) => Wn a -> Pt a -> Bool-pt_in_window w p =- let ((lx,ly),(dx,dy)) = wn_extract w- (x,y) = pt_xy p- (ux,uy) = (lx+dx,ly+dy)+pt_in_window (Wn (Pt lx ly) (Vc dx dy)) (Pt x y) =+ let (ux,uy) = (lx+dx,ly+dy) in x > lx && x < ux && y > ly && y < uy +-- | 'Wn' from /(lower-left,upper-right)/ extent.+wn_from_extent :: (Num a,Ord a) => (Pt a,Pt a) -> Wn a+wn_from_extent (Pt x0 y0,Pt x1 y1) = Wn (Pt x0 y0) (Vc (x1-x0) (y1-y0))+ -- | 'Wn' containing 'Ls'. -- -- > ls_window (ls' [(0,0),(1,1),(2,0)]) == wn' (0,0) (2,1) ls_window :: (Num a,Ord a) => Ls a -> Wn a-ls_window l =- let (p0,p1) = ls_minmax l- (x0,y0) = pt_xy p0- (x1,y1) = pt_xy p1- in (pt x0 y0,vc (x1-x0) (y1-y0))+ls_window = wn_from_extent . ls_minmax -- | A 'Wn' that encompasses both input 'Wn's. wn_join :: (Num a,Ord a) => Wn a -> Wn a -> Wn a-wn_join w0 w1 =- let ((x0,y0),(dx0,dy0)) = wn_extract w0- ((x1,y1),(dx1,dy1)) = wn_extract w1- x = min x0 x1+wn_join (Wn (Pt x0 y0) (Vc dx0 dy0)) (Wn (Pt x1 y1) (Vc dx1 dy1)) =+ let x = min x0 x1 y = min y0 y1 dx = max (x0+dx0) (x1+dx1) - x dy = max (y0+dy0) (y1+dy1) - y- in (pt x y,vc dx dy)+ in Wn (Pt x y) (Vc dx dy) -- | Predictate to determine if two 'Wn's intersect. wn_intersect :: (Num a,Ord a) => Wn a -> Wn a -> Bool-wn_intersect w0 w1 =- let ((x0,y0),(dx0,dy0)) = wn_extract w0- ((x1,y1),(dx1,dy1)) = wn_extract w1+wn_intersect w0 w1 =+ let (Wn (Pt x0 y0) (Vc dx0 dy0)) = w0+ (Wn (Pt x1 y1) (Vc dx1 dy1)) = w1 in not (x0 > x1+dx1 || x1 > x0+dx0 || y0 > y1+dy1 || y1 > y0+dy0) -- | Are all points at 'Ls' within the 'Wn'.@@ -869,19 +745,202 @@ in i : g (dropWhile (not . pt_in_window w) xs') in filter (not . null) . g --- | Given a 'Wn' for a 'Ls', normalise the 'Ls' to lie within (0,1).+-- | Normalisation function for 'Wn', ie. map 'Pt' to lie within (0,1).+wn_normalise_f :: Wn R -> Pt R -> Pt R+wn_normalise_f (Wn (Pt x0 y0) (Vc dx dy)) (Pt x y) =+ let z = max dx dy+ in Pt ((x - x0) / z) ((y - y0) / z)++-- | Given 'Wn' normalise the 'Ls'. ls_normalise_w :: Wn R -> Ls R -> Ls R-ls_normalise_w w =- let ((x0,y0),(dx,dy)) = wn_extract w- z = max dx dy- f p = let (x,y) = pt_xy p- in pt ((x - x0) / z) ((y - y0) / z)- in map f+ls_normalise_w w = map (wn_normalise_f w) --- | Shift lower left 'Pt' of 'Wn' by indicated 'Pt' (ie. 'pt_add').+-- | Given 'Wn' normalise 'Ln'.+ln_normalise_w :: Wn R -> Ln R -> Ln R+ln_normalise_w w (Ln p q) =+ let f = wn_normalise_f w+ in Ln (f p) (f q)++-- | Shift lower left 'Pt' of 'Wn' by indicated 'Pt'. pt_shift_w :: Num a => Pt a -> Wn a -> Wn a-pt_shift_w p (dp,ex) = (p `pt_add` dp,ex)+pt_shift_w p (Wn dp ex) = Wn (p + dp) ex -- | Negate /y/ field of lower left 'Pt' of 'Wn'. wn_negate_y :: Num a => Wn a -> Wn a-wn_negate_y (p,v) = (pt_negate_y p,v)+wn_negate_y (Wn p v) = Wn (pt_negate_y p) v++-- * Matrix++-- | Transformation matrix data type.+data Matrix n = Matrix n n n n n n deriving (Eq,Show)++-- | Enumeration of 'Matrix' indices.+data Matrix_Index = I0 | I1 | I2++mx_row :: Num n => Matrix n -> Matrix_Index -> (n,n,n)+mx_row (Matrix a b c d e f) i =+ case i of+ I0 -> (a,b,0)+ I1 -> (c,d,0)+ I2 -> (e,f,1)++mx_col :: Num n => Matrix n -> Matrix_Index -> (n,n,n)+mx_col (Matrix a b c d e f) i =+ case i of+ I0 -> (a,c,e)+ I1 -> (b,d,f)+ I2 -> (0,0,1)++mx_multiply :: Num n => Matrix n -> Matrix n -> Matrix n+mx_multiply a b =+ let f i j = let (r1,r2,r3) = mx_row a i+ (c1,c2,c3) = mx_col b j+ in r1 * c1 + r2 * c2 + r3 * c3+ in Matrix (f I0 I0) (f I0 I1) (f I1 I0) (f I1 I1) (f I2 I0) (f I2 I1)++-- | Pointwise unary operator.+mx_uop :: (n -> n) -> Matrix n -> Matrix n+mx_uop g (Matrix a b c d e f) =+ Matrix (g a) (g b) (g c) (g d) (g e) (g f)++-- | Pointwise binary operator.+mx_binop :: (n -> n -> n) -> Matrix n -> Matrix n -> Matrix n+mx_binop g (Matrix a b c d e f) (Matrix a' b' c' d' e' f') =+ Matrix (g a a') (g b b') (g c c') (g d d') (g e e') (g f f')++instance Num n => Num (Matrix n) where+ (*) = mx_multiply+ (+) = mx_binop (+)+ (-) = mx_binop (-)+ abs = mx_uop abs+ signum = mx_uop signum+ fromInteger n = let n' = fromInteger n+ in Matrix n' 0 0 n' 0 0++-- | A translation matrix with independent x and y offsets.+mx_translation :: Num n => n -> n -> Matrix n+mx_translation = Matrix 1 0 0 1++-- | A scaling matrix with independent x and y scalars.+mx_scaling :: Num n => n -> n -> Matrix n+mx_scaling x y = Matrix x 0 0 y 0 0++-- | A rotation matrix through the indicated angle (in radians).+mx_rotation :: Floating n => n -> Matrix n+mx_rotation a =+ let c = cos a+ s = sin a+ t = negate s+ in Matrix c s t c 0 0++-- | The identity matrix.+mx_identity :: Num n => Matrix n+mx_identity = Matrix 1 0 0 1 0 0++mx_translate :: Num n => n -> n -> Matrix n -> Matrix n+mx_translate x y m = m * (mx_translation x y)++mx_scale :: Num n => n -> n -> Matrix n -> Matrix n+mx_scale x y m = m * (mx_scaling x y)++mx_rotate :: Floating n => n -> Matrix n -> Matrix n+mx_rotate r m = m * (mx_rotation r)++mx_scalar_multiply :: Num n => n -> Matrix n -> Matrix n+mx_scalar_multiply scalar = mx_uop (* scalar)++mx_adjoint :: Num n => Matrix n -> Matrix n+mx_adjoint (Matrix a b c d x y) =+ Matrix d (-b) (-c) a (c * y - d * x) (b * x - a * y)++mx_invert :: Fractional n => Matrix n -> Matrix n+mx_invert m =+ let Matrix xx yx xy yy _ _ = m+ d = xx*yy - yx*xy+ in mx_scalar_multiply (recip d) (mx_adjoint m)++mx_list :: Matrix n -> [n]+mx_list (Matrix a b c d e f) = [a,b,c,d,e,f]++-- | Apply a transformation matrix to a point.+pt_transform :: Num n => Matrix n -> Pt n -> Pt n+pt_transform (Matrix a b c d e f) (Pt x y) =+ let x' = x * a + y * c + e+ y' = x * b + y * d + f+ in Pt x' y'++-- * Bezier functions.++bezier3 :: Num n => Pt n -> Pt n -> Pt n -> n -> Pt n+bezier3 (Pt x1 y1) (Pt x2 y2) (Pt x3 y3) mu = (Pt x y)+ where a = mu*mu+ b = 1 - mu+ c = b*b+ x = x1*c + 2*x2*b*mu + x3*a+ y = y1*c + 2*y2*b*mu + y3*a++-- | Four-point bezier curve interpolation. The index /mu/ is+-- in the range zero to one.+bezier4 :: Num n => Pt n -> Pt n -> Pt n -> Pt n -> n -> Pt n+bezier4 (Pt x1 y1) (Pt x2 y2) (Pt x3 y3) (Pt x4 y4) mu =+ let a = 1 - mu+ b = a*a*a+ c = mu*mu*mu+ x = b*x1 + 3*mu*a*a*x2 + 3*mu*mu*a*x3 + c*x4+ y = b*y1 + 3*mu*a*a*y2 + 3*mu*mu*a*y3 + c*y4+ in Pt x y++-- * Ord++-- | Given /left/ and /right/, is /x/ in range (inclusive).+--+-- > map (in_range 0 1) [-1,0,1,2] == [False,True,True,False]+in_range :: Ord a => a -> a -> a -> Bool+in_range l r x = l <= x && x <= r++-- * List++-- | Split list at element where predicate /f/ over adjacent elements+-- first holds.+--+-- > split_f (\p q -> q - p < 3) [1,2,4,7,11] == ([1,2,4],[7,11])+split_f :: (a -> a -> Bool) -> [a] -> ([a],[a])+split_f f =+ let go i [] = (reverse i,[])+ go i [p] = (reverse (p:i), [])+ go i (p:q:r) =+ if f p q+ then go (p:i) (q:r)+ else (reverse (p:i),q:r)+ in go []++-- | Variant on 'split_f' that segments input.+--+-- > segment_f (\p q -> abs (q - p) < 3) [1,3,7,9,15] == [[1,3],[7,9],[15]]+segment_f :: (a -> a -> Bool) -> [a] -> [[a]]+segment_f f xs =+ let (p,q) = split_f f xs+ in if null q+ then [p]+ else p : segment_f f q++-- | Delete elements of a list using a predicate over the+-- previous and current elements.+delete_f :: (a -> a -> Bool) -> [a] -> [a]+delete_f f =+ let go [] = []+ go [p] = [p]+ go (p:q:r) =+ if f p q+ then go (p:r)+ else p : go (q:r)+ in go++-- | All adjacent pairs of a list.+--+-- > pairs [1..5] == [(1,2),(2,3),(3,4),(4,5)]+pairs :: [x] -> [(x,x)]+pairs l =+ case l of+ x:y:z -> (x,y) : pairs (y:z)+ _ -> []
Data/CG/Minus/Arrow.hs view
@@ -6,7 +6,7 @@ -- | Given the arrow body 'Ln' and the arrow length and arrow angle -- (in radians) 'R' calculate the 'Pt' of each arrow tip. ----- > arrow_coord (ln' (0,0) (1,1)) 0.1 (pi/9)+-- > arrow_coord (Ln (Pt 0 0) (Pt 1 1)) 0.1 (pi/9) arrow_coord :: Ln R -> R -> R -> (Pt R,Pt R) arrow_coord l n a = let ((x0,y0),(x1,y1)) = ln_pt' l@@ -15,4 +15,4 @@ y2 = y1 + n * sin (a' - a) x3 = x1 + n * cos (a' + a) y3 = y1 + n * sin (a' + a)- in (pt x2 y2,pt x3 y3)+ in (Pt x2 y2,Pt x3 y3)
Data/CG/Minus/Bearing.hs view
@@ -12,7 +12,7 @@ -- | Bearing from 'Pt' /p/ to /q/. ----- > let f (x,y) = bearing (pt 0 0) (pt x y)+-- > let f (x,y) = bearing (Pt 0 0) (Pt x y) -- > map f [(0,1),(1,1),(1,0),(1,-1)] == [N,NE,E,SE] -- > map f [(0,-1),(-1,-1),(-1,0),(-1,1)] == [S,SW,W,NW] -- > map f [(1/4,1),(1,1/4),(1,-1/4),(1/4,-1)] == [NNE,ENE,ESE,SSE]@@ -25,7 +25,7 @@ -- | Bearing to nearest eight point compass bearing ----- > let f (x,y) = bearing_8 (pt 0 0) (pt x y)+-- > let f (x,y) = bearing_8 (Pt 0 0) (Pt x y) -- > map f [(1/4,1),(1,1/4),(1,-1/4),(1/4,-1)] == [N,E,E,S] bearing_8 :: Pt R -> Pt R -> Bearing bearing_8 p q =
Data/CG/Minus/Colour.hs view
@@ -2,8 +2,8 @@ module Data.CG.Minus.Colour where import Data.Colour {- colour -}-import Data.Colour.SRGB-import Data.Colour.Names as N+import qualified Data.Colour.SRGB as S {- colour -}+import qualified Data.Colour.Names as N {- colour -} -- | Opaque colour. type C = Colour Double@@ -13,12 +13,12 @@ -- | Grey 'Colour'. mk_grey :: (Ord a,Floating a) => a -> Colour a-mk_grey x = sRGB x x x+mk_grey x = S.sRGB x x x -- | Reduce 'Colour' to grey. Constants are @0.3@, @0.59@ and @0.11@. to_greyscale :: (Ord a,Floating a) => Colour a -> a to_greyscale c =- let (RGB r g b) = toSRGB c+ let (S.RGB r g b) = S.toSRGB c in r * 0.3 + g * 0.59 + b * 0.11 -- | 'mk_grey' '.' 'to_greyscale'.@@ -37,13 +37,13 @@ -- | Tuple to 'C', inverse of 'unC'. toC :: (Double,Double,Double) -> C-toC (r,g,b) = sRGB r g b+toC (r,g,b) = S.sRGB r g b -- | 'C' to /(red,green,blue)/ tuple. unC :: C -> (Double,Double,Double) unC x =- let x' = toSRGB x- in (channelRed x', channelGreen x', channelBlue x')+ let x' = S.toSRGB x+ in (S.channelRed x',S.channelGreen x',S.channelBlue x') -- | Tuple to 'Ca', inverse of 'unCa'. toCa :: (Double,Double,Double,Double) -> Ca@@ -52,42 +52,45 @@ -- | 'Ca' to /(red,green,blue,alpha)/ tuple unCa :: Ca -> (Double,Double,Double,Double) unCa x =- let x' = toSRGB (pureColour x)- in (channelRed x', channelGreen x', channelBlue x', alphaChannel x)+ let x' = S.toSRGB (pureColour x)+ in (S.channelRed x'+ ,S.channelGreen x'+ ,S.channelBlue x'+ ,alphaChannel x) -- * Constants -- | Venetian red (@#c80815@). venetianRed :: C-venetianRed = sRGB24read "#c80815"+venetianRed = S.sRGB24read "#c80815" -- | Swedish azure blue (@#005b99@). swedishAzureBlue :: C-swedishAzureBlue = sRGB24read "#005b99"+swedishAzureBlue = S.sRGB24read "#005b99" -- | Safety orange (@#ff6600@). safetyOrange :: C-safetyOrange = sRGB24read "#ff6600"+safetyOrange = S.sRGB24read "#ff6600" -- | Dye magenta (@#ca1f7b@). dyeMagenta :: C-dyeMagenta = sRGB24read "#ca1f7b"+dyeMagenta = S.sRGB24read "#ca1f7b" -- | Candlelight yellow (@#fcd116@). candlelightYellow :: C-candlelightYellow = sRGB24read "#fcd116"+candlelightYellow = S.sRGB24read "#fcd116" -- | Subtractive primary cyan (@#00B7EB@). subtractivePrimaryCyan :: C-subtractivePrimaryCyan = sRGB24read "#00B7EB"+subtractivePrimaryCyan = S.sRGB24read "#00B7EB" -- | Fern green (@#009246@). fernGreen :: C-fernGreen = sRGB24read "#009246"+fernGreen = S.sRGB24read "#009246" -- | Sepia brown (@#704214@). sepiaBrown :: C-sepiaBrown = sRGB24read "#704214"+sepiaBrown = S.sRGB24read "#704214" -- | The set of named colours defined in this module. non_svg_colour_set :: [C]@@ -107,150 +110,150 @@ -- alphabetical order). svg_colour_set :: [C] svg_colour_set =- [aliceblue- ,antiquewhite- ,aqua- ,aquamarine- ,azure- ,beige- ,bisque- ,black- ,blanchedalmond- ,blue- ,blueviolet- ,brown- ,burlywood- ,cadetblue- ,chartreuse- ,chocolate- ,coral- ,cornflowerblue- ,cornsilk- ,crimson- ,cyan- ,darkblue- ,darkcyan- ,darkgoldenrod- ,darkgray- ,darkgreen- ,darkgrey- ,darkkhaki- ,darkmagenta- ,darkolivegreen- ,darkorange- ,darkorchid- ,darkred- ,darksalmon- ,darkseagreen- ,darkslateblue- ,darkslategray- ,darkslategrey- ,darkturquoise- ,darkviolet- ,deeppink- ,deepskyblue- ,dimgray- ,dimgrey- ,dodgerblue- ,firebrick- ,floralwhite- ,forestgreen- ,fuchsia- ,gainsboro- ,ghostwhite- ,gold- ,goldenrod- ,gray- ,grey- ,green- ,greenyellow- ,honeydew- ,hotpink- ,indianred- ,indigo- ,ivory- ,khaki- ,lavender- ,lavenderblush- ,lawngreen- ,lemonchiffon- ,lightblue- ,lightcoral- ,lightcyan- ,lightgoldenrodyellow- ,lightgray- ,lightgreen- ,lightgrey- ,lightpink- ,lightsalmon- ,lightseagreen- ,lightskyblue- ,lightslategray- ,lightslategrey- ,lightsteelblue- ,lightyellow- ,lime- ,limegreen- ,linen- ,magenta- ,maroon- ,mediumaquamarine- ,mediumblue- ,mediumorchid- ,mediumpurple- ,mediumseagreen- ,mediumslateblue- ,mediumspringgreen- ,mediumturquoise- ,mediumvioletred- ,midnightblue- ,mintcream- ,mistyrose- ,moccasin- ,navajowhite- ,navy- ,oldlace- ,olive- ,olivedrab- ,orange- ,orangered- ,orchid- ,palegoldenrod- ,palegreen- ,paleturquoise- ,palevioletred- ,papayawhip- ,peachpuff- ,peru- ,pink- ,plum- ,powderblue- ,purple- ,red- ,rosybrown- ,royalblue- ,saddlebrown- ,salmon- ,sandybrown- ,seagreen- ,seashell- ,sienna- ,silver- ,skyblue- ,slateblue- ,slategray- ,slategrey- ,snow- ,springgreen- ,steelblue+ [N.aliceblue+ ,N.antiquewhite+ ,N.aqua+ ,N.aquamarine+ ,N.azure+ ,N.beige+ ,N.bisque+ ,N.black+ ,N.blanchedalmond+ ,N.blue+ ,N.blueviolet+ ,N.brown+ ,N.burlywood+ ,N.cadetblue+ ,N.chartreuse+ ,N.chocolate+ ,N.coral+ ,N.cornflowerblue+ ,N.cornsilk+ ,N.crimson+ ,N.cyan+ ,N.darkblue+ ,N.darkcyan+ ,N.darkgoldenrod+ ,N.darkgray+ ,N.darkgreen+ ,N.darkgrey+ ,N.darkkhaki+ ,N.darkmagenta+ ,N.darkolivegreen+ ,N.darkorange+ ,N.darkorchid+ ,N.darkred+ ,N.darksalmon+ ,N.darkseagreen+ ,N.darkslateblue+ ,N.darkslategray+ ,N.darkslategrey+ ,N.darkturquoise+ ,N.darkviolet+ ,N.deeppink+ ,N.deepskyblue+ ,N.dimgray+ ,N.dimgrey+ ,N.dodgerblue+ ,N.firebrick+ ,N.floralwhite+ ,N.forestgreen+ ,N.fuchsia+ ,N.gainsboro+ ,N.ghostwhite+ ,N.gold+ ,N.goldenrod+ ,N.gray+ ,N.grey+ ,N.green+ ,N.greenyellow+ ,N.honeydew+ ,N.hotpink+ ,N.indianred+ ,N.indigo+ ,N.ivory+ ,N.khaki+ ,N.lavender+ ,N.lavenderblush+ ,N.lawngreen+ ,N.lemonchiffon+ ,N.lightblue+ ,N.lightcoral+ ,N.lightcyan+ ,N.lightgoldenrodyellow+ ,N.lightgray+ ,N.lightgreen+ ,N.lightgrey+ ,N.lightpink+ ,N.lightsalmon+ ,N.lightseagreen+ ,N.lightskyblue+ ,N.lightslategray+ ,N.lightslategrey+ ,N.lightsteelblue+ ,N.lightyellow+ ,N.lime+ ,N.limegreen+ ,N.linen+ ,N.magenta+ ,N.maroon+ ,N.mediumaquamarine+ ,N.mediumblue+ ,N.mediumorchid+ ,N.mediumpurple+ ,N.mediumseagreen+ ,N.mediumslateblue+ ,N.mediumspringgreen+ ,N.mediumturquoise+ ,N.mediumvioletred+ ,N.midnightblue+ ,N.mintcream+ ,N.mistyrose+ ,N.moccasin+ ,N.navajowhite+ ,N.navy+ ,N.oldlace+ ,N.olive+ ,N.olivedrab+ ,N.orange+ ,N.orangered+ ,N.orchid+ ,N.palegoldenrod+ ,N.palegreen+ ,N.paleturquoise+ ,N.palevioletred+ ,N.papayawhip+ ,N.peachpuff+ ,N.peru+ ,N.pink+ ,N.plum+ ,N.powderblue+ ,N.purple+ ,N.red+ ,N.rosybrown+ ,N.royalblue+ ,N.saddlebrown+ ,N.salmon+ ,N.sandybrown+ ,N.seagreen+ ,N.seashell+ ,N.sienna+ ,N.silver+ ,N.skyblue+ ,N.slateblue+ ,N.slategray+ ,N.slategrey+ ,N.snow+ ,N.springgreen+ ,N.steelblue ,N.tan- ,teal- ,thistle- ,tomato- ,turquoise- ,violet- ,wheat- ,white- ,whitesmoke- ,yellow- ,yellowgreen]+ ,N.teal+ ,N.thistle+ ,N.tomato+ ,N.turquoise+ ,N.violet+ ,N.wheat+ ,N.white+ ,N.whitesmoke+ ,N.yellow+ ,N.yellowgreen]
Data/CG/Minus/Colour/Planck.hs view
@@ -1,14 +1,13 @@ -- | Planck radiation equation. module Data.CG.Minus.Colour.Planck where -import Data.CG.Minus (R) import Data.CG.Minus.Colour -- | Given wavelength (in microns) and temperature (in degrees Kelvin) -- solve Planck's radiation equation. -- -- > planck_rad_eq 0.7 2600 == 8.22656629154115e7-planck_rad_eq :: R -> R -> R+planck_rad_eq :: Floating a => a -> a -> a planck_rad_eq l t = let k0 = 3.7403e10 k1 = -5.0@@ -28,7 +27,7 @@ -- -- > let h (r,g,b) = let f = floor . (*) 255 in (f r,f g,f b) -- > in map (h . k_to_rgb) [2600,28000] == [(255,95,22),(49,118,254)]-k_to_rgb :: R -> (R,R,R)+k_to_rgb :: (Floating t, Ord t) => t -> (t,t,t) k_to_rgb k = let r = planck_rad_eq 0.7000 k g = planck_rad_eq 0.5461 k@@ -37,5 +36,5 @@ in (r * s,g * s,b * s) -- | 'toC' '.' 'k_to_rgb'.-k_to_colour :: R -> C+k_to_colour :: Double -> C k_to_colour = toC . k_to_rgb
README view
@@ -5,7 +5,7 @@ [hs]: http://haskell.org/ -© [rohan drape][rd], 2009-2012, [gpl]+© [rohan drape][rd], 2009-2013, [gpl] [rd]: http://rd.slavepianos.org/ [gpl]: http://gnu.org/copyleft/
hcg-minus.cabal view
@@ -1,10 +1,10 @@ name: hcg-minus-version: 0.12+version: 0.14 synopsis: haskell cg (minus) description: cg (minus) library license: BSD3 category: Math-copyright: (c) rohan drape, 2011-2012+copyright: (c) rohan drape, 2011-2013 author: Rohan Drape maintainer: rd@slavepianos.org stability: Experimental@@ -16,7 +16,7 @@ data-files: README library- build-depends: base==4.*,colour,SG+ build-depends: base==4.*,colour ghc-options: -Wall -fwarn-tabs exposed-modules: Data.CG.Minus Data.CG.Minus.Arrow