Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.BezierSpline

Description

Synopsis

newtype BezierSpline n d r = BezierSpline (LSeq (1 + n) (Point d r))
controlPoints :: Iso (BezierSpline n1 d1 r1) (BezierSpline n2 d2 r2) (LSeq (1 + n1) (Point d1 r1)) (LSeq (1 + n2) (Point d2 r2))
fromPointSeq :: Seq (Point d r) -> BezierSpline n d r
evaluate :: (Arity d, Ord r, Num r) => BezierSpline n d r -> r -> Point d r
split :: forall n d r. (KnownNat n, Arity d, Ord r, Num r) => r -> BezierSpline n d r -> (BezierSpline n d r, BezierSpline n d r)
subBezier :: (KnownNat n, Arity d, Ord r, Num r) => r -> r -> BezierSpline n d r -> BezierSpline n d r
tangent :: (Arity d, Num r, 1 <= n) => BezierSpline n d r -> Vector d r
approximate :: forall n d r. (KnownNat n, Arity d, Ord r, Fractional r) => r -> BezierSpline n d r -> [Point d r]
parameterOf :: (Arity d, Ord r, Fractional r) => BezierSpline n d r -> Point d r -> r
snap :: (Arity d, Ord r, Fractional r) => BezierSpline n d r -> Point d r -> Point d r
pattern Bezier2 :: Point d r -> Point d r -> Point d r -> BezierSpline 2 d r
pattern Bezier3 :: Point d r -> Point d r -> Point d r -> Point d r -> BezierSpline 3 d r
colinear :: (Ord r, Fractional r) => r -> BezierSpline 3 2 r -> Bool
lineApproximate :: (Ord r, Fractional r) => r -> BezierSpline 3 2 r -> [Point 2 r]
quadToCubic :: Fractional r => BezierSpline 2 2 r -> BezierSpline 3 2 r

Documentation

newtype BezierSpline n d r Source #

Datatype representing a Bezier curve of degree $n$ in $d$-dimensional space.

Constructors

BezierSpline (LSeq (1 + n) (Point d r))

Instances

Instances details

Arity d => Functor (BezierSpline n d) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods fmap :: (a -> b) -> BezierSpline n d a -> BezierSpline n d b # (<$) :: a -> BezierSpline n d b -> BezierSpline n d a #
Arity d => Foldable (BezierSpline n d) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods fold :: Monoid m => BezierSpline n d m -> m # foldMap :: Monoid m => (a -> m) -> BezierSpline n d a -> m # foldMap' :: Monoid m => (a -> m) -> BezierSpline n d a -> m # foldr :: (a -> b -> b) -> b -> BezierSpline n d a -> b # foldr' :: (a -> b -> b) -> b -> BezierSpline n d a -> b # foldl :: (b -> a -> b) -> b -> BezierSpline n d a -> b # foldl' :: (b -> a -> b) -> b -> BezierSpline n d a -> b # foldr1 :: (a -> a -> a) -> BezierSpline n d a -> a # foldl1 :: (a -> a -> a) -> BezierSpline n d a -> a # toList :: BezierSpline n d a -> [a] # null :: BezierSpline n d a -> Bool # length :: BezierSpline n d a -> Int # elem :: Eq a => a -> BezierSpline n d a -> Bool # maximum :: Ord a => BezierSpline n d a -> a # minimum :: Ord a => BezierSpline n d a -> a # sum :: Num a => BezierSpline n d a -> a # product :: Num a => BezierSpline n d a -> a #
Arity d => Traversable (BezierSpline n d) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods traverse :: Applicative f => (a -> f b) -> BezierSpline n d a -> f (BezierSpline n d b) # sequenceA :: Applicative f => BezierSpline n d (f a) -> f (BezierSpline n d a) # mapM :: Monad m => (a -> m b) -> BezierSpline n d a -> m (BezierSpline n d b) # sequence :: Monad m => BezierSpline n d (m a) -> m (BezierSpline n d a) #
PointFunctor (BezierSpline n d) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods pmap :: (Point (Dimension (BezierSpline n d r)) r -> Point (Dimension (BezierSpline n d s)) s) -> BezierSpline n d r -> BezierSpline n d s Source #
(Arity d, Eq r) => Eq (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods (==) :: BezierSpline n d r -> BezierSpline n d r -> Bool # (/=) :: BezierSpline n d r -> BezierSpline n d r -> Bool #
(Arity d, Show r) => Show (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods showsPrec :: Int -> BezierSpline n d r -> ShowS # show :: BezierSpline n d r -> String # showList :: [BezierSpline n d r] -> ShowS #
(Arity n, Arity d, Arbitrary r) => Arbitrary (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods arbitrary :: Gen (BezierSpline n d r) # shrink :: BezierSpline n d r -> [BezierSpline n d r] #
(Fractional r, Arity d, Arity (d + 1), Arity n) => IsTransformable (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline Methods transformBy :: Transformation (Dimension (BezierSpline n d r)) (NumType (BezierSpline n d r)) -> BezierSpline n d r -> BezierSpline n d r Source #
type NumType (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline type NumType (BezierSpline n d r) = r
type Dimension (BezierSpline n d r) Source #
Instance details Defined in Data.Geometry.BezierSpline type Dimension (BezierSpline n d r) = d

controlPoints :: Iso (BezierSpline n1 d1 r1) (BezierSpline n2 d2 r2) (LSeq (1 + n1) (Point d1 r1)) (LSeq (1 + n2) (Point d2 r2)) Source #

Bezier control points. With n degrees, there are n+1 control points.

fromPointSeq :: Seq (Point d r) -> BezierSpline n d r Source #

Constructs the Bezier Spline from a given sequence of points.

evaluate :: (Arity d, Ord r, Num r) => BezierSpline n d r -> r -> Point d r Source #

Evaluate a BezierSpline curve at time t in [0, 1]

pre: $t \in [0,1]$

split :: forall n d r. (KnownNat n, Arity d, Ord r, Num r) => r -> BezierSpline n d r -> (BezierSpline n d r, BezierSpline n d r) Source #

Split a Bezier curve at time t in [0, 1] into two pieces.

subBezier :: (KnownNat n, Arity d, Ord r, Num r) => r -> r -> BezierSpline n d r -> BezierSpline n d r Source #

Restrict a Bezier curve to th,e piece between parameters t < u in [0, 1].

tangent :: (Arity d, Num r, 1 <= n) => BezierSpline n d r -> Vector d r Source #

Tangent to the bezier spline at the starting point.

approximate :: forall n d r. (KnownNat n, Arity d, Ord r, Fractional r) => r -> BezierSpline n d r -> [Point d r] Source #

Approximate Bezier curve by Polyline with given resolution.

parameterOf :: (Arity d, Ord r, Fractional r) => BezierSpline n d r -> Point d r -> r Source #

Given a point on (or close to) a Bezier curve, return the corresponding parameter value. (For points far away from the curve, the function will return the parameter value of an approximate locally closest point to the input point.)

snap :: (Arity d, Ord r, Fractional r) => BezierSpline n d r -> Point d r -> Point d r Source #

Snap a point close to a Bezier curve to the curve.

pattern Bezier2 :: Point d r -> Point d r -> Point d r -> BezierSpline 2 d r Source #

Quadratic Bezier Spline

pattern Bezier3 :: Point d r -> Point d r -> Point d r -> Point d r -> BezierSpline 3 d r Source #

Cubic Bezier Spline

colinear :: (Ord r, Fractional r) => r -> BezierSpline 3 2 r -> Bool Source #

Return True if the curve is definitely completely covered by a line of thickness twice the given tolerance. May return false negatives but not false positives.

lineApproximate :: (Ord r, Fractional r) => r -> BezierSpline 3 2 r -> [Point 2 r] Source #

Approximate curve as line segments where no point on the curve is further away from the nearest line segment than the given tolerance.

quadToCubic :: Fractional r => BezierSpline 2 2 r -> BezierSpline 3 2 r Source #

Convert a quadratic bezier to a cubic bezier.