Safe Haskell	None
Language	Haskell2010

Data.Geometry.BezierSpline

Synopsis

newtype BezierSpline n d r = BezierSpline (LSeq (1 + n) (Point d r))
controlPoints :: forall n d r n d r. Iso (BezierSpline n d r) (BezierSpline n d r) (LSeq ((+) 1 n) (Point d r)) (LSeq ((+) 1 n) (Point d r))
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

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

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 # 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 :: forall n d r n d r. Iso (BezierSpline n d r) (BezierSpline n d r) (LSeq ((+) 1 n) (Point d r)) (LSeq ((+) 1 n) (Point d r)) Source #

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 #

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