Data.Geometry.BezierSpline

Documentation

newtype BezierSpline n d r

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)

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)

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)

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)

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

(Arity d, Eq r) => Eq (BezierSpline n d r)

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)

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)

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)

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

type NumType (BezierSpline n d r)

Defined in Data.Geometry.BezierSpline

type NumType (BezierSpline n d r) = r

type Dimension (BezierSpline n d r)

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))

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

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

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

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)

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

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

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]

Approximate Bezier curve by Polyline with given resolution.

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

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

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

Quadratic Bezier Spline

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

Cubic Bezier Spline

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

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]

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

Convert a quadratic bezier to a cubic bezier.