Linear.NURBS

Documentation

binomial :: Integral a => a -> a -> a

size :: (Additive f, Floating a, Foldable f) => f a -> a

data Weight f a

Constructors

Weight (f a) a

Instances

Functor f => Functor (Weight f)

Foldable f => Foldable (Weight f)

Affine f => Affine (Weight f)

Metric f => Metric (Weight f)

Additive f => Additive (Weight f)

(Eq a, Eq (f a)) => Eq (Weight f a)

(Ord a, Ord (f a)) => Ord (Weight f a)

(Read a, Read (f a)) => Read (Weight f a)

(Show a, Show (f a)) => Show (Weight f a)

(Metric f, Ord a, Floating a, SimEq a) => SimEq (Weight f a)

type Diff (Weight f) = Weight (Diff f)

ofWeight :: Additive f => f a -> a -> Weight f a

weight :: (Additive f, Fractional a) => Lens' (Weight f a) a

wpoint :: (Additive f, Additive g, Fractional a) => Lens (Weight f a) (Weight g a) (f a) (g a)

data Span a

Constructors

Span

Fields

_spanStart :: a

_spanEnd :: a

Instances

Eq a => Eq (Span a)

Ord a => Ord (Span a)

Read a => Read (Span a)

Show a => Show (Span a)

spanStart :: forall a. Lens' (Span a) a

spanEnd :: forall a. Lens' (Span a) a

spanId :: (Ord a, Num a) => a -> Span a -> a

Piecewise constant function, returns 1 in span, 0 otherwise

grow :: (Ord a, Fractional a) => a -> Span a -> a

Grow within span from 0 to 1

fall :: (Ord a, Fractional a) => a -> Span a -> a

Fall function, opposite to grow

coords :: (Eq a, Fractional a) => Span a -> Iso' a a

Map value to span coordinates, span start mapped to 0, end to 1

rangeSpan :: [a] -> Span a

Make span from knot vector

mergeSpan :: Ord a => Span a -> Span a -> Span a

Merge spans

knotSpans :: Int -> [a] -> [Span a]

Generate knot spans of degree

growSpans :: Int -> [a] -> [Span a]

Generate drow spans of degree

fallSpans :: Int -> [a] -> [Span a]

Generate fall spans of degree

data KnotData a

Knot evaluation data

Constructors

KnotData a [(Span a, a)]

Instances

Eq a => Eq (KnotData a)

Ord a => Ord (KnotData a)

Read a => Read (KnotData a)

Show a => Show (KnotData a)

knotData :: Lens' (KnotData a) [(Span a, a)]

makeData :: (Ord a, Num a) => [a] -> a -> KnotData a

Make initial knot data

iterData :: (Ord a, Fractional a) => KnotData a -> KnotData a

Eval basis function for next degree

evalData :: (Ord a, Fractional a) => Int -> KnotData a -> KnotData a

Eval for n degree

basis :: (Ord a, Fractional a) => [a] -> Int -> Int -> a -> a

Nᵢ,ₙ — n-degree basis function for i-th control point

rbasis :: (Ord a, Fractional a) => [a] -> [a] -> Int -> Int -> a -> a

Rᵢ,ₙ — n-degree rational basis function for i-th control point

data NURBS f a

Constructors

NURBS [Weight f a] [a]

Instances

(Eq a, Eq (f a)) => Eq (NURBS f a)

(Ord a, Ord (f a)) => Ord (NURBS f a)

(Read a, Read (f a)) => Read (NURBS f a)

(Show a, Show (f a)) => Show (NURBS f a)

(Metric f, Ord a, Floating a, SimEq (f a)) => SimEq (NURBS f a)

eval :: (Additive f, Ord a, Fractional a) => NURBS f a -> a -> f a

Evaluate nurbs point

uniformKnot :: Fractional a => Int -> Int -> [a]

Generate knot of degree for points

degree :: Fractional a => Lens' (NURBS f a) Int

wpoints :: Fractional a => Lens (NURBS f a) (NURBS g a) [Weight f a] [Weight g a]

knotVector :: Eq a => Lens' (NURBS f a) [a]

iknotVector :: (Eq a, Fractional a) => Lens' (NURBS f a) [a]

knotSpan :: (Eq a, Fractional a) => Lens' (NURBS f a) (Span a)

normalizeKnot :: (Eq a, Fractional a) => NURBS f a -> NURBS f a

nurbs :: (Additive f, Fractional a) => Int -> [f a] -> NURBS f a

Make nurbs of degree from points

wnurbs :: (Additive f, Fractional a) => Int -> [Weight f a] -> NURBS f a

Make nurbs of degree from weighted points

insertKnot :: (Additive f, Ord a, Fractional a) => a -> NURBS f a -> NURBS f a

Insert knot

insertKnots :: (Additive f, Ord a, Fractional a) => [(Int, a)] -> NURBS f a -> NURBS f a

Insert knots

appendPoint :: (Eq a, Fractional a) => a -> Weight f a -> NURBS f a -> NURBS f a

Append point

prependPoint :: (Eq a, Fractional a) => a -> Weight f a -> NURBS f a -> NURBS f a

Prepend point

split :: (Additive f, Ord a, Fractional a) => a -> NURBS f a -> (NURBS f a, NURBS f a)

Split NURBS

cut :: (Additive f, Ord a, Fractional a) => Span a -> NURBS f a -> NURBS f a

Cut NURBS

removeKnot :: (Foldable f, Additive f, Ord a, Floating a, SimEq (NURBS f a)) => a -> NURBS f a -> Maybe (NURBS f a)

Remove knot

removeKnot_ :: (Foldable f, Additive f, Ord a, Floating a, SimEq (NURBS f a)) => a -> NURBS f a -> NURBS f a

Try remove knot

removeKnots :: (Foldable f, Additive f, Ord a, Floating a, SimEq (NURBS f a)) => [(Int, a)] -> NURBS f a -> NURBS f a

Remove knots

purgeKnots :: (Foldable f, Additive f, Ord a, Floating a, SimEq (NURBS f a)) => NURBS f a -> NURBS f a

Try remove knots

ndist :: (Metric f, Ord a, Floating a) => f a -> f a -> a

class SimEq a where

Minimal complete definition

Nothing

Methods

(≃) :: a -> a -> Bool

(≄) :: a -> a -> Bool

Instances

(Ord a, Floating a) => SimEq a

(Metric f, Ord a, Floating a, SimEq a) => SimEq (f a)

SimEq a => SimEq (Maybe a)

(Metric f, Ord a, Floating a, SimEq a) => SimEq (Weight f a)

(Metric f, Ord a, Floating a, SimEq (f a)) => SimEq (NURBS f a)

joint :: (Ord a, Num a, Floating a, Foldable f, Metric f, SimEq (Weight f a), SimEq (NURBS f a)) => NURBS f a -> NURBS f a -> Maybe (NURBS f a)

(⊕) :: (Ord a, Num a, Floating a, Foldable f, Metric f, SimEq (Weight f a), SimEq (NURBS f a)) => NURBS f a -> NURBS f a -> Maybe (NURBS f a)