Math.Spline.Knots

Documentation

data Knots a

Knot vectors - multisets of points in a 1-dimensional space.

Instances

Foldable Knots

Eq a => Eq (Knots a)

Ord a => Ord (Knots a)

Show a => Show (Knots a)

Ord a => Monoid (Knots a)

empty :: Knots a

An empty knot vector

isEmpty :: Knots a -> Bool

knot :: Ord a => a -> Knots a

Create a knot vector consisting of one knot.

multipleKnot :: Ord a => a -> Int -> Knots a

Create a knot vector consisting of one knot with the specified multiplicity.

mkKnots :: Ord a => [a] -> Knots a

Create a knot vector consisting of all the knots in a list.

fromList :: Ord k => [(k, Int)] -> Knots k

Create a knot vector consisting of all the knots and corresponding multiplicities in a list.

numKnots :: Knots t -> Int

Returns the number of knots (not necessarily distinct) in a knot vector.

lookupKnot :: Int -> Knots a -> Maybe a

toList :: Eq k => Knots k -> [(k, Int)]

Returns a list of all distinct knots in ascending order along with their multiplicities.

numDistinctKnots :: Eq t => Knots t -> Int

Returns the number of distinct knots in a knot vector.

lookupDistinctKnot :: Eq a => Int -> Knots a -> Maybe a

knots :: Knots t -> [t]

Returns a list of all knots (not necessarily distinct) of a knot vector in ascending order

knotsVector :: Knots t -> Vector t

Returns a vector of all knots (not necessarily distinct) of a knot vector in ascending order

distinctKnots :: Eq t => Knots t -> [t]

Returns a list of all distinct knots of a knot vector in ascending order

multiplicities :: Eq t => Knots t -> [Int]

distinctKnotsVector :: Eq t => Knots t -> Vector t

Returns a vector of all distinct knots of a knot vector in ascending order

multiplicitiesVector :: Eq a => Knots a -> Vector Int

distinctKnotsSet :: Eq k => Knots k -> Set k

Returns a Set of all distinct knots of a knot vector

toMap :: Ord k => Knots k -> Map k Int

fromMap :: Eq k => Map k Int -> Knots k

toVector :: Eq k => Knots k -> Vector (k, Int)

fromVector :: Ord k => Vector (k, Int) -> Knots k

splitLookup :: Int -> Knots a -> (Knots a, Maybe a, Knots a)

splitLookup n kts: Split a knot vector kts into 3 parts (pre, mbKt, post) such that:

• All the keys in pre, mbKt (viewed as a knot vector of either 0 or 1 knot), and post are disjoint and ordered * Putting the 3 parts back together yields exactly the original knot vector * The n'th knot, if one exists, will be in mbKt along with its multiplicity

takeKnots :: Int -> Knots a -> Knots a

dropKnots :: Int -> Knots a -> Knots a

splitKnotsAt :: Int -> Knots a -> (Knots a, Knots a)

takeDistinctKnots :: Ord a => Int -> Knots a -> Knots a

dropDistinctKnots :: Ord a => Int -> Knots a -> Knots a

splitDistinctKnotsAt :: (Ord a, Eq a) => Int -> Knots a -> (Knots a, Knots a)

maxMultiplicity :: Ord t => Knots t -> Int

knotMultiplicity :: Ord k => k -> Knots k -> Int

Looks up the multiplicity of a knot (which is 0 if the point is not a knot)

setKnotMultiplicity :: Ord k => k -> Int -> Knots k -> Knots k

Returns a new knot vector with the given knot set to the specified multiplicity and all other knots unchanged.

splitFind :: Ord k => k -> Knots k -> (Knots k, Knots k, Knots k)

fromAscList :: Eq k => [(k, Int)] -> Knots k

Create a knot vector consisting of all the knots and corresponding multiplicities in a list ordered by the knots' Ord instance. The ordering precondition is not checked.

fromDistinctAscList :: Eq k => [(k, Int)] -> Knots k

Create a knot vector consisting of all the knots and corresponding multiplicities in a list ordered by the knots' Ord instance with no duplicates. The preconditions are not checked.

valid :: (Ord k, Num k) => Knots k -> Bool

Check the internal consistency of a knot vector

knotSpan :: Knots a -> Int -> Int -> Maybe (a, a)

knotSpan kts i j returns the knot span extending from the i'th knot to the j'th knot, if i <= j and both knots exist.

knotsInSpan :: Knots a -> Int -> Int -> Knots a

knotsInSpan kts i j returns the knots in the knot span extending from the i'th knot to the j'th knot

knotSpans :: Knots a -> Int -> [(a, a)]

knotSpans kts width returns all knot spans of a given width in ascending order.

For example, knotSpans (mkKnots [1..5]) 2 yields [(1,3), (2,4), (3,5)].

knotDomain :: Knots a -> Int -> Maybe (a, a)

knotDomain kts p returns the domain of a B-spline or NURBS with knot vector kts and degree p. This is the subrange spanned by all except the first and last p knots. Outside this domain, the spline does not have a complete basis set. De Boor's algorithm assumes that the basis functions sum to 1, which is only true on this range, and so this is also precisely the domain on which de Boor's algorithm is valid.

uniform :: (Ord s, Fractional s) => Int -> Int -> (s, s) -> Knots s

uniform deg nPts (lo,hi) constructs a uniformly-spaced knot vector over the interval from lo to hi which, when used to construct a B-spline with nPts control points will yield a clamped spline with degree deg.

minKnot :: Eq a => Knots a -> Maybe (a, Int)

maxKnot :: Eq a => Knots a -> Maybe (a, Int)