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)

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.

knots :: Knots t -> [t]

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

numKnots :: Knots t -> Int

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

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

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

distinctKnots :: Knots t -> [t]

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

numDistinctKnots :: Knots t -> Int

Returns the number of distinct knots in a knot vector.

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.

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

knotDomain kts p return 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.