splines-0.1: B-Splines, other splines, and NURBS.

Math.Spline

Synopsis

# Documentation

class (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline s v whereSource

A spline is a piecewise polynomial vector-valued function. The necessary and sufficient instance definition is `toBSpline`.

Methods

splineDomain :: s v -> Maybe (Scalar v, Scalar v)Source

Returns the domain of a spline. In the case of B-splines, this is the domain on which a spline with this degree and knot vector has a full basis set. In other cases, it should be no larger than `splineDomain . toBSpline`, but may be smaller. Within this domain, `evalSpline` should agree with `evalSpline . toBSpline` (not necessarily exactly, but up to reasonable expectations of numerical accuracy).

evalSpline :: s v -> Scalar v -> vSource

splineDegree :: s v -> IntSource

knotVector :: s v -> Knots (Scalar v)Source

toBSpline :: s v -> BSpline vSource

Instances

 (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline BSpline v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline BezierCurve v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline MSpline v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline ISpline v

data Knots a Source

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)

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

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

knots :: Knots t -> [t]Source

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

data BezierCurve v Source

A BezierCurve curve on `0 <= x <= 1`.

Instances

 Spline BezierCurve v => ControlPoints BezierCurve v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline BezierCurve v Eq v => Eq (BezierCurve v) Ord v => Ord (BezierCurve v) Show v => Show (BezierCurve v)

bezierCurve :: [v] -> BezierCurve vSource

Construct a Bezier curve from a list of control points. The degree of the curve is one less than the number of control points.

data BSpline v Source

Instances

 Spline BSpline v => ControlPoints BSpline v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline BSpline v (Eq (Scalar v), Eq v) => Eq (BSpline v) (Ord (Scalar v), Ord v) => Ord (BSpline v) (Show (Scalar v), Show v) => Show (BSpline v)

bSpline :: Knots (Scalar a) -> [a] -> BSpline aSource

`bSpline kts cps` creates a B-spline with the given knot vector and control points. The degree is automatically inferred as the difference between the number of spans in the knot vector (`numKnots kts - 1`) and the number of control points (`length cps`).

data MSpline v Source

M-Splines are B-splines normalized so that the integral of each basis function over the spline domain is 1.

Instances

 Spline MSpline v => ControlPoints MSpline v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline MSpline v (Eq (Scalar v), Eq v) => Eq (MSpline v) (Ord (Scalar v), Ord v) => Ord (MSpline v) (Show (Scalar v), Show v) => Show (MSpline v)

mSpline :: Knots (Scalar a) -> [a] -> MSpline aSource

`mSpline kts cps` creates a M-spline with the given knot vector and control points. The degree is automatically inferred as the difference between the number of spans in the knot vector (`numKnots kts - 1`) and the number of control points (`length cps`).

toMSpline :: Spline s v => s v -> MSpline vSource

data ISpline v Source

The I-Spline basis functions are the integrals of the M-splines, or alternatively the integrals of the B-splines normalized to the range [0,1]. Every I-spline basis function increases monotonically from 0 to 1, thus it is useful as a basis for monotone functions. An I-Spline curve is monotone if and only if every non-zero control point has the same sign.

Instances

 Spline ISpline v => ControlPoints ISpline v (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline ISpline v (Eq (Scalar v), Eq v) => Eq (ISpline v) (Ord (Scalar v), Ord v) => Ord (ISpline v) (Show (Scalar v), Show v) => Show (ISpline v)

iSpline :: Knots (Scalar a) -> [a] -> ISpline aSource

`iSpline kts cps` creates an I-spline with the given knot vector and control points. The degree is automatically inferred as the difference between the number of spans in the knot vector (`numKnots kts - 1`) and the number of control points (`length cps`).

toISpline :: (Spline s v, Eq v) => s v -> ISpline vSource