Safe Haskell | None |
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- class (VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline s v where
- splineDomain :: s v -> Maybe (Scalar v, Scalar v)
- evalSpline :: s v -> Scalar v -> v
- splineDegree :: s v -> Int
- knotVector :: s v -> Knots (Scalar v)
- toBSpline :: s v -> BSpline Vector v

- class Spline s v => ControlPoints s v where
- controlPoints :: s v -> Vector v

- data Knots a
- mkKnots :: Ord a => [a] -> Knots a
- knots :: Knots t -> [t]
- data BezierCurve t
- bezierCurve :: Vector t -> BezierCurve t
- data BSpline v t
- bSpline :: Vector v a => Knots (Scalar a) -> v a -> BSpline v a
- data MSpline v
- mSpline :: Knots (Scalar a) -> Vector a -> MSpline a
- toMSpline :: Spline s v => s v -> MSpline v
- data ISpline v
- iSpline :: Knots (Scalar a) -> Vector a -> ISpline a
- toISpline :: (Spline s v, Eq v) => s v -> ISpline v
- data CSpline a
- cSpline :: Ord (Scalar a) => [(Scalar a, a, a)] -> CSpline a

# 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`

.

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

(not
necessarily exactly, but up to reasonable expectations of numerical
accuracy).
`evalSpline`

. `toBSpline`

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

splineDegree :: s v -> IntSource

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

(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 | |

(VectorSpace a, Fractional (Scalar a), Ord (Scalar a)) => Spline CSpline a | |

(VectorSpace a, Fractional (Scalar a), Ord (Scalar a), Vector v a, Vector v (Scalar a)) => Spline (BSpline v) a | |

(VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline (BSpline Vector) v |

class Spline s v => ControlPoints s v whereSource

controlPoints :: s v -> Vector vSource

Spline BezierCurve v => ControlPoints BezierCurve v | |

Spline MSpline v => ControlPoints MSpline v | |

Spline ISpline v => ControlPoints ISpline v | |

(Spline (BSpline v) a, Vector v a) => ControlPoints (BSpline v) a | |

Spline (BSpline Vector) a => ControlPoints (BSpline Vector) a |

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

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

data BezierCurve t Source

A Bezier curve on `0 <= x <= 1`

.

Spline BezierCurve v => ControlPoints BezierCurve v | |

(VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline BezierCurve v | |

Eq t => Eq (BezierCurve t) | |

Ord t => Ord (BezierCurve t) | |

Show v => Show (BezierCurve v) |

bezierCurve :: Vector t -> BezierCurve tSource

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

A B-spline, defined by a knot vector (see `Knots`

) and a sequence of control points.

(Spline (BSpline v) a, Vector v a) => ControlPoints (BSpline v) a | |

Spline (BSpline Vector) a => ControlPoints (BSpline Vector) a | |

(VectorSpace a, Fractional (Scalar a), Ord (Scalar a), Vector v a, Vector v (Scalar a)) => Spline (BSpline v) a | |

(VectorSpace v, Fractional (Scalar v), Ord (Scalar v)) => Spline (BSpline Vector) v | |

(Eq (Scalar a), Eq (v a)) => Eq (BSpline v a) | |

(Ord (Scalar a), Ord (v a)) => Ord (BSpline v a) | |

(Show (Scalar a), Show a, Show (v a)) => Show (BSpline v a) |

bSpline :: Vector v a => Knots (Scalar a) -> v a -> BSpline v 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`

).

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

mSpline :: Knots (Scalar a) -> Vector 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`

).

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.

iSpline :: Knots (Scalar a) -> Vector 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`

).

Cubic Hermite splines. These are cubic splines defined by a sequence of control points and derivatives at those points.

(VectorSpace a, Fractional (Scalar a), Ord (Scalar a)) => Spline CSpline a |