`DataInterpolations.AkimaInterpolation`

— Type`AkimaInterpolation(u, t; extrapolate = false)`

It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: https://en.wikipedia.org/wiki/Akima_spline. Extrapolation extends the last cubic polynomial on each side.

**Arguments**

`u`

: data points.`t`

: time points.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.BSplineApprox`

— Type`BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = false)`

It is a regression based B-spline. The argument choices are the same as the `BSplineInterpolation`

, with the additional parameter `h < length(t)`

which is the number of control points to use, with smaller `h`

indicating more smoothing. For more information, refer http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf. Extrapolation is a constant polynomial of the end points on each side.

**Arguments**

`u`

: data points.`t`

: time points.`d`

: degree of the piecewise polynomial.`h`

: number of control points to use.`pVecType`

: symbol to parameters vector,`:Uniform`

for uniform spaced parameters and`:ArcLen`

for parameters generated by chord length method.`knotVecType`

: symbol to knot vector,`:Uniform`

for uniform knot vector,`:Average`

for average spaced knot vector.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.BSplineInterpolation`

— Type`BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolate = false)`

It is a curve defined by the linear combination of `n`

basis functions of degree `d`

where `n`

is the number of data points. For more information, refer https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html. Extrapolation is a constant polynomial of the end points on each side.

**Arguments**

`u`

: data points.`t`

: time points.`d`

: degree of the piecewise polynomial.`pVecType`

: symbol to parameters vector,`:Uniform`

for uniform spaced parameters and`:ArcLen`

for parameters generated by chord length method.`knotVecType`

: symbol to knot vector,`:Uniform`

for uniform knot vector,`:Average`

for average spaced knot vector.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.ConstantInterpolation`

— Type`ConstantInterpolation(u, t; dir = :left, extrapolate = false)`

It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on `dir`

. If it is `:left`

, then the value at the left point is chosen and if it is `:right`

, the value at the right point is chosen. Extrapolation extends the last constant polynomial at the end points on each side.

**Arguments**

`u`

: data points.`t`

: time points.

**Keyword Arguments**

`dir`

: indicates which value should be used for interpolation (`:left`

or`:right`

).`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.CubicSpline`

— Type`CubicSpline(u, t; extrapolate = false)`

It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous. Second derivative on both ends are zero, which are also called "natural" boundary conditions. Extrapolation extends the last cubic polynomial on each side.

**Arguments**

`u`

: data points.`t`

: time points.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.LagrangeInterpolation`

— Type`LagrangeInterpolation(u, t, n = length(t) - 1; extrapolate = false)`

It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.

**Arguments**

`u`

: data points.`t`

: time points.`n`

: order of the polynomial. Currently only (k-1)th order where k is the number of data points.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.LinearInterpolation`

— Type`LinearInterpolation(u, t; extrapolate = false)`

It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line. Extrapolation extends the last linear polynomial on each side.

**Arguments**

`u`

: data points.`t`

: time points.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.QuadraticInterpolation`

— Type`QuadraticInterpolation(u, t, mode = :Forward; extrapolate = false)`

It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial. Extrapolation extends the last quadratic polynomial on each side.

**Arguments**

`u`

: data points.`t`

: time points.`mode`

:`:Forward`

or`:Backward`

. If`:Forward`

, two data points ahead of the point and one data point behind is taken for interpolation. If`:Backward`

, two data points behind and one ahead is taken for interpolation.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.

`DataInterpolations.QuadraticSpline`

— Type`QuadraticSpline(u, t; extrapolate = false)`

It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous. Extrapolation extends the last quadratic polynomial on each side.

**Arguments**

`u`

: data points.`t`

: time points.

**Keyword Arguments**

`extrapolate`

: boolean value to allow extrapolation. Defaults to`false`

.