page_title: Cubic Hermite spline
section_title: Finite difference
hierarchical_section_title: Cubic Hermite spline / Interpolating a data set / Finite difference
caption_attribution_description: English: Example for en:Cubic_Hermite_spline
context_page_description: In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the corresponding domain interval.
  Cubic Hermite splines are typically used for interpolation of numeric data specified at given argument values, to obtain a continuous function. The data should consist of the desired function value and derivative at each. The Hermite formula is applied to each interval separately. The resulting spline will be continuous and will have continuous first derivative.
  Cubic polynomial splines can be specified in other ways, the Bezier cubic being the most common. However, these two methods provide the same set of splines, and data can be easily converted between the Bézier and Hermite forms; so the names are often used as if they were synonymous.
  Cubic polynomial splines are extensively used in computer graphics and geometric modeling to obtain curves or motion trajectories that pass through specified points of the plane or three-dimensional space.
context_section_description: The simplest choice is the three-point difference, not requiring constant interval lengths,
  for internal points , and one-sided difference at the endpoints of the data set.
caption: Example with finite difference tangents
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