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namespace IStation.Numerics.Interpolation
{
    /// <summary>
    /// Interpolation within the range of a discrete set of known data points.
    /// </summary>
    public interface IInterpolation
    {
        /// <summary>
        /// Gets a value indicating whether the algorithm supports differentiation (interpolated derivative).
        /// </summary>
        bool SupportsDifferentiation { get; }

        /// <summary>
        /// Gets a value indicating whether the algorithm supports integration (interpolated quadrature).
        /// </summary>
        bool SupportsIntegration { get; }

        /// <summary>
        /// Interpolate at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated value x(t).</returns>
        double Interpolate(double t);

        /// <summary>
        /// Differentiate at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated first derivative at point t.</returns>
        double Differentiate(double t);

        /// <summary>
        /// Differentiate twice at point t.
        /// </summary>
        /// <param name="t">Point t to interpolate at.</param>
        /// <returns>Interpolated second derivative at point t.</returns>
        double Differentiate2(double t);

        /// <summary>
        /// Indefinite integral at point t.
        /// </summary>
        /// <param name="t">Point t to integrate at.</param>
        double Integrate(double t);

        /// <summary>
        /// Definite integral between points a and b.
        /// </summary>
        /// <param name="a">Left bound of the integration interval [a,b].</param>
        /// <param name="b">Right bound of the integration interval [a,b].</param>
        double Integrate(double a, double b);
    }
}