Table of Contents

Interface IInterpolation<T>

Namespace
AiDotNet.Interfaces
Assembly
AiDotNet.dll

Defines an interface for interpolation algorithms that estimate values between known data points.

public interface IInterpolation<T>

Type Parameters

T

The numeric type used for calculations (e.g., double, float).

Remarks

For Beginners: This interface defines a method for "filling in the gaps" between known data points.

Imagine you have a few data points:

  • You know that at 9:00 AM, the temperature was 65°F
  • You know that at 12:00 PM, the temperature was 75°F
  • But you don't have a measurement for 10:30 AM

Interpolation helps you make a reasonable guess about that missing value. It's like drawing a smooth line through your known points and then reading the value at any position along that line.

Common types of interpolation include:

  • Linear: Draws straight lines between points (like connecting dots)
  • Polynomial: Creates smooth curves that pass through all points
  • Spline: Creates a series of curves that connect smoothly
  • Nearest neighbor: Uses the value of the closest known point

Interpolation is used in many AI applications:

  • Filling gaps in time series data
  • Creating smooth transitions in animations
  • Estimating values between training examples
  • Generating new data points based on existing ones

Methods

Interpolate(T)

Calculates an interpolated value at the specified point.

T Interpolate(T x)

Parameters

x T

The point at which to interpolate.

Returns

T

The interpolated value at point x.

Remarks

For Beginners: This method estimates a value at a specific point using surrounding known data points.

The parameter:

  • x: The point where you want to estimate a value (like asking "what was the temperature at 10:30 AM?")

What this method does:

  1. Takes your input point (x)
  2. Looks at the known data points that were used to create this interpolator
  3. Applies a mathematical formula to estimate the value at your requested point
  4. Returns that estimated value

Different implementations of this interface will use different mathematical techniques to make this estimation, which affects how smooth or accurate the results are.

For example:

  • Linear interpolation draws straight lines between points
  • Cubic interpolation creates smoother curves
  • Spline interpolation ensures smooth transitions between segments

The type parameter T could be a simple number (like double) for 1D interpolation, or it could be a more complex type for multi-dimensional interpolation.

Edit this page