Interpolation

Interpolation is a fundamental technique in numerical analysis used to estimate unknown values between known data points. It plays a crucial role in various fields of engineering and science, where accurate data representation is essential for analysis and decision-making. In SepalSolver, we implement various interpolation methods to provide engineers with tools for approximating functions and datasets.

Interpolation techniques are widely used in applications such as computer graphics, signal processing, and data fitting. They help in reconstructing continuous functions from discrete data, enabling better visualization and analysis of complex phenomena.

In this chapter, we will explore different interpolation methods, their implementations in SepalSolver, and practical examples demonstrating their applications.

• Linear Interpolation
  • Linear Interpolation
    • 1. The Mathematical Formula
    • 2. Implementation in SepalSolver
  • Examples
    • Exercise: Manual Implementation
  • 2D Linear Interpolation (Interp2)
    • 1. How it Works
    • 2. Data Structure
  • Examples
• Interpolation by Polynomial
  • Interpolation via Polynomial Fitting
    • 1. The Strategy
    • 2. Global vs. Local Interpolation
  • Examples
    • Exercise: Choosing the Degree
    • Multivariate Application
• Hemite Spline
  • Hermite Interpolation
    • 1. The Cubic Hermite Spline
    • 2. Implementation in SepalSolver
  • Examples
    • Key Difference: Hermite vs. Cubic Spline
    • Exercise: Animation of Slope Impact
• Bezier Spline
  • Bézier Splines
    • 1. The Mathematical Formula (Quadratic)
    • 2. Implementation in SepalSolver
  • Examples
• Exercise On Interpolation