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Session 7
Numerical Methods

Spline Interpolation and Curve Fitting

3.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Advanced interpolation techniques using cubic splines, B-splines, and least squares curve fitting. Natural and clamped boundary conditions, spline properties, and applications in computer graphics.

Learning Objectives
By the end of this session, you should be able to:
  • Derive and implement natural cubic spline interpolation
  • Understand clamped and not-a-knot boundary conditions for splines
  • Master the construction of cubic spline systems and their solution
  • Apply B-spline basis functions for flexible curve representation
  • Implement least squares polynomial fitting for overdetermined systems
  • Compare spline interpolation with polynomial interpolation advantages
Course Materials
Download materials for offline study and reference
Spline Theory and Mathematical Foundations (42 pages)
Available material
Cubic Spline Implementation Algorithms
Available material
Boundary Condition Analysis and Applications
Available material
B-spline Basis Functions and Properties
Available material
Least Squares Curve Fitting Methods
Available material
Computer Graphics Applications
Available material
Spline Construction Programming Project
Available material
Comparative Analysis of Interpolation Methods
Available material