Cubic spline interpolation for smooth curves through discrete data points. More...

#include <gin_spline.h>

Classes
class	Element

Public Member Functions
	Spline (const juce::Array< Point< double > > &points)

double	operator[] (double x) const

double	interpolate (double x) const

Detailed Description

Cubic spline interpolation for smooth curves through discrete data points.

Spline provides cubic spline interpolation, creating a smooth curve that passes through all given data points. Unlike linear interpolation, cubic splines have continuous first and second derivatives (C1 and C2 continuity), resulting in very smooth, natural-looking curves.

Cubic spline interpolation is ideal for:

Smooth animation curves
Data visualization and smoothing
Upsampling discrete data
Creating smooth parameter transitions
Generating lookup tables

Key Features:

C1 and C2 continuity (smooth first and second derivatives)
Passes exactly through all input points
Efficient evaluation using piecewise cubic polynomials
Natural boundary conditions
Operator[] syntax for convenient evaluation

Important: Points must be added in increasing x order.

Usage:

juce::Array<Point<double>> points;
points.add({0.0, 0.0});
points.add({1.0, 2.5});
points.add({2.0, 1.8});
points.add({3.0, 4.0});
points.add({4.0, 3.2});
 
Spline spline(points);
 
// Interpolate at any x position
double y1 = spline[1.5];      // Using operator[]
double y2 = spline.interpolate(2.7);  // Using interpolate()
 
// Evaluate many points for smooth curve
for (double x = 0.0; x <= 4.0; x += 0.1)
{
    double y = spline[x];
    // ... use interpolated value
}