Interpolation.h File Reference

Fractional-position interpolation for delay lines, tables and buffers. More...

#include "DspMath.h"
#include <cassert>
#include <cmath>

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Namespaces
namespace	dspark
	Main namespace for the DSPark framework.

Functions
template<FloatType T>
T	dspark::interpolateLinear (T y0, T y1, T frac) noexcept
	Linear interpolation between two adjacent samples.
template<FloatType T>
T	dspark::interpolateLinear (const T *buffer, int length, T position) noexcept
	Linear interpolation reading directly from a circular buffer.
template<FloatType T>
T	dspark::interpolateHermite (T y0, T y1, T y2, T y3, T frac) noexcept
	4-point, 3rd-order Hermite interpolation (optimized x-form).
template<FloatType T>
T	dspark::interpolateHermite (const T *buffer, int length, T position) noexcept
template<FloatType T>
T	dspark::interpolateCubic (const T *buffer, int length, T position) noexcept
	Alias of interpolateHermite (Catmull-Rom evaluated in Hermite form). Kept for backward compatibility.
template<FloatType T>
T	dspark::interpolateLagrange (T y0, T y1, T y2, T y3, T frac) noexcept
	4-point Lagrange interpolation from discrete samples.
template<FloatType T>
T	dspark::interpolateLagrange (const T *buffer, int length, T position) noexcept
template<FloatType T>
T	dspark::interpolateAllpass (T currentSample, T previousSample, T frac, T &state) noexcept
	Allpass interpolation (first-order Thiran) for fractional delay.

Detailed Description

Fractional-position interpolation for delay lines, tables and buffers.

4-point Lagrange interpolation reading directly from a circular buffer.

4-point Hermite interpolation reading directly from a circular buffer.

Free-function interpolators used across the framework (RingBuffer's interpolated reads, modulated delay lines). All of them are small scalar helpers that inline into the caller's loop; none allocates or locks.

Method	Points	Quality	CPU Cost	Use case
Linear	2	Low	Ultra-Low	LFOs, crossfades
Hermite	4	Good+	Low	Modulated delays (default)
Lagrange	4	High	Low	Precision fractional reads
Allpass	2	Frequency-dep	Low	Static fractional delays

Polynomial accuracy: Linear reconstructs degree-1 signals exactly, Hermite (Catmull-Rom) degree 2, Lagrange degree 3. Hermite is the recommended default for modulated delay lines (chorus, vibrato, reverb modulation): it is stateless and C1-continuous across segments, so fast frac changes never destabilise anything, unlike the recursive Allpass interpolator.

Two overload families:

• Raw-sample overloads (y0..y3, frac): no bounds logic at all, the fastest path. The container handles buffer wrapping (RingBuffer uses these).
• (buffer, length, position) overloads: treat the buffer as CIRCULAR; neighbours needed beyond either end wrap around to the other end. Meant for ring buffers and periodic tables. On a plain linear buffer, positions within one sample of the edges (4-point methods) blend in samples from the opposite end.

Threading: all functions are pure and re-entrant; the Allpass state lives in the caller. Real-time safe: no allocation, no locks, no modulo; the only floating-point division is the Allpass coefficient (one per call).

Dependencies: DspMath.h (FloatType concept).

Interpolates between buffer[floor(position)] and the next sample; the two outer neighbours wrap around the buffer ends (circular contract, see notes).

Parameters

buffer	Pointer to the start of the audio buffer.
length	Size of the buffer in samples (must be > 0).
position	Absolute read position.

Returns

Interpolated sample.

Precondition

0 <= position < length. Violations assert in debug builds; release builds clamp to the nearest valid sample (NaN reads position 0).

Definition in file Interpolation.h.