C++ Interpolation & Spline Libraries: tinyspline vs Eigen Splines vs Boost.Math vs GSL

Interpolation — estimating values between known data points — is fundamental to scientific computing, game development, robotics, and data visualization. Whether you’re smoothing sensor data, generating animation curves, or fitting experimental measurements, the quality of your interpolation library directly impacts result accuracy. This guide compares four C++ interpolation and spline libraries: tinyspline, Eigen’s Spline module, Boost.Math Interpolation, and the GNU Scientific Library (GSL).

Why C++ Interpolation Libraries Matter

Numerical interpolation appears in virtually every engineering and scientific domain:

• Robotics and control systems — trajectory planning between waypoints
• Game development — smooth camera movement, animation blending
• Data science — resampling time-series data to uniform intervals
• CAD/CAM — NURBS surface fitting for manufacturing
• Signal processing — reconstructing continuous signals from discrete samples

Choosing a library involves tradeoffs between accuracy (how closely the interpolant matches the true function), performance (evaluation speed for real-time use), curve types (linear, polynomial, spline, NURBS), and API ergonomics (header-only vs system library).

tinyspline: Lightweight B-Spline and NURBS Library

tinyspline (1,339 stars) is an ANSI C library with C++, C#, Java, Lua, and Python bindings. It provides the most complete NURBS and B-Spline support among the four libraries and handles arbitrary-dimensional curves.

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#include <tinysplinecxx.h>
#include <vector>
#include <iostream>

int main() {
    // Define control points for a 2D B-spline
    std::vector<double> ctrlp = {
        0.0, 0.0,   // P0
        1.0, 2.0,   // P1
        3.0, 1.0,   // P2
        4.0, 3.0,   // P3
        6.0, 2.0    // P4
    };
    
    // Create a cubic B-spline with 5 control points in 2D
    auto spline = ts::BSpline::interpolate(ctrlp, 2)
        .degree(3);
    
    // Evaluate at parameter t = 0.5
    auto result = spline.evaluate(0.5).result();
    std::cout << "Point at t=0.5: (" 
              << result[0] << ", " << result[1] << ")\n";
    
    // Get first derivative (velocity)
    auto deriv = spline.derive();
    auto vel = deriv.evaluate(0.5).result();
    std::cout << "Velocity at t=0.5: (" 
              << vel[0] << ", " << vel[1] << ")\n";
    
    // Sample 100 points along the curve
    for (size_t i = 0; i <= 100; i++) {
        double t = static_cast<double>(i) / 100.0;
        auto pt = spline.evaluate(t).result();
        // Use pt[0], pt[1] for rendering
    }
    
    return 0;
}

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# CMake integration for tinyspline
include(FetchContent)
FetchContent_Declare(tinyspline
    GIT_REPOSITORY https://github.com/msteinbeck/tinyspline.git
    GIT_TAG v0.6.0)
FetchContent_MakeAvailable(tinyspline)
target_link_libraries(my_app PRIVATE tinysplinecxx)

tinyspline’s standout feature is arbitrary-dimensional interpolation — you can interpolate 3D position+orientation paths for robotics, 4D color+alpha ramps for rendering, or N-dimensional parameter spaces for optimization.

Eigen Splines: Header-Only, High-Performance

Eigen’s unsupported Spline module provides B-Spline and Bezier curve fitting using Eigen’s optimized linear algebra backend. As a header-only library, integration requires only an include path.

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#include <Eigen/Dense>
#include <unsupported/Eigen/Splines>
#include <vector>
#include <iostream>

int main() {
    typedef Eigen::Spline<double, 1> Spline1D;
    typedef Eigen::SplineFitting<Spline1D> Fitting;
    
    // Data points for 1D interpolation
    std::vector<double> x = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    std::vector<double> y = {0.0, 2.1, 1.3, 3.5, 4.2, 3.8};
    
    // Convert to Eigen vectors
    Eigen::VectorXd xe = Eigen::Map<Eigen::VectorXd>(x.data(), x.size());
    Eigen::RowVectorXd ye = Eigen::Map<Eigen::RowVectorXd>(y.data(), y.size());
    
    // Fit a cubic B-spline with 3 internal knots
    const int degree = 3;
    auto spline = Fitting::Interpolate(ye, degree, xe);
    
    // Evaluate at arbitrary points
    Eigen::RowVectorXd query(1);
    query << 2.5;
    Eigen::RowVectorXd result;
    result = spline(query);
    std::cout << "Interpolated at x=2.5: " << result(0) << "\n";
    
    // Derivatives
    auto deriv = spline.derivatives(query, 1);
    std::cout << "Value+Derivative: " << deriv << "\n";
    
    return 0;
}

Eigen Splines excel in performance-critical applications thanks to Eigen’s SIMD-optimized matrix operations. The API is Eigen-idiomatic, making it natural for projects already using Eigen for linear algebra. The main limitation is lack of NURBS support and restriction to 1D curves.

Boost.Math Interpolation: The C++ Standard Library Companion

Boost.Math provides several interpolation methods including barycentric rational interpolation, cubic B-spline interpolation, and Whittaker-Shannon (sinc) interpolation:

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#include <boost/math/interpolators/barycentric_rational.hpp>
#include <boost/math/interpolators/cubic_b_spline.hpp>
#include <boost/math/interpolators/whittaker_shannon.hpp>
#include <vector>
#include <iostream>

int main() {
    // ---- Barycentric Rational Interpolation ----
    std::vector<double> x = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
    std::vector<double> y = {0.0, 2.1, 1.3, 3.5, 4.2, 3.8};
    
    using boost::math::interpolators::barycentric_rational;
    auto interpolator = barycentric_rational<double>(
        x.data(), y.data(), x.size(), 3  // order = 3
    );
    
    double val = interpolator(2.5);
    std::cout << "Barycentric at x=2.5: " << val << "\n";
    
    // ---- Cubic B-Spline ----
    using boost::math::interpolators::cubic_b_spline;
    auto spline = cubic_b_spline<double>(
        y.data(), y.size(), 0.0, 1.0  // t0, step
    );
    
    double spline_val = spline(2.5);
    double spline_deriv = spline.prime(2.5);
    std::cout << "B-Spline: " << spline_val 
              << ", deriv: " << spline_deriv << "\n";
    
    // ---- Whittaker-Shannon (bandlimited) interpolation ----
    using boost::math::interpolators::whittaker_shannon;
    double data[] = {0.5, 1.2, -0.3, 0.8, -0.1};
    auto ws = whittaker_shannon<double>(data, 5, 0.5);
    
    std::cout << "Whittaker-Shannon at 1.7: " << ws(1.7) << "\n";
    
    return 0;
}

Boost.Math interpolation is ideal for scientific C++ applications that already depend on Boost. The barycentric rational interpolator is particularly good at avoiding Runge’s phenomenon (oscillation at interval edges) that plagues high-degree polynomial interpolation.

GSL Splines: Battle-Tested Scientific Computing

The GNU Scientific Library (GSL) provides cubic spline, Akima spline, and Steffen spline interpolation through a well-tested C API:

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#include <gsl/gsl_spline.h>
#include <gsl/gsl_interp.h>
#include <vector>
#include <iostream>

int main() {
    const size_t n = 10;
    double x[n] = {0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5};
    double y[n] = {0.0, 0.48, 0.84, 1.0, 0.91, 0.6, 0.14, -0.35, -0.76, -0.96};
    
    // ---- Cubic Spline ----
    auto* cubic_acc = gsl_interp_accel_alloc();
    auto* cubic_spline = gsl_spline_alloc(gsl_interp_cspline, n);
    gsl_spline_init(cubic_spline, x, y, n);
    
    double result = gsl_spline_eval(cubic_spline, 2.3, cubic_acc);
    std::cout << "Cubic at x=2.3: " << result << "\n";
    
    // ---- Akima Spline (avoids overshoot) ----
    auto* akima_spline = gsl_spline_alloc(gsl_interp_akima, n);
    gsl_spline_init(akima_spline, x, y, n);
    double akima_val = gsl_spline_eval(akima_spline, 2.3, cubic_acc);
    std::cout << "Akima at x=2.3: " << akima_val << "\n";
    
    // ---- Steffen Spline (monotonicity-preserving) ----
    auto* steffen_spline = gsl_spline_alloc(gsl_interp_steffen, n);
    gsl_spline_init(steffen_spline, x, y, n);
    double steffen_val = gsl_spline_eval(steffen_spline, 2.3, cubic_acc);
    std::cout << "Steffen at x=2.3: " << steffen_val << "\n";
    
    // Derivative
    double deriv = gsl_spline_eval_deriv(akima_spline, 2.3, cubic_acc);
    std::cout << "Akima derivative: " << deriv << "\n";
    
    // Cleanup
    gsl_spline_free(cubic_spline);
    gsl_spline_free(akima_spline);
    gsl_spline_free(steffen_spline);
    gsl_interp_accel_free(cubic_acc);
    
    return 0;
}

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# Install GSL on Debian/Ubuntu
sudo apt install libgsl-dev

# Install GSL on macOS
brew install gsl

GSL’s Akima spline is particularly useful for experimental physics and engineering data where ordinary cubic splines produce unrealistic oscillations between data points. The Steffen spline preserves monotonicity — critical when interpolating cumulative distribution functions or physical quantities that must be non-decreasing.

Choosing the Right Interpolation Library

Use tinyspline when you need NURBS curves, multi-dimensional control points, or language bindings beyond C++. It’s the only option for 3D path planning, surface fitting, and CAD-oriented applications.

Use Eigen Splines if your project already depends on Eigen and you need header-only integration with SIMD acceleration. The clean Eigen-idiomatic API makes it natural for robotics and computer vision pipelines.

Use Boost.Math Interpolation for scientific C++ projects that already use Boost libraries. The barycentric rational interpolator provides excellent accuracy without overshoot, and the Whittaker-Shannon interpolator is ideal for bandlimited signal reconstruction.

Use GSL Splines when reliability and numerical stability are paramount — GSL has been validated across decades of scientific computing. The Akima and Steffen spline types address specific failure modes (overshoot, non-monotonicity) that general-purpose splines exhibit.

Why Self-Host Your Interpolation Pipeline

Numerical interpolation is a computational primitive that appears throughout your codebase — in sensor fusion, path planning, data visualization, and simulation. Choosing the right library affects not just accuracy but also predictability: self-hosting the interpolation implementation means deterministic behavior across platforms, no cloud dependency, and full control over numerical edge cases.

For teams building robotics and control systems, interpolation quality directly affects physical safety margins. A poorly chosen spline type can produce overshoot that causes a robot arm to exceed joint limits or a drone to fly an unsafe trajectory.

If you’re working with numerical optimization to fit interpolation parameters, see our numerical optimization engines guide. For mathematical computing platforms that include interpolation as part of a broader toolkit, check out our mathematical computing comparison. If your interpolation feeds into frequency-domain processing, our FFT libraries guide covers the complementary signal processing side.

FAQ

What’s the difference between interpolation and curve fitting?

Interpolation passes exactly through all data points, producing zero error at the measured values. Curve fitting (regression) finds an approximate function that minimizes overall error — it may miss individual points but generalizes better when data is noisy. Use interpolation for exact measurements (sensor calibration data); use curve fitting for noisy observations (experimental data with error bars).

Why do cubic splines sometimes oscillate wildly?

This is Runge’s phenomenon: equally-spaced high-degree polynomial interpolation oscillates at the edges. Cubic splines mitigate this by using piecewise low-degree polynomials, but still overshoot when data changes sharply. Akima splines (GSL) and Steffen splines add constraints to prevent oscillation at the cost of slightly reduced smoothness.

Can tinyspline handle closed curves (loops)?

Yes — tinyspline supports periodic B-Splines and closed NURBS curves. Set the knot vector appropriately and the end of the curve connects smoothly to the beginning. This is essential for representing circular paths, race tracks, or closed boundary contours.

Is Eigen’s Spline module production-ready?

The Eigen Spline module lives in unsupported/ — it’s functional and well-tested but the API may change between releases. Many production projects use it successfully, but pin your Eigen version and test thoroughly after upgrades. For mission-critical applications, GSL (stable C API, 25+ years of releases) provides stronger API stability guarantees.

How do I interpolate unevenly-spaced time series data?

All four libraries support non-uniform x-coordinates. Boost.Math’s barycentric_rational and GSL’s spline interpolators accept arbitrary, monotonically increasing x-values. For time series specifically, consider Boost.Math’s whittaker_shannon interpolator if your signal is bandlimited (sampled above the Nyquist rate).

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