spline — Construct or evaluate a cubic spline interpolant.

spline(x, y) returns a piecewise-polynomial structure for cubic spline interpolation. spline(x, y, xq) evaluates that spline directly at query points.

Syntax

pp = spline(x, y)
yq = spline(x, y, xq)

• x is a strictly increasing vector of sample locations.
• y contains the sampled values to interpolate.
• spline(x, y) returns a piecewise-polynomial structure compatible with ppval.
• spline(x, y, xq) evaluates the cubic spline directly at query points.
• Standalone spline extrapolates outside the sample range using the first or last polynomial piece.

How spline works

• Returns a pp structure with form, breaks, coefs, pieces, order, and dim fields.
• The direct evaluation form extrapolates outside the sample range, matching MATLAB's standalone spline behavior.
• Dense real numeric inputs are supported in the initial implementation.

Examples

Build and evaluate a spline

x = [1 2 3];
y = [1 4 9];
pp = spline(x, y);
yq = ppval(pp, [1.5 2.5])

Expected output:

yq = [2.25 6.25]

Direct evaluation

x = [1 2 3];
y = [1 4 9];
yq = spline(x, y, 1.5)

Expected output:

yq = 2.25

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how spline works, line by line, in Rust.

• View spline.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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