Common Tasks

Use this page when you know what you want to do, but want the right class, tutorial, or code pattern quickly. If you are still choosing between the main classes, start with Which Class Should I Use?.

Interpolate exact data in one dimension

• Use InterpolatingSpline
• Start with Spline Interpolation

t = linspace(0, 1, 20)';
x = sin(2*pi*t);
f = InterpolatingSpline.fromGriddedValues(t, x, S=3);
xq = f(linspace(t(1), t(end), 200)');

Interpolate exact data on a rectilinear grid

• Use InterpolatingSpline
• Pass one grid vector per dimension

F = InterpolatingSpline.fromGriddedValues({x, y}, V, S=[3 3]);
Vq = F(Xq, Yq);

Fit noisy data

• Use ConstrainedSpline
• Start with Fitting Noisy Data

noiseModel = NormalDistribution(0.05);
fit = ConstrainedSpline.fromData(t, xObs, S=3, splineDOF=12, distribution=noiseModel);

To match the least-squares polynomial fit from polyfit(t, x, N-1), use S=N-1 and splineDOF=N. For rectilinear grids in two or more dimensions, use ConstrainedSpline.fromGriddedValues(...).

Fit noisy data with outliers

• Use ConstrainedSpline with StudentTDistribution
• Start with Robust Fitting with Outliers

fit = ConstrainedSpline.fromData(t, xObs, S=3, splineDOF=12, ...
    distribution=StudentTDistribution(sigma=0.05, nu=3));

Add local value or derivative constraints

• Use PointConstraint
• Start with Local Point Constraints

constraints = [
    PointConstraint.equal(0.5, value=1)
    PointConstraint.equal(0.5, D=1, value=0)
];

fit = ConstrainedSpline.fromData(t, xObs, S=3, splineDOF=12, constraints=constraints);

Add global positivity or monotonicity constraints

• Use GlobalConstraint
• Start with Global Shape Constraints

fit = ConstrainedSpline.fromData(t, xObs, S=3, splineDOF=12, ...
    constraints=GlobalConstraint.monotonicIncreasing());

Add a 2D constraint on a rectilinear grid

• Use ConstrainedSpline with GlobalConstraint.monotonicIncreasing
• Start with 2D Constraints

fit = ConstrainedSpline.fromGriddedValues({x, y}, VObs, S=[3 3], splineDOF=[10 10], ...
    constraints=GlobalConstraint.monotonicIncreasing(dimension=2));

Fit a planar trajectory from shared-parameter samples

• Use TrajectorySpline
• Start with the TrajectorySpline class reference

trajectory = TrajectorySpline.fromData(t, x, y, S=3);
tq = linspace(t(1), t(end), 200)';

xq = trajectory.x(tq);
yq = trajectory.y(tq);
uq = trajectory.u(tq);
vq = trajectory.v(tq);

For persisted restart or prefit component splines, construct the canonical state directly with TrajectorySpline(t=t, x=xSpline, y=ySpline).

Work directly with basis matrices

• Use BSpline.matrixForDataPoints or TensorSpline.matrixForPointMatrix
• Start with BSpline Foundations or TensorSpline Foundations

knotPoints = BSpline.knotPointsForDataPoints(t, S=3);
B = BSpline.matrixForDataPoints(t, knotPoints=knotPoints, S=3);
xi = B \ x;