Splines can be used to approximate a \"parametric curve\" (x(t), y(t)) by using

Question

Splines can be used to approximate a "parametric curve" (x(t), y(t)) by using a spline for each of the functions separately and then plotting the resulting function y vs. x. Draw a script letter on a graph paper, place a few points on the letter and take down the coordinates of the points (it doesn't have to be many points: 5 to 12 points is enough, depending on the chosen letter, if chosen wisely). Create two arrays with these data and find the spline approximations S_y(t) and S_x(t) for each of the functions y(t) and x(t) with parameter t representing the array index. Plot the resulting S_y vs. S_x. Despite only using a few points for each letter, the resulting plot should be nice and smooth. Experiment with different "end conditions". Explain your choice.

Explanation / Answer

Let us perform this operation in MATLAB.

Syntax

s = spline(x,y,xq)

pp = spline(x,y)

Description

s = spline(x,y,xq) returns a vector of interpolated values s corresponding to the query points in xq. The values of s are determined by cubic spline interpolation of x and y.

pp = spline(x,y) returns a piecewise polynomial structure for use by ppval and the spline utility unmkpp.

This example fits some data using a cubic spline interpolant and several smoothing splines.

Create the variables in your workspace:

Open the Curve Fitting app by entering:

Select x and y from the X data and Y data lists.

The Curve Fitting app fits and plots the data.

Fit the data with a cubic spline interpolant by selecting Interpolant fit type and the Method Cubic.

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