Skip to content



A spline is a continuous function Math image which coincides with a polynomial on every subinterval Math image of the whole interval Math image on which Math image is defined. In other words, splines are functions which are piecewise polynomial. The coefficients of the polynomial differs from interval to interval, but the order Math image of the polynomial is the same. Splines are often named after the order Math image of the spline, e.g. cubic splines correspond to Math image .

An essential feature of splines is that function Math image is continuous – i.e. has no breaks on the boundaries between two adjacent intervals. Besides the continuity of the function Math image itself, for many types of splines the first derivatives of Math image are also continuous. (For example, for cubic splines the first derivative Math image is continuous too, while derivatives of higher order, e.g. Math image are not continuous). This property makes splines look as rather smooth functions.

Splines are widely used for interpolation and approximation of data sampled at a discrete set of points – e.g. for time series interpolation.

Besides one-dimensional splines (i.e. functions Math image of a single variable Math image ), there are also two-dimensional splines, which are functions Math image of two variables, say, Math image and Math image . Two-dimensional splines are used, for example, to interpolate spatial fields from results of their measurements in a finite set of Math image points Math image .

Browse Other Glossary Entries

Test Yourself

Planning on taking an introductory statistics course, but not sure if you need to start at the beginning? Review the course description for each of our introductory statistics courses and estimate which best matches your level, then take the self test for that course. If you get all or almost all the questions correct, move on and take the next test.

Data Analytics

Considering becoming adata scientist, customer analyst or our data science certificate program?

Analytics Quiz

Advanced Statistics Quiz

Statistics Quiz


Looking at statistics for graduate programs or to enhance your foundational knowledge?

Statistics 1 Quiz

Regression Quiz

Regression Quiz


Entering the biostatistics field? Test your skill here.

Biostatistics Quiz

Advanced Statistics Quiz

Statistics 2 Quiz

Stay Informed

Our Blog

Read up on our latest blogs


Learn about our certificate programs


Find the right course for you

Contact Us

We'd love to answer your questions

Our mentors and academic advisors are standing by to help guide you towards the courses or program that makes the most sense for you and your goals.

300 W Main St STE 301, Charlottesville, VA 22903

(434) 973-7673

By submitting your information, you agree to receive email communications from All information submitted is subject to our privacy policy. You may opt out of receiving communications at any time.