# About Splines

A spline is a smooth curve that passes through or near a set of points that influence

the shape of the curve.

By default, a spline is a series of blended curve segments of degree 3 (also called

cubic) polynomials. These curves are technically called *nonuniform rational B-splines (NURBS)*, but are referred to as splines for simplicity. Cubic splines are the most common,

and mimic the splines that are created manually using flexible strips that are shaped

by weights at data points.

In the following example, a spline was used to create the highlighted boundary of

the concrete walkway.

## Understand Control Vertices and Fit Points

You can create or edit splines using either *control vertices*, or *fit points*. The spline on the left displays control vertices along a *control polygon*, and the spline on the right displays fit points.

Use the triangular grip on a selected spline to switch between displaying control

vertices and displaying fit points. You can use the round and square grips to modify

a selected spline.

selected spline to degree 3. Splines originally created using higher-degree equations

will likely change shape as a result.

## Create Splines Using Fit Points

When you create splines using fit points, the resulting curve passes through the specified

points, and is influenced by the spacing of mathematical *knots* in the curve.

You can choose the spacing of these knots with the *knot parameterization* option, which will result in different curves as shown in the example.

parameterization is commonly used, and the square root (centripetal) parameterization

often produces better curves depending on the data set.

When the Tolerance value is set to 0, the spline passes directly through the fit points.

With larger tolerance values, the spline passes near the fit points. Optionally, you

can specify the tangent direction for the spline at each end.

## Special Cases

You can create a spline with a parabolic shape by specifying a degree 2 spline created

with exactly 3 control vertices as shown on the left. Degree 3 splines created with

4 control vertices have the same shape as Bezier curves of degree 3 as shown on the

right.

sp>About Splines. A **spline** is a smooth curve that passes through or near a set of points that influence the shape of the curve. … These curves are technically called nonuniform rational B-**splines** (NURBS), but are referred to as **splines** for simplicity.splines is the 1946 paper by Schoenberg, which is probably the first place that the word "**spline**" is used in connection with smooth, piecewise polynomial approximation. However, the ideas have their roots in the aircraft and shipbuilding industries.Spline Interpolation. I got into **splines** the way many people do: I wanted a way to draw smooth, attractive connectors between graphic objects in a very general …spline fitting in Curve Fitting Toolbox.about spline at Encyclopedia.com. Make research projects and school reports **about spline** easy with credible articles from …… On Apr 24, 2:56pm, Gwenaël Guillard wrote: > Subject: [vtkusers] **about splines** > Hi, > > I have two questions **about splines**. One general and …… You can add and remove edit points **on** a **spline**, but usually, when you are trying to make a smooth curve, using as few points as possible is …