# [vtkusers] about splines

Randy Heiland heiland at ncsa.uiuc.edu
Thu Apr 24 10:15:49 EDT 2003

```On Apr 24,  2:56pm, Gwenaël Guillard wrote:
> Subject: [vtkusers] about splines
> Hi,
>
> I have two questions about splines. One general and one more specific to
> vtk.
> 1. It is possible to compute a spline given two points and two vectors
> such that the curve has the two points for extremities end the two
> vectors for tangent at these extremities. That is to say it is possible
> to draw a spline with extremities and tangent line at the extremities
> given.

Yes.  Do a search for 'hermite cubic spline'.

>Is it possible to draw a spline with extremities, tangent lines
> and  tangent PLANES given, ie with two points and four vectors?

You're trying to hurt my brain, aren't you?  I don't know what you mean by
"extremities".  Nor do I know how a tangent plane (2 vectors) at an endpoint
would be used to uniquely define the spline.  Maybe you can clarify.

> 2. How to do that with vtk?

I believe VTK currently has classes that deal only with *interpolating* splines
(search for 'spline' at public.kitware.com/VTK/doc/nightly/html/classes.html),
ie, given a set of points, draw a curve through those points.  So, in addition
to your given endpoints, you'd need to calculate the additional 2 interpolating
spline from the Hermite form.  The exercise is left to the reader :)

--Randy

```