## Re: [Algorithms] spline name

 Re: [Algorithms] spline name From: Jarkko Lempiainen - 2008-11-04 18:30:21 Thanks Jon. I think there's quite good consensus with the name now (: I'm using this in generalized curve fitting in arbitrary dimensions (e.g. rotation & translation compression of animation data). Cheers, Jarkko -----Original Message----- From: Jon Watte [mailto:jwatte@...] Sent: Tuesday, November 04, 2008 8:03 PM To: Game Development Algorithms Subject: Re: [Algorithms] spline name Jarkko Lempiainen wrote: > > Does anyone know if there is a name for a cubic spline which goes > through all the defined control points p0..p3 in the interval t=[0, > 1], so that q(0)=p0, q(1/3)=p1, q(2/3)=p2 and q(1)=p3? I solved the > basis matrix for it, but don't know what's the name of the wheel I > just reinvented ;) > I would call that an "interpolating cubic spline" (or even "the interpolating ..."). It's used a lot in 1D, where it is a fast and cheap interpolator for sample rate conversion where you want continuous pitch bend and can't use a (pre-computed) polyphase interpolator, for example. Additionally, I've used it in 2D for interpolating height maps to get smoother sub-sample areas. However, when you have a spline longer than 4 control points, you typically formulate it so that p0 is at t(-1), p1 is at t(0), p2 is at t(1) and p3 is at t(2). Then you slide the entire set of control points over and start over from a new "t(0)" after reaching t(1). That way, you get an arbitrary length C1 continuous spline that interpolates all the points. Sincerely, jw ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ GDAlgorithms-list mailing list GDAlgorithms-list@... https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list