## Re: [Algorithms] spline name

 Re: [Algorithms] spline name From: Jarkko Lempiainen - 2008-11-04 13:22:00 Attachments: Message as HTML I must applaud you for spelling my name right ;) But yeah, the motivation was just that I could call it with some recognizable name in code rather than invent something off the top of my head. I would have thought there is a name for it since it can be quite useful way for defining a curve. Cheers, Jarkko _____ From: Willem H. de Boer [mailto:willem@...] Sent: Tuesday, November 04, 2008 3:05 PM To: Game Development Algorithms Subject: Re: [Algorithms] spline name I know, it's called a Lempiainen curve! Seriously, there are many ways of defining a curve, many of which do not have a name, since it's fairly easy to come up with one and its basis matrix. Cheers, Willem ----- Original Message ----- From: Jarkko Lempiainen To: 'Game Development Algorithms' Sent: Tuesday, November 04, 2008 12:53 PM Subject: Re: [Algorithms] spline name Yes, M_interp looks awfully familiar (: Cheers, Jarkko _____ From: Simon Fenney [mailto:simon.fenney@...] Sent: Tuesday, November 04, 2008 2:28 PM To: andrew.vidler@...; Game Development Algorithms Subject: Re: [Algorithms] spline name No. AFAICS (and assuming my maths is correct) the cubic spline Jarkko has described has the following basis matrix: [ -9 27 -27 9] M_interp =1/2 [ 18 -45 36 -9] [-11 18 -9 2] [ 2 0 0 0] Whereas for a Hermite spline we have (from Foley et al) [ 2 -2 1 1] M_hermite = [-3 3 -2 -1] [0 0 1 0] [1 0 0 0] Simon _____ From: Andrew Vidler [mailto:andrew.vidler@...] Sent: 04 November 2008 11:38 To: 'Game Development Algorithms' Subject: Re: [Algorithms] spline name I think you've just found a way of specifying the tangents for a cubic hermite curve? http://en.wikipedia.org/wiki/Cubic_Hermite_spline If you look at the formula for q(1/3) and q(2/3) then you'll get two equations in terms of the endpoints and the tangent at each endpoint - just rearranging for the tangents gives you two equations (one for each tangent) in terms of the endpoints and q(1/3), q(2/3) - which is what you've got. Unless there's some other characteristic of the spline that means it's not a Hermite? Cheers, Andrew. _____ From: Jarkko Lempiainen [mailto:altairx@...] Sent: 04 November 2008 11:10 To: 'Game Development Algorithms' Subject: [Algorithms] spline name Hi, 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 ;) Cheers, Jarkko ______________________________________________________________________ This email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ _____ ------------------------------------------------------------------------- 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