From: Willem H. de Boer <willem@wh...>  20081104 13:05:33

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://moblincontest.org/redirect.php?banner_id=100&url=/  _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist 