Re: [Algorithms] spline name

 Re: [Algorithms] spline name From: Jarkko Lempiainen - 2008-11-04 12:53:56 Attachments: Message as HTML 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 ______________________________________________________________________