## Re: [Algorithms] spline name

 Re: [Algorithms] spline name From: Jarkko Lempiainen - 2008-11-04 12:39:39 Attachments: Message as HTML ```Well, with the same logic you could call it to B-spline or Bezier spline since any cubic spline can be transformed to another ;) Cheers, Jarkko _____ From: Andrew Vidler [mailto:andrew.vidler@...] Sent: Tuesday, November 04, 2008 2:33 PM To: 'Game Development Algorithms' Subject: Re: [Algorithms] spline name A Catmull-Rom spline is just a Cubic Hermite with a certain scheme for working out the tangents. :) See further down the Wikipedia page for details. _____ From: Jarkko Lempiainen [mailto:altairx@...] Sent: 04 November 2008 12:26 To: andrew.vidler@...; 'Game Development Algorithms' Subject: RE: [Algorithms] spline name I don't think it's cubic Hermite curve since it's defined with 4 points rather than 2 points + their tangents. I think Catmull-Rom would be a closer match, but it doesn't go through all the points within t=[0, 1] interval. Cheers, Jarkko _____ From: Andrew Vidler [mailto:andrew.vidler@...] Sent: Tuesday, November 04, 2008 1:38 PM 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 email has been scanned by the MessageLabs Email Security System. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ ```