A Catmull-Rom spline is just a Cubic Hermite with a certain scheme for working out the tangents. :)

From: Jarkko Lempiainen [mailto:altairx@gmail.com]
Sent: 04 November 2008 12:26
To: andrew.vidler@ninjatheory.com; '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@ninjatheory.com]
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?

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@gmail.com]
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

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