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.
From: Andrew Vidler
Sent: Tuesday, November 04, 2008 1:38 PM
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?
From: Jarkko Lempiainen [mailto:email@example.com]
Sent: 04 November 2008 11:10
Game Development Algorithms'
Subject: [Algorithms] spline name
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 ;)
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