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@powervr.com]
Sent: Tuesday, November 04, 2008 2:28 PM
To: andrew.vidler@ninjatheory.com; 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@ninjatheory.com]
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@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 donít know whatís the name of the wheel I just reinvented ;)

 

 

Cheers, Jarkko

 


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