Talk:Cubic Hermite spline

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[edit] Hermite pronunciation

IPC pronounciation for Hermite anyone? (I dont know, but it seems like a huge fad at wikipedia) -- dormant25

Can be found at Charles Hermite. -- Slowmover 20:54, 15 June 2006 (UTC)

[edit] The x parameter

This page does not explain what the xk parameter is in the set (x_k,\boldsymbol{p}_k). Cww 00:42, 23 March 2007 (UTC)

I added some content on this issue. Berland 16:05, 23 March 2007 (UTC)

[edit] m_i ?

In the three-point difference expression for the tangent vector, the tangent itself is labelled with subscript i, where all expressions in its definition are labelled with subscript k. This computation represents the kth tangent, not the ith, yes? 64.247.224.252 15:01, 30 March 2007 (UTC)

Seemed like a blatant error yes. I replaced m_i with m_k. --Berland 15:33, 30 March 2007 (UTC)

[edit] y0 and y1 need to be normalized too, not mentioned on this page

I just implemented a cubic hermite spline function according to this description. However, there is one problem with the p(t) formula: The x values get normalized by substituting them with t. But there is no mention of normalizing yk and yk+1. If I don't normalize them similar to y0' = y0 / (xk+1 - xk) and y1' = y1 / (xk+1 - xk), then the effect of the tangents in p(t) is not correct. I'm not very good at formulating mathematical things so I rather would have someone else fix the page. Maybe the expression 'normalizing the interval' implies normalizing the y values as well, but to me it seems you'd have to be a well-versed mathematician to understand that ;-) Just wanted to point this out... Cwienands 04:04, 12 April 2007 (UTC)

You are right, this has to be sorted out. --Berland 20:22, 26 June 2007 (UTC)
I think this is now correctly handled for the finite difference choice of tangents, but there might still be some consistency issues for the other listed tangent choices. --Berland (talk) 21:05, 10 December 2007 (UTC)
I think the handling of 'h' in the second and fourth part of the equation in the non-uniform case isn't correct (or the specifications of the tangents are not). Iff h >> 1 (eg. 100) this becomes pretty obvious: Catmull-Rom would yield m_0=(100-0)/2=50 for A={(0,0), (100,50), (200,100), (300,0)} => h*m_0 = 100 * 50 >> maxP(A)
This would result in a very strongly oscillating function (try it with Excel, Gnumeric or Pages and plot the result)
Either removing 'h' from this equation or mentioning that m_k has to be normalized to yield the real slope (the one which would be the result of the derivative of f(x)=p_0+(x-x_0)*(p_1-p_0)/(x_1-x_0))
Was this clear? If not, don't hesitate to ask.--SvenHerzberg (talk) 04:19, 26 December 2007 (UTC)

[edit] Merge

I suggest merging the articles Catmull-Rom spline and Cardinal spline into this article. The contents of those articles are almost only formulas for determining the shared tangent of cubic Hermite splines, and thus fits nicely in as subsections in this article. Berland 18:55, 21 June 2007 (UTC)

[edit] Agree

I agree with this whole-heartedly. The two topics are very closely related and are also both short. Putting them together (in an organized, logically flowing way, of course!) would be a definite improvement. We would have to make sure that the links to these pages are properly resolved as well.
-- Bill 15:15, 15 November 2007 (UTC)

I must say that when trying to look up cardinal splines I had a hard time finding out the specifics of it, the Wikipedia article helped. If it is merged then a redirect to the sub-section(not just the page) will be essential. 1 != 2 16:35, 4 December 2007 (UTC)
I agree with the second writer here. This was the place that I actually found out what 'Cardinal Spline' meant. The other page would simply have baffled me completely. 10 December 2007 —Preceding unsigned comment added by 217.45.199.166 (talk) 12:14, 10 December 2007 (UTC)

Then the merge should be completed. I will leave Catmull-Rom spline and Cardinal spline for a few days to verify everything has been merged in before they are replaced with redirects to the subsections. --Berland (talk) 20:22, 10 December 2007 (UTC)

[edit] New external link

I'm not sure which of the many spline pages this would be best for... but after not finding a nice summary on the web for the most common spline equations for graphics I made one myself that I think will be very useful for others as well. You can see it at: http://www.blackpawn.com/texts/splines/ Should I add it as an external link?

Blackpawn (talk) 23:37, 19 April 2008 (UTC)