Talk:Control point (mathematics)
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Attempt at refinement
[edit]The present text is imprecise and even misleading. In CAGD, based on Bezier's representation of a polynomial curve, it has become customary the refer to the d-vectors p_i in a parametric representation sum_i p_i phi_i of a curve or surface in d-space as control points, while the scalar-valued functions phi_i, defined over the relevant parameter domain, are the corresponding weight or blending functions. Some would reasonably insist that the blending functions form a nonnegative partition of unity, i.e., the phi_i are nonnegative and sum to 1. Deboor (talk) 20:36, 12 March 2014 (UTC)
- Point taken that my original content was insufficient; however, I think the new content is too specific. The term control point seems to be a generally understood one in curve-related mathematics, but its meaning is elusive to those of us who are not as immersed in the field. Hence, I'm restoring my original definition above the more specific example. Please edit as you see fit, but also please include a summary that the casual-but-curious reader can grasp. Thanks! --Jhfrontz (talk) 09:05, 30 April 2014 (UTC)
- The rough definition re-inserted seems flawed on two points: it refers to control points on a curve when, perhaps, it should refer to control points for a curve; also, it restricts attention to curves while control points are used, more generally, for surfaces and even higher-dimensional objects. Perhaps you can make clear to me, e.g., by asking questions, what makes the definition I proposed ungraspable. With such additional input, I would try to improve the text accordingly. I am not wiki-versed enough to know how to turn this comment into an email to User:Jhfrontz. Deboor (talk) 00:56, 2 May 2014 (UTC)
- I'll incorporate your changes for the summary -- "for" vs. "on" and more general application to surfaces. But, again, my layperson's terminology is probably going to be suspect. Would a "higher-dimensional object" be best described as an n-manifold or something else? --Jhfrontz (talk) 13:33, 4 May 2014 (UTC)
- Yes, objects --> manifolds
- What about questions that illustrate how my definition of control points to be ungraspable? And where can I find out how I can email comments such as this to you? Deboor (talk) 04:16, 5 May 2014 (UTC)
- I think your expanded definition is probably fine -- it was the synopsis/abstract/introduction that I was focusing on. I think it's probably in an OK state now, though I'm unsure of limiting the term to CAGD (I'm asking for clarification on that over here: http://math.stackexchange.com/questions/782684/what-is-a-control-point ). Doesn't it have a more broad use?
- Oh, we should keep the discussion here so that others can benefit/contribute. I"ll get notified if/when you add a comment. --Jhfrontz (talk) 22:16, 5 May 2014 (UTC)
- Ok, I am happy to forego any emailing now that I know that you will be notified of any comments I might make here.
- I have seen the term `control point' only used in the context of CAGD; in a more general mathematical context, they would be called `vector-valued expansion coefficients' or some such. To me, these become `control points' only when the corresponding function terms or 'weight functions' or 'blending functions' in the expansion are nonnegative and add up to 1. Deboor (talk) 23:19, 5 May 2014 (UTC)
- I'll incorporate your changes for the summary -- "for" vs. "on" and more general application to surfaces. But, again, my layperson's terminology is probably going to be suspect. Would a "higher-dimensional object" be best described as an n-manifold or something else? --Jhfrontz (talk) 13:33, 4 May 2014 (UTC)
- The rough definition re-inserted seems flawed on two points: it refers to control points on a curve when, perhaps, it should refer to control points for a curve; also, it restricts attention to curves while control points are used, more generally, for surfaces and even higher-dimensional objects. Perhaps you can make clear to me, e.g., by asking questions, what makes the definition I proposed ungraspable. With such additional input, I would try to improve the text accordingly. I am not wiki-versed enough to know how to turn this comment into an email to User:Jhfrontz. Deboor (talk) 00:56, 2 May 2014 (UTC)
Original commentary
[edit]This page used to redirect to the page about splines-- the destination page mentioned "control points" repeatedly but never bothered to define them. Since the term "control point" is used in several other pages, I'm hoping that someone can clean up my perfunctory definition and then we can link other usages here. --Jhfrontz (talk) 16:09, 7 March 2013 (UTC)
- In response to the below comment, it's not clear to me that the term "control point" is sufficiently well-defined, as an isolated idea, to warrant its own page. The term should be defined on the pages of the objects which it controls. At best, I can imagine this page giving a list of graphic objects which are generally manipulated using control points (splines, Bézier curves, etc). If someone wants to make the stub useful in a quick way, they could make that list. Right now, it is confusing, and doing more harm than good, since it gives the false impression that there is more information about control point somewhere (furthermore, the (mathematics) label seems incorrect). Lewallen (talk) 12:53, 31 May 2013 (UTC)