Talk:Composite Bézier curve

message: Isn't this a special case of a b-spline?
In B-spline it says that Bézier spline are a special case of b-spline. So it could be made more explicit here. MathMartin 13:02, 29 Nov 2004 (UTC)
thread_title: Bézier spline special case of [[B-spline]]

message: The "Vector graphics" article redirects to this article under the name "Bezigon."  However, the latter term is not defined in this article.
I am still not certain what a "bezigon" is supposed to be.  I would guess that it is a geometric shape composed of multiple segments which are Bezier curves.  Will an expert please add an appropriate section to this article?
66.168.74.119 23:07, 13 June 2007 (UTC)
replies: text: . This article now has a definition for "bezigon". Your guess is right. --DavidCary (talk) 05:12, 10 February 2013 (UTC)
thread_title:  "Bezigon" 

message: I realize that this is only a stub but the article is way too gear-headed. Rigorous mathematical explanations are generally a good thing but, frankly, it is more important for math articles to include a brief segment that amounts to something like "In case you don't know much about this here's a short, practical description of this that you can use in everyday applications". In this case, providing a simple algebraic function that converts the real-valued control points and an interpolation variable into a real-valued interpolation result would make the article much more accessible (even that would be a subset of the general topic it would illustrate what is being discussed in a way that many more readers could understand it).
---Mcorazao (talk) 22:57, 16 May 2009 (UTC)
thread_title:  Gear headed 

message: The article and subsequent discussions seems to lead to considerable confusion; especially to a reader who just wants to know what a "Bézier spline" is.  It is my understanding that a Bézier spline is essentially a spline using Bézier curves, and not simply a synonym of "Bézier curve".  The article as written might include that meaning, but would require interpretation.  Perhaps a discussion of the distinction between a curve and a spline would be useful; especially in non-mathematical terms.  71.23.89.42 (talk) 11:27, 12 July 2010 (UTC)
thread_title:  "spline" vs. "curve" confusion? 

message: I suggest merging beziergon into Bézier spline.
As far as I can tell, whenever the last endpoint on the last Bézier curve of a Bézier spline is placed exactly on top of the first endpoint of the first Bézier curve of that Bézier spline, the result is a beziergon, and all beziergons can be formed in that way.
The difference between them is small enough that I think it makes more sense to have one merged article cover both kinds of splines, with a short paragraph mentioning the subtle difference.
--DavidCary (talk) 20:45, 4 July 2011 (UTC)
replies: text: . --DavidCary (talk) 17:43, 8 February 2013 (UTC)
thread_title:  merge 

message: The algorithm described in the General Case section is really poor. The results look horrible for large angles.  It cannot create the approximation discussed above it in the Using Four Curves section.  Even a cursory glance reveals that there is no way to generate the sqrt(2) value.  The cited article for that section says it is for very small angles only.  But, even for small angles, there are superior ways to do this.
:The graph of the sinc function approximation is contained in an SVG file, with SVG using Bezier spline.  The points defining the curves, as well as the segmentation of the graph into individual curves, were computed via an algorithm, with individual segments based on a least squares fit. It's not a simple algorithm, to say the least. --Aflafla1 (talk) 06:35, 1 May 2014 (UTC)
thread_title:  General case 

message: The sources I've look at diverge a bit on this. (See smoothness#Geometric_continuity for background.) I'm not entirely sure if the issue can be glossed over [as trivial reparametrization] or not. I'll have to read/think about it some more. JMP EAX (talk) 17:37, 19 August 2014 (UTC)
thread_title:  G vs C continuity  

message: The general case section starts of with " Let the arc start at point A and end at point B placed at equal distances above and below the x-axis".
Two questions:
# Does that mean that (A.y == (B.y * -1)) must be true?
# Why this restriction?  — Preceding unsigned comment added by EliseVanLooij (talk • contribs) 12:13, 14 July 2016 (UTC)
thread_title:  General case 

message: While it is written that "The geometric condition for C2 continuity is C1 continuity, with the additional constraint that the control points are equidistant from the endpoint", it seems these conditions are not enough for C2 continuity of cubic Beziers.
Given a curve $[a0, a1, a2, a3]$, the curve $[b0, b1, b2, b3]$ concatenates smoothly if:
$b0 = a3$
$b1 = 2*a3 - a2$
$b2 = 4*a3 -4*a2 + a1$
and you can choose $b3$
: . It was pretty confusing before yeah, I rewrote the entire section, hopefully I got everything right and didn't go into too much detail! The C^3 section could be removed if we want to shorten it, but I think it's an interesting fact that it will collapse the entire spline into a single curve FreyaHolmer (talk) 19:44, 29 July 2022 (UTC)
thread_title:  Smooth Joining 

message: An editor has identified a potential problem with the redirect :Reticulating splines and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 August 24#Reticulating splines until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  signed, Rosguill talk 15:28, 24 August 2022 (UTC)
thread_title:  "Reticulating splines" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]