Talk:Bézier surface

Picture
Seems to me the article should at least one fucking picture - it is after all an article about geometrical shapes.

This article contains material from FOLDOC, used by permission.

There's a lot more that can be said about this topic; I know enough to know I have forgotten most of it. Basis vectors, vector spaces, continuity, tensors, topology... -- Karada 12:37, 31 Jul 2003 (UTC)

From memory:
 * Note that this property is not in general true of arbitary lines in (u,v) space.

I think that's true: can someone confirm it? -- Karada 13:06, 31 Jul 2003 (UTC)

Concerning your last two paragraphs: See "Bezier and B-Spline Techniques" (Prautzsch et al) pp 166 for conversion between tensor product and triangular patches. Your are right that a m times n patch can be represented as a single m+n triangular patch, since both represent polynomial surfaces of the same degree. I think you just have to transform the input domain from square to barycentric coordinates, though I am not sure how you would do that. An idea how you might convert the control points for 1x1 TP -> 2x2 triangular is represented here: http://www.mmweg.rwth-aachen.de/~arne.schmitz/download/tensor.png -- dunno if that is correct, but I think it makes sense. Root 42 20:26, 29 Jan 2004 (UTC)

Definition of Bézier surface
I modified the definition of a Bézier surface. Strictly speaking, the poles are defined in an affine space and are not vectors. Typically, a vector does not depend on the choosing of the origin, but a point does depend. Also, I specified the range of the parameters (u,v), since it can be convenient to change this range when converting into orthogonal polynomials basis like Legendre or Tchebychev. I did not mention this in my editing.

Error
I'm probably not doing this right, but I'm just learning about wikipedia. In the sentence

All u = constant and v = constant lines in the (u, v) space, and, in particular, all four edges of the deformed (u, v) unit square are Bézier curves.

you really mean to say that the _images_ of these lines are Bezier curves, don't you? This is what people mean by a Bezier curve; the image. (Notwithstanding that in differential geometry 'curve' technically means the mapping itself. And yes, these lines (u=const, v=const)in the domain itself are also trivially Bezier curves, but no way do you mean that -- you write too well for any such unbridled pedantry)

Finn 68.55.44.143 01:31, 9 January 2007 (UTC)

taxonomic rank

 * Bézier surfaces are a species of mathematical spline ...

'Species' implies less variation than I think it ought. How about 'family'? —Tamfang (talk) 23:23, 15 November 2010 (UTC)

I miss the article about Bicubic patches in general. — Preceding unsigned comment added by 37.44.138.209 (talk) 20:02, 19 February 2017 (UTC)

Proposed merge of Biharmonic Bézier surface into Bézier surface
The concept of Biharmonic Bézier surface doesn't really seem to be notable enough for its own article, but it might fit in possibly to the main article about Bézier surfaces as a topic snood1205(Say Hi! (talk)) 19:18, 28 November 2021 (UTC)


 * The topic of Bezier surfaces is too abstract as presented. Merging the content of Biharmonic Bezier surface to the Bezier surface topic would only complicate learning instead of spreading knowledge faster. The best compromise is to add a link in the Bezier surface topic's SEE ALSO section pointing to the Biharmonic Bezier surface topic. 2601:183:857F:E370:E833:E389:A109:F6ED (talk) 14:33, 3 April 2022 (UTC)
 * Closing, given the uncontested objection and no support. Klbrain (talk) 17:43, 2 October 2022 (UTC)