Wouf' s Blog

The blog of Wouf

Wouf' s Blog header picture 2

Curve of B zier, they clear the undergrowth!

July, 25th, on 2008 6 Comments

First of all the curves of B zier belong to the mathematical vocabulary:

The curves of B zier are polynomiales parametric curves described for the first time in 1962 by the French engineer Pierre B zier who used them to conceive rooms of cars with the aid of computers. They have many applications in the synthesis of pictures and the return of cast iron. They gave birth to many other mathematical objects.

The amateur of vectorial computer graphics owes of maitriser, and this ticket aims at clearing the undergrowth a bit from the heterogeneous contents of the worldwide cloth, to draw primordial information, the substantifique marrow which will allow each to arrest them better.

We will recall here only the curves of cubic B zier, in two knots (terminals).

bezier2

If they dive into the lexical field of computer graphics, points A and B are knots. They determine origin and end of our first curve of B zier. Points E and F are handles (or dawned of control).

In Inkscape, to draw this, I have choose the curved tool of B zier in the menu (or SHIFT F6), I clicked to procreate the first point (A) and double clicked to end the curve and to create the second point (B)

I then chose the tool of edition of knots (F2) then clicked on the curve (by supporting the supported button) and displaced slightly the mouse. Handles then appeared and I have them moved l g rement by using the same technology.

Some years ago, when I met my first curve of B zier, I found this entertaining, but it is necessary me to confess it: I worked in let us try to reach a (mediocre) result without including what I made

What it is necessary to include:

Points E and F serve respectively for pointing out how the curve leaves the point A, and how it arrives at the point B. Without speaking about vector or about tangent not to scare you off, it is possible to consider that these points E and F stages on some itinerary are, and that the curved, lazy and a bit sharper, gives phantasm to the observers put at first and at the arrival which she crosses to it, while she strives to cover the shortest possible distance.

It is this a bit childish way of seeing the things with me help to maitriser this fabulous tool!

I recalled here only curves having two final knots, (a click for the first, a double click for the second) but it is possible to construct curves having several intermediate knots. (click, click, and double click to end, for a curve of B zier in three knots). They consid rera while it is a phased running, with even rules!

Strong in what we learnt, the next small exercise should not pose problem.

In the following curves, the only two of them enter have more than two knots.

bezier

Which?

(An indication, both figures give then my born department, post his leader simply place in comment and you are my hero)

Inkscape
Mathematics and TICE, passionately

If you liked this ticket, these could please you:

Graffiti: daily

6 responses so far

  • 1 davidNo Gravatar//july 26, on 2008 at 11:12

    Valence?

  • 2No Gravatar//july 26, on 2008 at 12:39

    It would not be Valence incidentally? ^^
    (or Arras but ok needs to know in which order)

    Thank you for your explanation, I just search the maximum of pedagogy to teach to somebody illustrator. :)

    The quotation of introduction is nevertheless a bit complicated, me one had taught him to me just like that:
    A brilliant guy has there, who is called B zier, and who found that any curve could represented by a mathematical expression.
    (the teacher makes us a gribouilli in the picture with features in everything senses)
    Here is! He found a way to represent this by a mathematical expression. :)
    Suddenly, the stocking is much lighter, redimension is not any more a problem because it is enough to augment (or diminish) the factor of expression.

    It is not completely precise but this had appeared to me so clearly.

    Good continuance, I am going to look at what you wrote of other one:p

    Al

  • 3 WoufNo Gravatar//july 27, on 2008 at 7:04

    La_ristourne, you are therefore my hero!
    It was indeed about Arras (62), the nicest city of the world (David was not far, except in flight of birds)

    Thank you for your complement which it is true can clarify ideas a bit.

    Curves 2 and 6 cannot indeed be constructed with only two final knots:

    For the curve 2, they imagine well where is the intermediate knot: in the point extremely right of the curve the continuity of this one, angular, are possible arouse suspicion.

    For the curve 6:
     the curve, lazy and a bit sharper, gives phantasm to the observers put at first and at the arrival which it crosses on the points of control, while it strives to cover the shortest possible distance 

    By thinking with this axiom at the head, they quickly understand, that without intermediate knot, there would have been curl never!

    Good Sunday to all!

  • 4 beep beepNo Gravatar//May, 19, on 2009 at 21:35

    I had a headache but by reading you it is worse B zier? I I m well Toulouse, Fabien Pelouse

  • 5 Unknown man//july 26, on 2008 at 6:39

    Curve of B zier, they clear the undergrowth!

    Trackback

  • 6 Inkscape, holiday homework for starting computer graphics specialist//july 28, on 2008 at 9:01

    [] Wouf' s Blog The blog of Wouf Curve of B zier, they clear the undergrowth! [...]

CommentLuv Enabled

2006-2007 Wouf' s Blog Sitemap Cutline by