
Bezier Curves and Picasso - SanderMak
http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/
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zalzane
Impressive introduction to bezier curves. I still remember my first exposure
to them; I was looking for a way to model a ship hull without making a full
blown 3d-editor. After a bit of googling I found the article on bezier curves
and spent the rest of the day digesting it all. Very interesting stuff. I
couldn't figure out bezier surfaces for my life though, so instead I opted for
having the 3 sets of bezier curves to represent the different profiles of the
ship, then rasterizing them together. I'm pretty happy with how it ended up
coming out; <http://i.imgur.com/qv7WAJ7.png>

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doorhammer
Every time I read one of this guys blog posts, I want to post it a million
places. I just finished reading through "Graph Theory (for the math-phobic)"
and it was really enjoyable.

He seems to have a real knack for distilling reality down into simpler and
simpler concepts until it disappears and you're only left with the abstract,
barely having noticed it happened.

Okay. I do go on, but _still_.

tldr: I'm a fan.

~~~
schrodinger
Here's the aforementioned article, if anyone else is compelled to read it like
I was

[http://jeremykun.com/2011/06/26/teaching-mathematics-
graph-t...](http://jeremykun.com/2011/06/26/teaching-mathematics-graph-
theory/)

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dleibovic
Another great article on bezier curves that I've used is:
<http://pomax.github.io/bezierinfo/>

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jaryd
Thanks for this link. I found the article to be fascinating (albeit the math
got a bit over my head). I was particularly interested in the "The Bull"
series by Picasso pictured mid-way through. I ducked around a bit, and found
an interesting write up on the back story of these sketches. Check it out:
[http://drawingdownthevision.com/the-bull-how-picasso-
practic...](http://drawingdownthevision.com/the-bull-how-picasso-practiced-
being-concise/)

~~~
slacka
Me too. You view all of the eleven lithographs here:

<http://www.slideshare.net/sotos1/pablo-picasso-bulls-111>

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srean
Fond memories. One of my first job out of college was to approximate splines
by a sequence of straightlines and arcs. I rolled my own dynamic programming
hack for that. On getting my first paycheck my first reaction was, "Whoa! what
? I can write code that people are willing to pay real money for". Given that
I was not trained in CS, that was an empowering feeling.

On Picasso, I recall he was deeply affected by the cave paintings of Altamira.
I think the influence clearly shows in his bull. He also said something to the
effect that painting as a craft has not seen much innoavation since those
Altamira artists. I dont know whether to agree or disagree, but the Altamira
paintings do have this something very powerful and visceral about it.

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asimeqi
This is a good article. One can read about Bezier curves in a lot of places. I
took a Computer Graphics course a long time ago and every so often I get
introduced to a new graphics programming framework that provides some ways to
draw Bezier curves. But I think the real trick is how to choose the curves to
approximate a certain drawing. In this article the author provides an
approximation for a Picaso drawing. I wish he would have detailed how he chose
the curves that he did. He promises to describe an algorithm in the next
article. Can't wait for it.

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ceautery
I concur with all the Kudos to Jeremy, this is another very nice piece.

Bezier curves show up in some unexpected places. I was pretty taken aback when
I traced through Java's 2D library [1] and saw that it uses them for circles
instead of doing the more processor-intensive sin/cos or r^2 = x^2 + y^2 math.

[1] - [http://cautery.blogspot.com/2010/09/bezier-curves-as-
ellipse...](http://cautery.blogspot.com/2010/09/bezier-curves-as-
ellipses.html)

~~~
jamessb
A nice feature of Bezier curves (and B-splines) is the convex hull property:
since the curve must lie within the convex hull of the control points, any
point outside the convex hull cannot be within the area bounded by the curve.

So if you have a set of points and need to test which are inside a curve, you
can immediately eliminate any that are outside the convex hull, potentially
saving a lot of computation.

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markhelo
Not sure if the artistic pun was intended but his signature can probably be
expressed as a bezier curve as well :)

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zafka
Damn!!, That is really cool. Now I want to spend next week drawing pictures on
the computer. There is a special place in the next realm for folks who bring
math to life for us simple folks.

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kzrdude
Here I also learned about the use of the 'French Curve' tool, which is a nice
parallel to the Bézier curve being a "French curve" itself.

Add: By the way, the coefficients are missing in the first display of the
cubic Bézier curve formula.

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alex_doom
As someone who's worked in Illustrator for many years, it was rather
fascinating to learn about the lines I've been abusing for so long.

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bflbfl
Very very cool! Those Picasso minimalist sketches have intrigued me as well.

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jacob019
thanks for this, now I'm going to have to get a print and put in on my wall
:-)

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DustinCalim
Great

