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<p>I don't know how to draw leaves. I would look up how to draw a
maple leaf or fern with fractals (Michael Barnsley comes to mind).
It might be easier to start off with a bunch of images/pictures.
The way they do movies these days is project the background onto a
wall, then the actors act in front of it. Why fake nature when you
can sample the real thing?<br>
</p>
<p>I used surfaces for 3D "roses" in college a bit, with Newton's
method. I haven't done it recently, because I proved to myself
that internal intersections weren't found.<br>
</p>
<p>Mostly I use quadrilaterals or triangles to draw things. I did
Maurer Roses in 1981-1982 on Apple II+ before "Maurer" existed.
You can find formulas in old or new CRC Math books, perhaps. I
used the 25th version or older. The book has been updated, and I
can't find the same thing in the online version.<br>
</p>
<p>This might be an unorganized introduction (warning, some Perl
required):</p>
<p><a class="moz-txt-link-freetext" href="https://coderextreme.net/orbit/">https://coderextreme.net/orbit/</a></p>
<p>But they aren't "roses" per se. For more unrealistic things
(animation), look at:</p>
<p><a class="moz-txt-link-freetext" href="https://coderextreme.net/flower/">https://coderextreme.net/flower/</a></p>
<p>I would search through SIGGRAPH conference proceedings in hope of
getting something realistic.</p>
<p>I am not your "curve" person. For 3D you're looking for someone
who knows bicubics or NURBS, but really they pretty much get split
up into triangles by the graphics card or CPU, so knowing about
triangle sets and triangle fans are probably useful. What I do is
take a tessellated sphere from Blender or a grid IFS from X3D and
offset the position to make the "rose" surface, and ensure you've
got enough resolution so the result doesn't look crappy. Also,
some work was done on the mailing list with FX3D/FVRML way back in
the distant past. That would help fit your formulas into an X3D
mindset. At this point, if you want to animate the surface, I
think your best bet is to go with something like GLSL.<br>
</p>
<p>I don't know about volumes at all, just surfaces. I've only
rendered up to 7 animated "roses" at a time--it's easy to add
more, but I get concerned about heat, etc.<br>
</p>
<p>Here's a sample of something you might get if you use PHP to draw
things:</p>
<p><a class="moz-txt-link-freetext" href="https://code.tutsplus.com/tutorials/rendering-text-and-basic-shapes-using-gd--cms-31767">https://code.tutsplus.com/tutorials/rendering-text-and-basic-shapes-using-gd--cms-31767</a></p>
<p>If you really want better 2D flowers, I highly recommend
contacting @sxywu on Twitter. She may be working on 3D as well.</p>
<p>"Curves" indicates you're using 2D? There's Processing.JS for
JavaScript.</p>
<p>So start small, with 2D vector/SVG drawing (see @sxywu), use
polar coordinates in an equation like</p>
<p>r = 100+100*cos(2*phi)<br>
</p>
<p>You have to figure out how to convert to Cartesian coordinates,
but that's easy to find. Break the curve into a series of lines
by stepping through values of phi in a loop. Make the delta phi
small enough.<br>
</p>
<p>I hope you know what a loop is.</p>
<p>I'm pretty much at the point where I want to draw fractal
"roses."<br>
</p>
<p>John Carlson<br>
</p>
<div class="moz-cite-prefix">On 7/3/21 7:44 PM, Konstantin Smirnov
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAD1qDjR36ioDUAJQWpjqQ3fOt=Ghruv4yfpGf-AuA_3xN69wPw@mail.gmail.com">
<div dir="auto">Yes! I am looking for simple code that can use
curves of roses to draw them</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">вс, 4 июл. 2021 г., 03:40 John
Carlson <<a href="mailto:yottzumm@gmail.com"
moz-do-not-send="true">yottzumm@gmail.com</a>>:<br>
</div>
<blockquote class="gmail_quote">
<div dir="auto">Not using my imagination here much…would
something like this do the trick?</div>
<div dir="auto"><br>
</div>
<div dir="auto">
<div><a
href="https://www.php.net/manual/en/function.imageline.php"
target="_blank" rel="noreferrer" moz-do-not-send="true">https://www.php.net/manual/en/function.imageline.php</a></div>
<br>
</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Jul 3, 2021 at
7:37 PM Konstantin Smirnov <<a
href="mailto:konstantin.e.smirnov@gmail.com"
target="_blank" rel="noreferrer"
moz-do-not-send="true">konstantin.e.smirnov@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div dir="auto">Thanks! I saw your links
<div dir="auto">Fibonacci on other sites really exist.
Formulas for roses not clear how to apply, </div>
<div dir="auto">I am looking for those that can be
plugged in simple languages such as php or
JavaScript, </div>
<div dir="auto"><br>
</div>
<div dir="auto">More important is to have formulas.
For example for drawing leaves. At first for php,
then for 3d</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">вс, 4 июл. 2021 г.,
03:15 John Carlson <<a
href="mailto:yottzumm@gmail.com" target="_blank"
rel="noreferrer" moz-do-not-send="true">yottzumm@gmail.com</a>>:<br>
</div>
</div>
<div class="gmail_quote">
<blockquote class="gmail_quote">
<div dir="auto">Ah, GD, I’ve used that in Perl, not
PHP. I was never really impressed by GD, but it
may work for 2D. I can help with JavaScript,
GLSL or maybe Perl (OBJ file) if you want 3D. I
don’t have my AppleSoft Basic around any more.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Maybe you want something like
vpython?</div>
<div dir="auto"><br>
</div>
<div dir="auto">You seem to be lazy and not even
using resources given to you? What kind of
flower do you want to draw?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Look up converting converting polar
or spherical coordinates to Cartesian coordinates
would be a good start. Also look up L-systems and
graftals.</div>
<div dir="auto"><br>
</div>
<div dir="auto">John </div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Jul 3,
2021 at 6:53 PM John Carlson <<a
href="mailto:yottzumm@gmail.com"
rel="noreferrer noreferrer" target="_blank"
moz-do-not-send="true">yottzumm@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div dir="auto">I would start out with
something like Processing, not php.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Good luck!</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat,
Jul 3, 2021 at 6:51 PM John Carlson <<a
href="mailto:yottzumm@gmail.com"
rel="noreferrer noreferrer"
target="_blank" moz-do-not-send="true">yottzumm@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div dir="auto">I’ve never heard of php
doing drawings. You mean SVG or X3D?</div>
<div dir="auto"><br>
</div>
<div dir="auto">
<div><a
href="https://en.m.wikipedia.org/wiki/Rose_(mathematics)"
rel="noreferrer noreferrer"
target="_blank"
moz-do-not-send="true">https://en.m.wikipedia.org/wiki/Rose_(mathematics)</a></div>
<div dir="auto"><br>
</div>
<div dir="auto">I don’t know about
real flowers. Good luck with that.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Number theory is
really an odd choice, but I guess I
suggested Fibonacci. That was more
for numbers of petals.</div>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">John</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On
Sat, Jul 3, 2021 at 6:41 PM
Konstantin Smirnov <<a
href="mailto:konstantin.e.smirnov@gmail.com"
rel="noreferrer noreferrer"
target="_blank"
moz-do-not-send="true">konstantin.e.smirnov@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div dir="auto">Thanks! I mean
simple algorithm or formulas,
for example on php, that can
easily draw flowers with math,
number theory. For example, some
flowers may have structure like
math equations solutions.
<div dir="auto"><br>
</div>
<div dir="auto">Or for
beginning, simply drawing a
flower on php code. </div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr"
class="gmail_attr">вс, 4 июл.
2021 г., 01:19 John Carlson
<<a
href="mailto:yottzumm@gmail.com"
rel="noreferrer noreferrer"
target="_blank"
moz-do-not-send="true">yottzumm@gmail.com</a>>:<br>
</div>
</div>
<div class="gmail_quote">
<blockquote class="gmail_quote">
<div dir="auto">Mathematical
Roses or Rhodonea should
jump start you. Also look
up @sxywu on Twitter. Her
data sketches book may have
specifics for a variety of
“flowers”. For a more techy
look, find Maurer Roses.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I don’t know
what you mean by Nt. You
can find shaders or
JavaScript code in
X3DJSONLD. File names with
“flower” or contents of
“rose” will likely give you
a jump start in 3D, but they
are quite artificial and
even more so animated. Plus
it seems like my code is
currently in a non-working
state.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I would try
something with Fibonacci,
golden ratio to get things
more natural, or perhaps
particle systems for
imperfections.</div>
<div dir="auto"><br>
</div>
<div dir="auto">For previews,
checkout <a
href="https://codextreme.net"
rel="noreferrer noreferrer
noreferrer"
target="_blank"
moz-do-not-send="true">https://codextreme.net</a>.
One can get quite a lot of
diversity with parametric
equations, especially when
animating parameters.</div>
<div dir="auto"><br>
</div>
<div dir="auto">
<div><a
href="http://www.grad.hr/sgorjanc/Links/roses.pdf"
rel="noreferrer
noreferrer noreferrer"
target="_blank"
moz-do-not-send="true">http://www.grad.hr/sgorjanc/Links/roses.pdf</a></div>
<br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">Good luck!</div>
<div dir="auto">
<div class="gmail_quote">
<div dir="ltr"
class="gmail_attr">On
Sat, Jul 3, 2021 at
11:45 AM Konstantin
Smirnov <<a
href="mailto:konstantin.e.smirnov@gmail.com"
rel="noreferrer
noreferrer noreferrer"
target="_blank"
moz-do-not-send="true">konstantin.e.smirnov@gmail.com</a>>
wrote:<br>
</div>
<blockquote
class="gmail_quote">
<div dir="auto">Hi
<div dir="auto">Who
knows formulas that
can be used for
drawing of flowers?
Nt or algorithms</div>
</div>
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</blockquote>
</div>
</div>
</blockquote>
</div>
</blockquote>
</div>
</div>
</blockquote>
</div>
</div>
</blockquote>
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