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Aung Moe
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Beauty and the Butterfly

💖 ❤ 💗 ❤ 💚 ❤ 😍 Good Morning, Good Afternoon & Good Evening to all my friends out there Globally! 😍 ❤ 💚 ❤ 💗 ❤ 💖

Butterfly, butterfly
Oh! Colourful butterfly,
I like you very much,
Red, blue, black,
Yellow, green, pink
are your colours.
You can fly so high in the sky,
I like you very much,
My dear butterfly!

?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑?

A butterfly
Arduously flies
From bough to a sprig
A broken wing enervates
Struggle for the life
Accidently tumbles

Beauty of the butterfly
Blows over the eye
Laid up and a cry
No way to classify

Jazzy beauty of its wings
And to perch on flowers
To suck nectar impalpably
It is called the butterfly

A worm with a wing
A hopeless life of sign
Not only up but down
A life of beauty is a Sin

?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑?

Hey! butterfly! butterfly!
Come by me
and tell me of your dreams.

Have you danced with fairies gay
and found your love and life?

Have you drunk the sweetest gold
and paused on the finest beds?

Hey, butterfly, butterfly
Rest on me
and sing your finest song

Have you heard the music
the music of all that is?

Have you seen the unseeable tones
and swam in the seas scent?

Have you danced with blossoms
and laid your babes to grow?

A fluttered dream of worms long dead
the hope of better things to come.

Hey, butterfly, butterfly
leave me not
But tell, what dreams dream of?
of worms? of God?
or Both?

?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑?

To one that has so much
some may say everything
what can i say
to make your happiness eternal
stay the course
oh beautiful butterfly
find that light
within yourself
and dont let it go
silence is supreme
be aware for conscious
sense the sublime
to make it all the way
keep to the air
oh butterfly
and fly towards your dreams
greatness is there
waiting for the butterfly

?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑? ?̮̑●̮̑?

butterflies, butterflies,
beautiful butterflies
wings spread out
for everyone to see

the colors of a rainbow
red to violet, violet to red
the patterns of a rainbow
sea to shore, shore to sea

i’m going to catch my butterfly
soaring through the stars
stars shining bright
as the sun shines

the wings of faith
fluttering across the sky
the wings of hope
helping with every hand


i’m going to catch my butterfly
soaring through the stars
stars shining bright
as the sun shines

the clouds of emptiness
Suffering with every silence
the clouds of dead air
just butterflies, shining the night

i’m going to catch my butterfly
soaring through the stars
stars shining bright
as the sun shines

butterflies




#Flower #Butterfly #Butterflyoftheday #poem #poemoftheday #poemlove #poem #poetry #gif #love #loop #love #goodluck #goodday #gif #heart #friends #friendship #lol #gifoftheday #gifofthedayindeed #gifoftheweek #gifoftheyear #goodmorning #goodafternoon #goodevening #goodnight #greeting #amazinggifs #stunninggif #awesomegifs
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Aung Moe

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Bézier curves

Say you have some dots and you want to draw a smooth curve that sorta almost goes through these dots.  Then you can use a Bézier curve.   Some drawing programs use this trick... and lots of fonts are drawn with the help of Bézier curves.

The math behind these curves had been known since 1912, but they were popularized by Pierre Bézier, an engineer who used them to design automobile bodies at Renault.

Can you figure out how they work just by looking at the movie?  An explanation in words sounds complicated... but it's really easy as pie.

It's like you've got 3 guys running along straight racetracks.  The 2 guys in back have rabbits that each chase the next guy, always heading straight toward that next guy.  And the guy at the very back also has a dog that chases straight after the next guy's rabbit.  Everyone starts at the same time and stops at the same time.  The dog follows the red curve.

In other words:

First draw gray lines between your dots P₀, P₁, P₂, P₃. 

Each green dot moves at a constant rate along a gray line.  All the green dots start at the same time, and finish at the same time. 

Then draw green lines connecting the green dots. 

Each blue dot moves at a constant rate along a green line.  All the blue dots start at the same time, and finish at the same time.

Then draw a blue line connecting the blue dots. 

The black dot moves at a constant rate along this blue line.  It starts at the same time as all the other dots, and finishes at the same time.

Get the pattern?   Each time we do this trick, there's one fewer dot.  There are 4 original dots, 3 green dots, 2 blue dots and 1 black dot.  So now you're done!

The black dot traces out the Bézier curve shown in red here. 

You can play this game starting with any number of dots.  When you start with n dots, you get a curve described by a polynomial equation of degree n-1.  So, this red curve is called a cubic Bézier curve. 

Puzzle 1: show that our cubic Bézier curve is given by the equation

C(t) =  (1-t)^3 P₀ + 3(1-t)^2 t P₁ + 3(1-t) t^2 P₂ + t^3 P₃

Puzzle 2: generalize this to more dots.  (Hint: binomial coefficients!)

When you've got a lot of dots, people usually break them into bunches and draw a quadratic or cubic Bézier curve through each bunch.  They match up at the ends, so this works, though frankly I often think it looks kind of lame.  This is called a composite Bézier curve.  PostScript, Asymptote, Metafont, and SVG use composite Bézier curves made of cubic Bézier curves to drawing curved shapes.

I imagine there are lots of tricks that are 'better' than Bézier curves, but I'm not an expert!  If I wanted to know more, I'd read about stuff like non-uniform rational B-splines, or NURBS:

https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

But I just read this:

https://en.wikipedia.org/wiki/Bézier_curve

because I liked the animated gif.

#geometry  
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Aung Moe changed his profile photo.

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The picture is beautiful
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Aung Moe

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Taylor Swift in NYC earlier today #14
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Brazil's Neymar out of #WorldCup2014 after suffering broken vertebrae in 2-1 win over Colombia http://ow.ly/yNyOV
FORTALEZA, Brazil — Brazil’s team doctor says Neymar will miss the rest of the World Cup after breaking a vertebrae during the team’s quarterfinal win over Colombia. Neymar was kneed in the back by Colombia defender Juan Camilo Zuniga in the second half of Brazil’s 2-1 win, and was in tears when he was carried off the field on a stretcher.
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