[Blackfield - Pain]

Here I'm standing on the sea shore
She is gone, now she's gone
All the angels praying for me
As I fall, As I fall

While I'm melting in the rain, deep in pain, she is so far
Will we ever meet again as friends, after so long?

To me nightmare with the devil
I'll go strong, I'll go strong
All my friends now try to save me
What a joke, what a joke

While I'm melting in the rain, deep in pain, she is so far
Will we ever meet again as friends, after so long?

While I'm melting in the rain, deep in pain, she is so far
Will we ever meet again as friends, after so long?

..

Wilson always has a word for me.

[Gravenhurst - The ice tree]

At six in the morning
the ice in the tree
thaws into the millpond
returns to the deep

I caress where my lover
once lay by my side
before i turned inwards
and forced her to fly

We try to connect
with the people outside
they pass through our slumber
like trains in the night 

I caress where my lover
once lay by my side
before I turned inwards
and forced her to fly

After the cold night
the raindrops that froze
melt into the thin air
like the footsteps of ghosts 

I caress where my lover
once lay by my side
before I turned inwards
and forced her to fly

For she could not know me
for I know not myself
and without understanding
love isn`t enough

God, why do you let us be brought to life just to feel so disarmed. Such I hate you.

Just a simple demo. The goal was to minimize the upper bound of needed checks along the tic-tac-toe gameboard.

Brief Explanation

The result was achieved by assuming that the elements of the 3x3 matrix could be mapped to the [1,9] interval in N by the bijective application (from [1,3]x[1,3] to [1,9]):

f(i,j)=i+3(j-1);

Now let n=f(i,j), for each i,j in [1,3].

• If n is 5, there are 4 checks needed (the middle row, the middle column, both diagonals);
• If n is any other odd number (1,3,7,9), it stays in the corner, so ther are only 3 checks needed (a row, a column, a diagonal);
• For even numbers the upper bound decreases to 2 (a row and a column only).

So the number of needed controls stays between 2 and 4, in a maximum range of 8 (3 rows, 3 columns, 2 diagonals) - it would be nice if tic-tac-toe was not a complete game in which neither player can win...:P

Here it goes the code and the link to the main article.

Do you remember chalk hearts melting on a playground wall
Do you remember dawn escapes from moon washed college halls
Do you remember the cherry blossom in the market square
Do you remember I thought it was confetti in our hair
By the way didnt I break your heart?
Please excuse me, I never meant to break your heart
So sorry, I never meant to break your heart
But you broke mine

Kayleigh is it too late to say Im sorry?
And kayleigh could we get it together again?
I just cant go on pretending that it came to a natural end

Kayleigh, oh I never thought Id miss you
And kayleigh I thought that wed always be friends
We said our love would last forever
So how did it come to this bitter end?

Do you remember barefoot on the lawn with shooting stars
Do you remember loving on the floor in belsize park
Do you remember dancing in stilettoes in the snow
Do you remember you never understood I had to go
By the way, didnt I break your heart?
Please excuse me, I never meant to break your heart
So sorry, I never meant to break your heart
But you broke mine

Kayleigh I just wanna say Im sorry
But kayleigh Im too scared to pick up the phone
To hear youve found another lover to patch up our broken home

Kayleigh Im still trying to write that love song
Kayleigh its more important to me now youre gone
Maybe it will prove that we were right
Or ever prove that I was wrong

It's never easy to do the right thing.

Su suggerimento di Andrea, ho scritto due righe che permettessero di disegnare curve piane parametriche, e questi sono i risultati =P

Appena ho un momento preparo un'applet in modo che tutti possiate vedere come dispongo inutilmente del mio tempo ^____^

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After a brief talk with Andrea, I've written a couple of code lines able to draw plain parametric curves, and these are the results.

As soon as I get a minute, I will export an applet so you can all see how well do I waste my time :P