Euler Rotation: Difference between revisions

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== Definitions ==
{{playerworld}}
Euler - Pronounced Oiler; discovered that as 1 is continuously compounded, it reaches a number, ''e''. However, Euler rotation is taking a 3-dimensional axes set and rotating them about the z-axis followed by a forward or backward rotation to create a new axes set.
For objects that inherit the property 'eulerrotation', the format is supposedly "Δ''α'' Δ''β'' Δ''γ''". Read further for a better explanation.


This server was the 15th server to ever be hosted on graal via Payed-Player-Hosted server. :-D.


''&theta;'': greek letter ''theta''<br />
{{stub}}
''&phi;'': greek letter ''phi''<br />
''theta'' and ''phi'' are commonly used in trigonometry for angles (but phi is most commonly used as a constant: 1.618...).<br />
''&alpha;'': 1<sup>st</sup> greek letter ''alpha''. For our purposes, it will represent The angle between the original x axis and the normal vector<sup>(1)</sup>.<br />
''&beta;'': 2<sup>nd</sup> greek letter ''beta''. For our purposes, it will represent the forward or backward "tilt".<br />
''&gamma;'': 3<sup>rd</sup> greek letter ''gamma''. For our purposes, it will represent the angle between the normal vector<sup>(1)</sup> and the new x axis.<br />


Therefore, images and text could be rotated, something that could not be done before, so that said image or text would have a three-dimensional effect. If all said is true, eulerrotation = "0 -pi/3 0"; for text would project it in a Star Wars-like fashion.
== The Modern Rivalry ==


sin(''&theta;'') = y / ''r'' (&Delta;y of a point from the center on a circle with radius ''r'')
Graal X was a very successful server during the 'older' days of Graal, holding quite an impressive playercount at the owner (KuJi)'s disposal.
cos(''&theta;'') = x / ''r'' (&Delta;x of a point from the center on a circle with radius ''r'')
sin(''&theta;'' &plusmn; ''&phi;'') = sin(''&theta;'') cos(''&phi;'') &plusmn; cos(''&theta;'') sin(''&phi;'')
-cos(''&theta;'' &plusmn; ''&phi;'') = -cos(''&theta;'') cos(''&phi;'') &plusmn; sin(''&theta;'') sin(''&phi;'')


In addition (not really useful):
Although later on the modern boom began, the early version of Atrius began, with MadJ clenching ideas, and power. KuJi began to consider Atrius a 'threat'.
tan(''&theta;'') = sin(''&theta;'') / cos(''&theta;'')
cot(''&theta;'') = cos(''&theta;'') / sin(''&theta;'')
sec(''&theta;'') = 1 / cos(''&theta;'')
csc(''&theta;'') = 1 / sin(''&theta;'')


<hr width="33%" NOSHADE>
KuJi went on to introduce Era-ish systems, which the players loved, such as more business's, Era-styled events, a fishing system, and worked on other jobs.
<sup>(1)</sup> The normal vector is the vector normal to the original z and the new z axes. This can be calculated through [[Cross Product|cross product]].
Players adored KuJi until MadJ pushed back a little bit with another update, cars.


== Rotation Matrices ==
Throughout the month's, KuJi and MadJ had a back and forth player war, trying to keep their players with newer and newer systems that other servers did not have, and KuJi was clearly the winner in the battle.
'''Note:''' The following example uses MATLAB notation for the matrix transformation.
 
[cos(''&gamma;'') sin(''&gamma;'') 0; -sin(''&gamma;'') cos(''&gamma;'') 0; 0 0 1] * ...
KuJi later kept his ground with newly created Spawn, Reborn, and even bypassed Era a few times.
[1 0 0; 0 cos(''&alpha;'') sin(''&alpha;''); 0 -sin(''&alpha;'') cos(''&alpha;'')] * ...
 
[cos(''&alpha;'') sin(''&alpha;'') 0; -sin(''&alpha;'') cos(''&alpha;'') 0; 0 0 1] * ...
Until Trinity came.
([x<sub>0</sub> y<sub>0</sub> z<sub>0</sub>]') = [x y z]'
 
Trinity bashed KuJi, and Graal X to the ground, and the new war between KuJi and new owner, James began.
 
Graal X later became a MIA project.
 
Years passed, with different Atrius versions comming out, and Graal X came back during the Jenn deficit of Era, which caused modern players to find another place to call their 'home'. Players equally spread out to new Atrian City, and Graal X to give the servers a try. There was really no competition throughout this time, as both owners figured they kept a good enough playercount at 20-30 players daily, they just kept their rivalry formal, and even got together a few times to help out one another.
 
Then 'tragedy' struck during Atrius Version 4, an attack was plotted on Atrius during one of the best times, and a hack script was unleashed on Atrius from one of the scripters, although James did not declare a full out war, many of the understaffmen, led by the Co-Owner, and the Manager, called an all out search to find out what happened, all evidence pointed to Graal X, and KuJi's new 'right hand man' after MadJ quit, G-Man.
 
After being yelled at to not do it by James and Mag, the Manager of Atrius 'infiltrated' Graal X, and pulled a hack script on there to even the score.
KuJi and G-Man were shocked, and placed the IP on full alert, KuJi and James were again at war, and the manager was punished, but never globally banned.
 
KuJi and G-Man later scrapped the project, and began to take a new side to Graal X.
Since G-Man worked on Icarus, a server that was brought up by MadJ and Drogan, he helped Icarus more then Graal X. Icarus was later scrapped due to the owners, and staff having real-life issues to attend to.
 
KuJi, knowing that time was running out for GX to properly hold a fight against Atrius, rumors came about that KuJi personally begged G-Man and Sage_Shadowbane to give him Icarus content, something that guaranteed him the ability to defeat Atrius in any battle, after the Icarus staff gave in to content that should not have even been theirs, KuJi worked on custom bodies.
 
Most content that you see today on Graal X was provided to Graal X by Icarus, by two staff members that really had no specific permission from Drogan or MadJ to give such content away anyway.
 
== Joey's stupidity ==
 
In May, 2007, Joey (Or KuJi to some) supposibly either issued himself, or asked someone to directly attack the server Atrius.
Atrius lost everything, and TheJames had to call Stefan to get the backups back.
Although at the moment nobody knows exactly HOW KuJi got onto Atrius, rumors are that he hacked in, other rumors are that he USDed a staff member to get him in, and another rumor was that Mike (Princeofkenshin) hired him.
When Stefan had to bring the backups back, he wasn't happy, and obviously all evidence pointed to KuJi;
Graal X was shutdown just hours after that, and KuJi was globally banned.

Revision as of 16:56, 30 June 2007

This article describes one of Graal's many playerworlds. If you have some information about this world's quests, staff, events or content, feel free to contribute to it by clicking the Edit link on the left side. Try to keep your edits as fair and unbiased as possible, though - the GraalBible is primarily for information, not for argument.


This server was the 15th server to ever be hosted on graal via Payed-Player-Hosted server. :-D.


This article is a stub - an incomplete placeholder article that gives some idea of what is being talked about, but fails to adequately elaborate on the given subject. Feel free to help GraalBible by expanding upon it.


The Modern Rivalry

Graal X was a very successful server during the 'older' days of Graal, holding quite an impressive playercount at the owner (KuJi)'s disposal.

Although later on the modern boom began, the early version of Atrius began, with MadJ clenching ideas, and power. KuJi began to consider Atrius a 'threat'.

KuJi went on to introduce Era-ish systems, which the players loved, such as more business's, Era-styled events, a fishing system, and worked on other jobs. Players adored KuJi until MadJ pushed back a little bit with another update, cars.

Throughout the month's, KuJi and MadJ had a back and forth player war, trying to keep their players with newer and newer systems that other servers did not have, and KuJi was clearly the winner in the battle.

KuJi later kept his ground with newly created Spawn, Reborn, and even bypassed Era a few times.

Until Trinity came.

Trinity bashed KuJi, and Graal X to the ground, and the new war between KuJi and new owner, James began.

Graal X later became a MIA project.

Years passed, with different Atrius versions comming out, and Graal X came back during the Jenn deficit of Era, which caused modern players to find another place to call their 'home'. Players equally spread out to new Atrian City, and Graal X to give the servers a try. There was really no competition throughout this time, as both owners figured they kept a good enough playercount at 20-30 players daily, they just kept their rivalry formal, and even got together a few times to help out one another.

Then 'tragedy' struck during Atrius Version 4, an attack was plotted on Atrius during one of the best times, and a hack script was unleashed on Atrius from one of the scripters, although James did not declare a full out war, many of the understaffmen, led by the Co-Owner, and the Manager, called an all out search to find out what happened, all evidence pointed to Graal X, and KuJi's new 'right hand man' after MadJ quit, G-Man.

After being yelled at to not do it by James and Mag, the Manager of Atrius 'infiltrated' Graal X, and pulled a hack script on there to even the score. KuJi and G-Man were shocked, and placed the IP on full alert, KuJi and James were again at war, and the manager was punished, but never globally banned.

KuJi and G-Man later scrapped the project, and began to take a new side to Graal X. Since G-Man worked on Icarus, a server that was brought up by MadJ and Drogan, he helped Icarus more then Graal X. Icarus was later scrapped due to the owners, and staff having real-life issues to attend to.

KuJi, knowing that time was running out for GX to properly hold a fight against Atrius, rumors came about that KuJi personally begged G-Man and Sage_Shadowbane to give him Icarus content, something that guaranteed him the ability to defeat Atrius in any battle, after the Icarus staff gave in to content that should not have even been theirs, KuJi worked on custom bodies.

Most content that you see today on Graal X was provided to Graal X by Icarus, by two staff members that really had no specific permission from Drogan or MadJ to give such content away anyway.

Joey's stupidity

In May, 2007, Joey (Or KuJi to some) supposibly either issued himself, or asked someone to directly attack the server Atrius. Atrius lost everything, and TheJames had to call Stefan to get the backups back. Although at the moment nobody knows exactly HOW KuJi got onto Atrius, rumors are that he hacked in, other rumors are that he USDed a staff member to get him in, and another rumor was that Mike (Princeofkenshin) hired him. When Stefan had to bring the backups back, he wasn't happy, and obviously all evidence pointed to KuJi; Graal X was shutdown just hours after that, and KuJi was globally banned.