2015. december 31., csütörtök

THE POWER OF RELIGION

The power of religion is misleading, lie, altering psychology, hallucination, distraction, war, damage, extremism... and the list is so long as the path to the Sun. BTW the our planet the Earth is orbiting around the SUN not the other way around. LOL!


2015. december 23., szerda

HOW THINGS ARE IN THE WORLD

Newborn
Mimic everything developing the base code through the little one express. This is the code the little one uses to express...
Going to school learning and forming to the standard of the society without thought to think it through.
First school, second school if you are not careful you have only a jerk around.
University? Are you kidding?
Whats next dear world, or should I put it this way; insane religious scientist who states that there are wormholes, or countless different particles that forms the nucleus, and they do mean it...
theoretical insanes all of them, while the world keep collapsing.
This is what happened to the little kid.

Porno, sexual slavery,violence rules in the business.
No basic human rights, no valid education.
The list is just as long as the path to the moon.
What will be the end?
The complete destruction of good human values!

Do not let the world destroyed by these. Do fight to put them off!





2015. november 13., péntek

TM AND CONDITIONING AND HOW IT RELATES TO EDUCATION

If you practice transcendental meditation you will be conditioned.
How is it differs from general education that some people defines "conditioning" as well.

In education the knowledge defines the way you express yourself, but you have your own opinion about it (about the knowledge), you decide it how you use it , "your self" is judging and keeping the information colored. "Its dumb, its clever, its ok" etc.

If you practice transcendental meditation this is not going to happen... You will be listening to the teaching and completely taking it in without your self being able to evaluate it properly. The way TM ers use it also tells that they are being conditioned. Why? Because they are not really able to utilize it, only "one directionally" repeat it.
Powerful regression happens if  somebody manages to deviate TMers from that direction, or somebody forces them to think it through.

Not to mention that the TMers's skin is active therefore further degrading the mental capabilities including intellect.
The guru used to say "intellect is the enemy", so the intellect is dead because of the mental state TM technique develops. If TMers doing analysis on TM makes the guru say: "the intellect is the enemy, meditate more and you will not need to ask to many questions about it". Its so true that
when TM in effect they dont care anymore about themselves, and the subject gets garbaged... so this is how they "killed" you.

Understand people please that TM is not a toy, its really a weapon, to target mental degradation for the society. This is how Indian religious extremist do. TM movement is one the most dangerous and threatening mental terrorist organization.



2015. október 27., kedd

RELIGIOUS WAR AND TERROR TO TAKE THE SOUL OF THE NATIONS.

What is a soul?
Soul is a mind or conscioussness, the way you feel generally in your life, including your tendencies like strenght to oppose to negative things, problem solving, will power etc.

What religion does?
It destroys and enslaves your soul, by implementing madness into your mind, madness that result in psychological responses leads to physiological responses results in psychological illnesses. Anxiety, hallucinations, anger attack, overwhelming emotions, extreme sadness, unfulfilled life etc.

Why they do that?
They do this today to eliminate opposition, to eliminate intellect, to eliminate the enemy nation and slave their own nation to follow commands without questioning it. To do whatever they want to do with you.

What is the future of religion?
Hopefully speaking, religion will not be allowed.
In reality: Like in transcendental meditation, they will convert you and force you without your own approval to religion like in TM to HINDU.
Religious war, like with Islam. Extreme use of the religious communities by politicians, like victor orban addressing (commanding) religion and religious communities to hate and take action against others.

What we can do?
Tell others their lies, how the live, they lie about god, the way it acts etc, and tell how many pedophiles and insane are in religion. Tell about killings tell about the past, tell about their insane capabilities and threat to the society. Tell about their poisoning medicines.

Thank you

2015. szeptember 26., szombat

START A WWW III TODAY?

Well, as I have been looking into this case , I would like to share with you that there is an extremely favorable day to start a world war III today.

pm modi, China's pm in USA! And from the Indian religious extremists perspective there is a full moon eclipse today! this might never happens in their life again. Its highly possible that they will attempt to terminate one of them. Maybe even us president is in danger.
In order to start a WWWIII a president dies as major act of aggression.

Lol even the Christian Pope is in the USA.

(well, these all above might sounds crazy, but remember this is all about from the Hindu religious extremist perspective)




2015. szeptember 13., vasárnap

INTELLIGENT SECONDARY SELF DETECTED IN TM MEDITATORS AND SIDHAS

(frame)
What is a secondary self?
Secondary self is a coexisting or switching self, that gets activating on skin activation or events that against specific conditioning, or in extreme cases its just simply rules the individual. (Some religious extremist have this as well due to extreme stress and conditioning.)

Quite often is also noted that the victim feels activated in the scruff and living his life entirely as a slave to the powerful self representation (the one which through the transcendental meditation technique forced into (hit into) the individual)

How to detect secondary self?
Through a series of control questions and motor activating response required tests. Also if you happened to meditate at least once in your life its likely that you have some self problem...
Modern EEG does it easily too. Those people who have secondary self they brain does the all famous alpha and theta waver while the victim is awake... (Most terrorist funded research tell that alpha and theta wave activity is great while you awake or in TM state, but in fact its extremely damaging for the mind)

What the secondary self does?
After the secondary self "awakens" in a primitive form in that way that it presents independence from the individual's will it can practically do anything against or "for the victim".
The most violent action types are Killing, violence on all levels, rape, pedophile etc.
The most important one the continuous molesting and bothering others and usually it comes with constant anxiety.

That you understand the importance of this issue. ANY TM MEMBER CAN BE TURNED TO A KILLER  IF THE SECONDARY SELF DOES. (reference : tm member shots and other one hallucinating she is sucking her energies, serious psychological treatment needed for 76 percent of those who transcendental meditation, tm member tries to kill his friend imagining the friends sucks his energies trough strings....  Hallucination caused by TM trainers's hit ("SKIN ACTIVATION BY SENSE OF SELF ACTIVATED INDIVIDUAL SHARING - ATTACKING WITH SELF, MY SELF TAKES IT AND I DON'T EVEN HAVE A CHANCE TO OPPOSE..., THEN I FIGHT AND SOMETIMES I MANAGE TO PULL IT OFF") experience while feeling very open or self hypnotic state - self referral state)

detail this:The body doesn't have time to actually chemically change that fast to trigger elevated changes and back so this whole self swap would be just a problems with the chemical balance of the brain or the body.

What these people feel who have secondary self?
They talk answer a lot to themselves, they have lots of fear, they have lots of pain, and they usually trying to keep it secret from the people. The secondary self often takes over, takes control. Loss of memory of the doings but no loss of reality. Serious sleeping problems, no dreaming or minimal in sleep. Extreme amount of daydreaming. Constant anxiety, fear.

All secondary self initiated action is violence based that means the secondary self employs violence to achieve the Guru's commands or religious views. On lower levies it means skin activation to feel spaced out, fear or other things. (for example skin activation on stomach makes the victim feel fear, or push in, and this way the secondary self controls the victims life.) In extremes it can terminate the victims life by causing extreme mental disaster by motion sense, push sense, and pain sense reverse activated, even direct muscle control is possible. If the individual doesn't die in it then the symptoms are usually increased until the victims dies.

Extremely important to understand this and immediately detain and put to into mental hospitals TM trainers and long term mediators or above (raja, guru etc). Nationwide warning required or major spread of special type of mental illness possible.

Important people who have been in contact with the TM technique:
Terrorist John Hagelin
Terrorist Girish Varma (in 15 years he raped over 200 girls in india and other countries. )
Terrorist  Bevan Morris
Victim David Lynch
Victim Russel Brand
Victim Arnold Schwarzenegger
Victim Sofia Vergara
Generals of US, India,Mozambique army
Nuclear weapon handlers of us army at NORAD and so on and so on.

Its extremely dangerous to employ anybody with tm technique to any part of the government.

refer to terrorism as "when, for religious or other reasons TM movement and its members doing harm to the country, population, military etc"

They are forcing people to hindu religion, making them secondary self, selling them poisoning ayurvedic medicines, causing them mental illness, and trying to control the education, health care, military, science...

Endless repetition to the society, thats the way the slowly transform the world to mental madness and mental slavery.

These all become major threats, these points must be taken care by society, police, nation protecting services, and military.








THE HIT, WEAPON OF THE RELIGOUS EXTREMIST TERRORISTS, EXTREMISTS

Whats is the hit?
The hit is a form of skin activation when you will be feeling a hit on your skin without actually having a direct contact to other people or objects.

How do I get a hit?
If you want to get hit like those hundreds of millions of insanes who living their life every day like squeezed lemons, just learn transcendental meditation, deeksha, theta healing, or any religion or lastly get drogged by marijuana, cocaine or designair drog.

Why people are hitting each other?
Originally they font want to hit each other but because of mental terrorism like tm movement (hindu religious extremist movement) are using this technology to kill nations mentally, and later completely push them to slavery. From the regular hits the major degradation is automatic.
Everybody will be full of tension, or overwhelmed in anything including "peace". The skin sensed possible 100 times more powerful than in normal human beings in any direction (softness or supercharged) They will become very impulsive or extremely dull. If they happen to witness a murder they might not even respond.

Why politicians all are hit?
Now rather say first, why they are not being treated by psychologist instead of letting them control the country in mentally dangerous states.
They are hit because often they take control, they get into office by this type violence which is so natural for them. They are usually weird people. They have received education but because of the hit they cant use a fraction of it. So practically they extremely dumb.

Dumbness, just see why all politicians are working so hard against their own country and other nations. Almost all actions of theirs creating threat for their nation and for other nations.

Solutions?
Again, politicians must be very cever and healthy people. They must not be hit, and they must work on increasing the level of eduction and health in the country they live in, they serve (serve?)
Politicians must undergo every day a psychological test, that validates their working capabality and mental balance.

If this doesn't get solved quickly we all going to die in impossible views (hit in) creates war and terror. And those who call these war and terror "home" they will laugh on us and slaughter and enslaves us again and again.











2015. szeptember 10., csütörtök

HOW UNDEREDUCATED LEADERSHIP DESTROYS THE WORLD


The undereducated leadership, what does this mean?
I doesnt mean that the number of PHD's decides how educated one can be.
Unfortunately its a much more complex term.

It means how human you are. How straight, simple, honest, intelligent, protective, foreseer and most importantly within this circle how action capable you are.

Want an example? Look at Obama. Everybody loves him. But he is the weakest mind ever recorded in the human history. The undereducated negroid who makes mental illness legal. For example drog, and gay. Both were related to health care and now they are now part of the very unlucky us nation. Practially it will bring further mental degradation and sexual problems to the American nation. Many mothers and fathers will cry because Obama wishes to make mental illness legal... Do you think that he want to take revenge for the negroid slavery back in time? Or should I ask do you think mentally Obama is actually Obama or a so called forced and transformed image only. That he have a commander inside his head that gives hir orders? Wow this sounds so weird.

Anyways lets get back to subject. Through Obama's example you maybe understand better what does it mean to be a true leader. Because he fails it. There are of course many other leaders who does. For example in many country there is a problem with the contaminated water. The leadership of the countries instead of clearing the water they let the nation's DNA base to rot, and let them marching forward extinction as well.
How insane they are.

Education and health care the most important thing humans can have. See which countries leadership cares about it. None of them.

See this is how they destroy you.

Why?

Dont you think they ain't giving a damn about it? People, wake up, attack them! Of course not like them you with weapons. But legally. Bring them to justice. Bring them hell of the justice. And publicize it. Dont be afraid of them, they cant kill billions of people.

Hard?
Not that much.






2015. szeptember 8., kedd

HOW THE HUMAN RACE MUST GO FORWARD?

Nature is such a dumb system where by trial and error trying to figure out what is best. It doesn't work on human race anymore.
Human race must be lead forward by the most intelligent individuals, not the most violent or troublesome or religious, who otherwise very successful based on the evolution system nature provided.

Unfortunately it means lots of uncomfortable point comes with this.
How to handle the human race's dna base. How to handle dna based diseases.
How to handle dna based mental incapabilities etc. How to handle the mental illness the human race developed in the past and keep dragging into the 21 century. (These are religion!, under education! poisoning medicines!, violence based solutions!, practically everything underdeveloped! )

I believe these uncomfortable points are one of the reasons why these "highly evolutionary" leaders trying to avoid the subject and playing the inhuman humanitarian role (with their "humanitarian" behavior pushing the human race towards extinction), not caring about the future at all and keeping their nation undereducated and underdeveloped. Lets not exclude that very evolutionary point in this, that this way all possible opponent is pushed off from the equation.

This system must be stopped and the most intelligent people at least when change happens must step forward and reorganize government into such system where there are no opponents but only brightest minds with best solutions. No more party, no more corruption, no more insanity.

United systems are much better, there is only one direction and better and better solutions for specific problems. These automatically creates less costly more effective solutions.

Try to get rid of the party system and make the world unified and work for the education and development of the human race.
(of course not like TM movement terrorist organization... trying to pose with higher education, giving the lowest, trying to pose no religion, giving the strongest religious conditioning evcr, trying to pose with healthy medicines, most of their medicines artificially contaminated with heavy metals, and metals. HAHAHAHAHAA we catch you!)

2015. augusztus 31., hétfő

IS Narendra Modi A TERRORIST? WHY?

Yes Modi is a terrorist.
Why?

Because he is hindu, and he is practicing the incredible threatening transcendental meditation, the deep conditioning method of hindu systems.
Those who practice it, they will be not anymore normal and healthy human beings. They are forced to follow orders if they are not then incredible pain, memory loss, secondary self takes control . He have strong connection to the RSS terrorist organization, and also to the worm (Girish Varma, the raper).

This terrorist organization plans conditioning as many Indians as possible with the TM system so that they will be a thinkless robots who will do whatever they say. If they don't do, they will have incredible pain for example at the tail bone, or hip bone, maybe head or chest as well... They called it shrink. The skin is strongly activated and motion, burning sensed on it.

He have in his min, internally a god like ruler (a distorted self like in multiple self disease), a supreme being implemented into his mind, that is capable to take over him, and give commands to him in the name of hindu religion and in the name of hindu payback.
He is incapable to deviate from the plan the TM movement terrorist implemented into his mind. If he would try to the pain what he gets by reverse activated senses (skin activation etc), (pain, sense loss, touch) would be so great that he might suicide or die in 1-2 days.
He is pretty much the world most dangerous person...

To prove this you only have to look up some police cases and psychological reports on TMers.

Here are some other RATs who have been confirmed to have the same state. All rajas of the TM movement and most of the TM trainers. Find their websites and the list of the names to contact them, tell them what TM movement does.
TMers must be sent to mental health institutes or military mental health institutes to further study the effect of transcendental meditation (psychological weapon)

Think what will come if Modi and his followers succeed.

There will be middle age level education, huge conditioning, mental degradation, no health care, waves of disease will wipe the population of earth, constant war etc.
---

One of modi's associate, the actual reason why modi is in office is the Girish family, the gnome's (maharishi's) family. This is how the stolen, cheated billions payed back. They thought him to meditate to became famous and supported his campaigns with hundreds of millions of dollars.

How modi will going to pay back to a religious extremist terrorist? Or in reality how he will serve them instead..

will be continuing...

more exact definition element
you have your skin and the skin activated state will be referred to as some others's self presence or skin. The reason for this is because the individual senses as the other is touching or connecting or hitting with his/her self.























































































































































































































































































THE PLANNED ATTACK OF THE TERRORIST INDIA

In the is extremely dumb world I have to write it out that we will be attacked by the religious extremist india "when the sun rises"...

What does the "sun rises" means? A special day in the vedic calendar? Or when everybody or sufficient number of people would be converted hindu terrorist by combined self-hypnotic and religious methods, or something else, like modi will be the president and the maharaja at the same time?

These converted hindu RATs are already in the USA key positions, like General, nuclear weapon controller. healthcare, goverment etc. The pose the biggest threat ever to the united states by carring an other self in their brain that self can activate any time and by reverse activating pain, touch or other senses or responses they can controll the life of the united states citizen!

What a shame to them, What a shame to them!

The terrorist india, planned to attack us since 1950 when finally the british empire left india. The gnome (maharishi) and deeksha and thetha healing and many other terrorist mostly called gurus left india to spread the mental weapon to the societies of the enemy in order to take controll them, and later overrun them and kill us all.

How dumb they are thinking that they will have good positions in that slavery they imagine us!








2015. augusztus 14., péntek

DESTRUCTION OF THE SOCIETY

What is causing the destruction of the society?
-Undereducated political leaders, undereducated citizens.

How high educated a politician must be to stop this destruction?
-At least 3 phd they must have.

What else they have to do to stop the destruction of the society.
Minimum university level education to everybody,
Maximum support for education and health care.

Practically this is it.
Now think, why the hell they dont do this?
How friendly isnt it?

Long term outcome of not doing it: world war III

2015. augusztus 5., szerda

MENTAL TERRORISM - RELIGIOUS TERROR IN THE 21 CENTURY.

Transcendental meditation, deeksha, theta healing, dream control, brain control etc all of these are the tools to destroy your personality your education your capabilities.

All trough bringing the individual to its sensors and sense, and change them in the name of god's will, spiritual master will, karma, even business etc.

As the senses misfunction because of the techniques that holds them or makes them loose will cause mental problems. These mental problems further misinterpreted by the instructions of the "highly trained" trainers. The image what unlucky follower develops about the world is completely mismapped. Why what is completeley gone. Mental degradation takes place.

It is a weapon, like deploy and forget, and in few decades it will destroy civilization. Education is gone, behaviour is out of control. Pornography violence rules. All signs of education are gone.

Congratulation for All Intelligence office and mental terrorist organizations because both needed to put an end to human life and value.

This it man. This is their play , this is what they want for you.

And dont forget after such level of deployment of series of psychological weapon, you can expect india, russia, and possibly china's united forces overrunning you.

The china's current prime minister would not go into a world war, but a termination of him by US probably initiate a war.

This will happen soon, because the constellation seems to be favourable. An extremely conditioned Indian prime minister modi, supported into office by terrorist, with the largest army behind him, plus a russian insane: Putin, who can do a world scale war as well.

But how to make Putin religious?

No need the religion because it is now hidden in you coupled with self hypnosis based mental techniques, without you knowing.
The risky parts are tought in o-language, or even not understandable forms.
This is it.




2015. március 3., kedd

PSYCHOLOGICAL WARFARE IN THE 20-21ST CENTURY

Psychological Warfare in the 20-21st century

Religions and mental techniques as a "self control systems" or insanity?

What is religion? Religion is a system where it explains and convince the individual that there is a supreme leader and that leader is the true controller of your existence, life. To this supreme leader the individual develops some relation. This relation can be intellectual or emotional.

The problem is that developing relations to non real things causes remapping. What is remapping? Everybody have relations, likes to things. These likes and relations can be shifted by changes in life.
For example a divorce can cause major remapping. Religion does the same. Why? Because it brings abstract values (leader) and relations, likes, even love to the individual. The love to wife, the love of the mathematics, the love of other people's life - value - changed. Everything shifted to a new perspective. Is it a self control?

Many religion very undervalues human life. Some says that your now is the result of your past action in your previous life, others says now is valued in terms of relation to leader. Is it a self control?

What does this do? It moves off people from reality, towards extremism and overwhelmness. The remapping could be so strong that people actually becoming seriously ill, mentally and physically.  Is it a self control or insanity?

Why would people do that? Remaining in the field of reason, there is only one way: They want to harm with it. Remapping influences every field of life, practically all fields of life suffers from it. Those people who are religious they tend to do more crimes, they tend to get overwhelmed more easily. Just see the news there are almost every day some major crime committed by a priest or a religious extremist. Remapping as observed is quite often unnecessary enthusiasm or extremism, this is what causing the problems. Split of the self, self injection, accumulation. stuck, war, all kinds of mental illnesses etc sprouts from this.

Now everybody know what it is. So why people do that?

Poor mans weapon/living: spiritual techniques.

As understood remapping causes mental illness, so what the spiritual techniques do?

They do even worse. Many of the spiritual techniques use religion as a base and combining it with self-hypnotic techniques and states. Like transcendental meditation. Allow me to use this example because its states that it is not a religion while it is entirely based on hindu religion. Those who spread this technique they are so remapped, so far away from respecting humanity in the name of humanity that they lie to people about what they learn, practice, they brake their basic human rights including constitutional rights. They poison them with ayurvedic medicines contains very high level metals, etc, they send them quickly into various mental dependencies like anxiety, extreme worry, etc.

Who and why would this to others? Maybe I should ask first who can do this? Only heavily conditioned, remapped humanoid looking things. They are the 20-21st century state of the art terrorists, and their assets. They are not using weapons, they using mental techniques like TM to destroy the enemy.

What will the enemy get? Mental problems, chaos, dna problems, cancer, killing, mental degradation. What the terrorists get? They get your money… They get your trust, they get your life…

Check out the reality of those who are practicing any of these mental techniques. Let me add, deeksha, theta healing, brain control, dream control etc to the long list of harmful mental techniques developed by religious extremists or simply insanes!

Please don't give them your life!

Thank you!








2015. február 1., vasárnap

DETERMINE THAT THE MESH POINTS/TRIANGLES/QUADS ARE IS INSIDE "D" DOMAIN

"EARLISH" DETERMINATION THAT THE POINT
IS INSIDE THE DOMAIN OF THE TRIANGLE OR NOT.

To check that T is actually in triangle P1,P2,P3 we need to add
the α,ß,Γ angles together. And if Ω<360.0 then it is outside of the domain of the triangle. To calculate these angles make 3 vectors out of the triangle points and T.

vec1 = normalize( P1-T)
vec2 = normalize( P2-T)
vec2 = normalize( P3-T)

Then the angles:
α = acos(dot vec1 vec2)
ß = acos(dot vec1 vec3)
Γ = acos(dot vec2 vec3)

Ω = α+ß+Γ
finally if Ω<360  then the point is outside of the triangle's domain.

If you have 3d system then flatten it to 2D first, and keep in mind that it is valid only for projection only.

2015. január 30., péntek

PROJECT A POINT ONTO THE SURFACE OF THE TRIANGLE

PROJECT A POINT ONTO THE SURFACE OF THE TRIANGLE

in the variable names d means distance,length, magnitude; 3d means three dimensional. If 3d not used then it is 2D.
To get IT point I will use line-line intersection.
The coordinates should be flattened so this time I project from above so I flatten Z.
Example:  P1 [x,y,z] = P1[x,y,0] or just use point2 variable type to calculate P1[x,y]
Draw a line L1 from any Triangle point to T point.
The Vector from P3 through T which is L1 will be then:
normalize(T-P3)


Now, this line we intersect with the other line P2-P1 to get the exact point through T lies on the Line.
This is necessary because our IT point lays exactly on this line.
Get the angles:
α = acos(dot normalize(P3-P2) normalize(P3-T))
Γ = acos(dot normalize(T-P3) normalize(P1-P2))
To Get the lenght of the dP2IP1 first get the lenght of dP2P3
dP2P3 = SQRT((P3.x-P2x)^2+(P3.y-P2y)^2)
Then
dP2P3/(sin Γ)=dP2IP1/(sin α) therefore:
dP2IP1 = asin (dP2P3/(sin Γ) * (sin α))
Make IP1 out of the gathered data:
IP1 = normalize(P2-P1)*dP2IP1 + P2





We have to convert this length dP2IP1 to the 3d lenght of the P2-IP1by using ratios. This means if the P2-IP1 lenght have a ratio of the whole length of the 2d P2-P1 line then the 3D line 3dP2IP1 lenght will have the same ratio. Therefore:
ratio = dP2IP1/dP2P1
Now have to caclulate the other lenght dTP3 and ratio2. Width 3dIP1P3 whic will give the IT point.
3dIP1P3 = SQRT((IP1.x-P3.x)^2+(IP1.y-P3.y)^2)
ratio2 = SQRT((T.x-P3.x)^2+(T.y-P3.y)^2)/3dIP1P3
Calulate the real 3d lenght of P2-P1 by using triagle law.
So it is dP2P1 2d lenght and the Z coords will make the other lenght of
the 90 degree triangle to calculate the 3d lenght of the P2-P1. 3ddP2P1 = SQRT(P2.z-P1.Z)^2+dP2P1^2)


Now the rest With 3d coords:
3dIP1 = normalize(P2-P1) * 3ddP2P1*ratio + P2
3ddP3IP1 = sqrt((IP1.z-P3.z)^2 + sqrt((IP1.x-P3.x)^2+(IP1.y-P3.y)^2))
Finally the T1 point:
T1=normalize (P3-IP1)*3ddP3IP1*ratio2 + P3

To accelerate the code use the magnitudes and normalizations only once where possible.


2015. január 29., csütörtök

"EARLISH" DETERMINATION THAT THE POINT IS INSIDE THE DOMAIN OF THE TRIANGLE OR NOT.

"EARLISH" DETERMINATION THAT THE POINT
IS INSIDE THE DOMAIN OF THE TRIANGLE OR NOT.

To check that T is actually in triangle P1,P2,P3 we need totest the α,ß,Γ angles individually. And if any of the angle is bigger than 180.0 then the point is outside of the domain.To calculate these angles make 3 vectors out of the triangle points and T.

vec1 = normalize( P1-T)
vec2 = normalize( P2-T)
vec3 = normalize( P3-T)

Then the angles:
α = acos (dot vec1 vec2)
ß = acos (dot vec1 vec3)
Γ = acos (dot vec3 vec2)

if α>180.0 or ß>180.0 or Γ>180.0 then the point is outside of the triangle's domain. Well if any of the angle is 180.0 degree exactly then it is on the circumference of the triangle.

Now  you got to watch out that the dumb acos cannot do more than 180.0 so if any of those 2 is equals to the third than it is likely that you have the smaller side so you have to 360-value to get the real, also if you add the angles together and it is not 360.0 you can be sure that acos did cheat on one of them and it does lies outside of a triangle!





2015. január 27., kedd

FAST LINE-CIRCLE INTERSECTION BASED ON TRIANGLE LAWS

"EARLY" DETERMINING INTERSECTION TYPE.

(Magnitude or distance variables are starting with d)

Get the distance (magnitude) in between center point C and P1 line point and C and P2 point
using triangle method.

dP1C = sqrt((C.x - P1.x)^2 + (C.y - P1.y)^2)
dP2C = sqrt((C.x - P2.x)^2 + (C.y - P2.y)^2)


If (dP1C==r and dP2C==r) then the line is a chord, therefore the intersection points are P1 and P2
If (dP1C<r and dP2C<r) then the line is inside the circle and it does not intersects.
If (dP1C<r and dP2C==r) or (dP1C==r and dP2C<r) then the line is inside the circle and the
intersection point is P1 or P2 based on which one is on the circle (dP1C or dP2C equals to radius).
If (dP1C==r and dP2C>r) or  (dP1C==r and dP2C>r)  or (dP1C>r and dP2C>r) then
the tangent angle THETA Θ and the angle OMEGA in between P1-C and P1-P2 will define
that the line is intersecting or not.

The tangent point is T1. The angle in between tangent
and radius is always 90 degree, therefore it is a triangle with 90 degree.

The tangent angle Θ = Asin(r/dP1C)  // (sin(90) = 1.0)
The omega: Ω = acos((dP1C^2 + dP1P2^2 - dP2C^2)/(2*dP1C*dP1P2))

If (Θ>Ω and dP1C==r and dP2C>r) or (Θ>Ω and dP2C==r and dP1C>r) then the line intersects
with the circle at two point and one of the point is the P1 or P2 depends on which one
is in the circumference (dP1C==r or dP2C==r). The other intersection point have to be calculated.
If (Θ<Ω and dP1C>r and dP2C>r) Then there is two intersection point and only this time both have
to be calculated.
If (Θ=Ω and dP1C==r) or (Θ=Ω and dP2C==r ) then the line will be tangent to
the circle and There is one intersection point.
If (Θ<Ω and dP1C==r and dP2c>r) or (Θ<Ω and dP2C==r and dP1c>r)
then the end of the line is on the cirlce.
Therefore the one (dP1C or dP2c) equals to the radius that point is on the circle.

FASTEST METHOD FOR DOUBLE OR SINGLE INTERSECTION  USING TRIANGLE CHORDS LAW.
(this method cant be used when
the dP1C<r and dP2C>r  or dP1C>r and dP2C<r for this call function below)

Reuse the variables from the early determination.
To get α = asin(dP1C/ (r/sin(Ω))
To get Γ= 180 - Ω - α
To get dP1IP1 = sin(Γ)*(r/sin(Ω))
To get ß=180-α
To get ε=180-2ß
dIP1IP2 = 2r*sin(ε/2)


So the intersection points are:
IP1 = (normalize P1-P2)*dP1IP1+P1
IP2 = (normalize P1-P2)*(IP1IP2+dP1IP1)+IP1

because the magnitude calculated before at early determination the normalization can be done by hand by dividing the translated vector with the magnitude. Saves some processing time.

If dP1C==r then reorganize your code that:

ß = Ω //calculated at early determination
ε =180-(2*BETA)
IP1 = P1 //  dP1C == r  therefore P1=IP1
dP1IP1 = 0
α = No need to calculate
Γ = No need to calculate

then like above:
dIP1IP2 = 2r*sin(ε/2)
So intersection points are:
IP1 = P1
IP2 = (normalize P1-P2)*dIP1IP2 +IP1


CALCULATE SINGLE INTERSECTION IN CASE ONE OF THE POINT IS INSIDE THE CIRCLE'S DOMAIN

To get Beta ß=acos(dot (normalize C-P1) (normalize P1-P2))
To get Gamma Γ=asin(dP1C/(r/sin(ß)))
To get Epsilon ε = 180-(Γ+ß)
To get P1-IP1's magnitude: dP1IP1 = (r/sin(ß))*sin(ε)
IP2 =(normalize(P1-P2)*dP1IP1)+P1





maxscript version of this system is downloadable below, please check the header for instruction.

maxscript version of the circle-line intersection

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