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Stupid noob questions regarding radius...


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#1 Orymus3   Crossbones+   -  Reputation: 8988

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Posted 31 August 2013 - 11:49 AM

Hi,

 

Disclaimer: I feel stupid about not remembering this...

 

I'm currently trying to create an algorithm for a project I'm working on, and I'm stuck with a stupid noob highschool maths question.

 

Essentially, I'm creating a system as a sphere, and I'm dividing it amongst players.

To do this, I take the 360 degrees and split them by the amount of players.

ex: 1 player (has the whole 360 degrees), 2 players (each have 180 degrees), etc (see examples below)

 

 

maths.png

 

That works great.

 

Now, I'm trying to put objects at a random x,y position into a specific player's 'zone of influence'.

Since I know that a player owns a specific arc (for example, player one will have from 0 degrees up to 360/amount of players), I know the range of degrees I can use for limits.

 

However, I'm somehow not able to remember how to trace that line (the relationship in increments of x and y that extrapolates from a specific degree).

 

I feel especially dumb since I realize that at 45 degrees, the increase in x and y is the same, but I can't explain it.

 

Anybody can remind me of how this works, or send me an article?

 

I feel ashamed that I can remember matrices and limits, but not this... I know its related to Sin and Cos, but I'm not sure how to do the math.


Edited by Orymus3, 31 August 2013 - 12:01 PM.


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#2 DT....   Members   -  Reputation: 487

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Posted 31 August 2013 - 12:29 PM


Now, I'm trying to put objects at a random x,y position into a specific player's 'zone of influence'.
Since I know that a player owns a specific arc (for example, player one will have from 0 degrees up to 360/amount of players), I know the range of degrees I can use for limits.
 
However, I'm somehow not able to remember how to trace that line (the relationship in increments of x and y that extrapolates from a specific degree).
 
I feel especially dumb since I realize that at 45 degrees, the increase in x and y is the same, but I can't explain it.
 
Anybody can remind me of how this works, or send me an article?

 

 

http://www.regentsprep.org/Regents/math/algtrig/ATM1/arclengthlesson.htm

http://math.tutorvista.com/geometry/arc-length-formula.html



#3 CombatWombat   Members   -  Reputation: 474

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Posted 31 August 2013 - 02:09 PM

If I understand your problem correctly:

You want to generate a random point (x,y) for a player that owns the chunk of circle between 0deg-15deg and your circle radius is 1 unit...

 

Randomly generate a vector as a length of 0-1 and an angle between 0-15deg.

The end point of that vector will be

x = L * cos(angle)

y = L * sin(angle)

 

You need to watch the convention of the sin/cos function you are using with regards to degrees vs radians.



#4 hanstt   Members   -  Reputation: 259

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Posted 01 September 2013 - 06:47 AM

If I understand your problem correctly:

You want to generate a random point (x,y) for a player that owns the chunk of circle between 0deg-15deg and your circle radius is 1 unit...

 

Randomly generate a vector as a length of 0-1 and an angle between 0-15deg.

The end point of that vector will be

x = L * cos(angle)

y = L * sin(angle)

 

You need to watch the convention of the sin/cos function you are using with regards to degrees vs radians.

 

Note that this will create a higher density of points close to the center of the disc. If you'd prefer a uniform distribution of points in the xy-plane, either generate (x, y)-pairs until one point falls within the circular sector of the player of interest, or scale the points by sqrt(L):

x = sqrt(L) * cos(angle);
y = sqrt(L) * sin(angle);

Read up on polar integration for more info.



#5 Rorakin   Members   -  Reputation: 618

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Posted 01 September 2013 - 09:38 AM

Why not just randomly generate an angle between 0 - 360. The maximum x and y using the random angle:

x = radius * cos(angle)

y = radius * sin(angle)

 

To randomize this, you simply also need to randomize the radius:

 

Rand(x) = Rand(radius) * cos(angle)

Rand(y) = Rand(radius) * sin(angle)

 

Since x and y are a computation of radius and angle, randomizing both angle and radius makes it a random point in the circle smile.png

And to simply constrict to a player's portion you just change the min and max of the random angle generation.


Edited by Rorakin, 01 September 2013 - 09:40 AM.


#6 Khatharr   Crossbones+   -  Reputation: 3001

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Posted 01 September 2013 - 01:44 PM

x = sqrt(L) * cos(angle);
y = sqrt(L) * sin(angle);

 

That totally looked wrong at first glance. Interesting.


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#7 Orymus3   Crossbones+   -  Reputation: 8988

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Posted 01 September 2013 - 09:56 PM

It is unfortunately the other way around:

 

a x and y coordinate are generated at random, and I need to check whether they fall within the area I'm looking for.

 

I have the angle in RAD to which I can refer.

 

I reckon the Vector would be much simpler, but let's assume I need to use this less efficient method.

How would I determine whether a specific (x,y) couple is in a specific chunk of the circle?



#8 Khatharr   Crossbones+   -  Reputation: 3001

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Posted 01 September 2013 - 10:35 PM

That's actually easier. Just atan2 the point and check which area the angle is in. If you need to know whether it's inside the radius then that's just Pythagoras. You should probably run Pythagoras first to see if it's inside the circle, then if it is you can atan2 to determine the angle.


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#9 Orymus3   Crossbones+   -  Reputation: 8988

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Posted 01 September 2013 - 11:56 PM

Yes, I did run the radius measure first, insuring I don't compute objects that are out of range.

 

atan2 seems to work wonderfully... for the first 'quadrant' only.

My circle is a 2*PI rad circumference, and I'm seeing that atan2 uses signs in someway and divides everything as 'PI/2' quadrants (basing itself off the signature).

 

Any ideas on reconciling the two?



#10 Rorakin   Members   -  Reputation: 618

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Posted 02 September 2013 - 12:24 AM

Radius check first, then atan(y/x) = angle. If angle between min and max angle of player portion, then it is in the player's area.



#11 Paradigm Shifter   Crossbones+   -  Reputation: 5372

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Posted 02 September 2013 - 04:20 AM

atan(y/x) only returns angles in the range -pi/2 to pi. You need to use atan2(y, x). Note the order of arguments (y is first). The angle is measured anticlockwise from the +x axis. (EDIT: And it returns negative values if y < 0, if you need positive values only add 2pi if atan2 returns an angle < 0).


Edited by Paradigm Shifter, 02 September 2013 - 04:22 AM.

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#12 Orymus3   Crossbones+   -  Reputation: 8988

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Posted 02 September 2013 - 11:17 AM

So here is what I did:

double atan2Random = math.atan2(randomY,randomX);if 
(atan2Random < 0) atan2Random = atan2Random + 2*(math.PI);

Sadly enough, I'm still only getting results in a single quadrant.

 

My conditions for detecting a valid 'object' are (sorry the indentation was lost by copy/pasting)

if (atan2Random > 
arcPlayerList[currentPlayer]){

if (atan2Random <= 
arcPlayerList[nextPlayer]){

if (rangeIsOk){

starListX[i] = randomX;
starListY[i] = randomY;
 
i++;
}
}
}

 

 arcPlayerList is a list that contains the angle(rad) for each player. I'm using it to define the 'range' each player has access to, by checking if its bigger than what the current player's start is and smaller or equal to the next player's value.

 

 

 


Edited by Orymus3, 02 September 2013 - 11:18 AM.


#13 Khatharr   Crossbones+   -  Reputation: 3001

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Posted 02 September 2013 - 02:38 PM

Are the values in 'arcPlayerList' correct?

 

What the hell is 'rangeIsOk'?

 

Are you aware that the && operator can combine conditions?


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#14 Paradigm Shifter   Crossbones+   -  Reputation: 5372

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Posted 02 September 2013 - 02:40 PM

Watch out for ranges that cross the 2pi boundary as well.

 

You should put a breakpoint on the code where the atan2random value is calculated and step through in the debugger, you should be able to work out what is wrong easily enough.


"Most people think, great God will come from the sky, take away everything, and make everybody feel high" - Bob Marley




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