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)

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.

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

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.

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):

[source lang="C++"]

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

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

[/source]

Read up on polar integration for more info.

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

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

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?

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?

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.