XNA Game Programming: Spawning Enemies in a circle (Code) - random

Question

Could someone please give me some direction on how to spawn enemies in a circle (XNA Programming)?
I want the enemies to randomly spawn along the circumference of a circle that is just outside the bounds of the window. I want them to move in straight lines through the center of the window and out to the opposite side of where they started (or as close to that as possible).
Ideally this would create an environment where enemies are randomly coming across from seemingly all directions.
Here's my enemy ("Baddies") class so far. I handle the position of in the SetupTraveling game state. What I'm doing isn't really working, so any help would be greatly appreciated.
public class Baddies : Sprite
{
public enum State
{
Inactive,
SetupTraveling,
Traveling,
SetupInactive,
}
public State CurrentState
{
set
{
currentState = value;
framesInStateCount = 0;
}
get
{
return currentState;
}
}
int framesInStateCount = 0;
State currentState = State.SetupInactive;
public Baddies()
{
Image = getImage("Bad");
Scale = .2f;
Rotation = 0f;
DRotation = .05f;
TurnedOn = true;
BounceOn = false;
WrapOn = false;
Gravity = 0f;
}
public override void Update()
{
framesInStateCount++;
switch (currentState)
{
case State.Inactive:
if (RandOneIn(100)) CurrentState = State.SetupTraveling;
break;
case State.SetupTraveling:
PositionX = ((Game1.vGameWidth + 100)/2) * (float)Math.Cos(Glob.rnd(0.0, 2.0 * Math.PI));
PositionY = ((Game1.vGameHeight + 100)/2) * (float)Math.Sin(Glob.rnd(0.0, 2.0 * Math.PI));
DDPositionY = 0;
DPositionY = -1;
DPositionX = 1f;
DDPositionX = 0f;
CurrentState = State.Traveling;
break;
case State.Traveling:
if (PositionX > Game1.vGameWidth + (Image.Width / 2) * Scale)
{
currentState = State.SetupInactive;
}
if (PositionX < -500f - (Image.Width / 2) * Scale)
{
currentState = State.SetupInactive;
}
if (PositionY > Game1.vGameHeight + (Image.Height / 2) * Scale)
{
currentState = State.SetupInactive;
}
if (PositionY < 0 - (Image.Height / 2) * Scale)
{
currentState = State.SetupInactive;
}
break;
case State.SetupInactive:
PositionX = -300f;
DPositionX = 0f;
DPositionY = 0f;
DDPositionX = 0f;
CurrentState = State.Inactive;
break;
}
base.Update();
}
}

Answer 1

Other approach with trigonometry:
Decide what is your circle radius... usually is:
raqdius = sqrt(Viewport.Size.Width^2 + Viewport.Size.Height^2) / 2;
Generate a random angle
angle = (float) Random.NextDouble() * MathHelper.PI * 2;
Your coordinates are
x = ViewPort.Center.X + radius * Math.Cos(angle);
y = ViewPort.Center.Y + radius * Math.Sin(angle);

Answer 2

How about this:
Decide what the raidius of your circle is, call it r
generate an X value from [-r, r]
Y = sqrt(r^2 - X^2)
randomly set Y to Y or -Y. Your cooridinates would be X,Y