/**
* Generate a random position that lies within a rectangle but outside of a circle.
*
* @param rnd the random generator to use
* @param rx1 top left x of the rectangle
* @param ry1 top left y of the rectangle
* @param rx2 bottom right x of the rectangle
* @param ry2 bottom right y of the rectangle
* @param cx x position of the circle
* @param cy y position of the circle
* @param cr the squared radius of the circle
* @return a vector specifying a random position
*/
public static Vector2 newRandomTarget(
Random rnd, int rx1, int ry1, int rx2, int ry2, int cx, int cy, int cr) {
assert cr < ExtraMath.square(ry2 - ry1);
float targetX, targetY;
/* The problem:
* We want to generate a random point within a rectangle (movementRect) but
* that lies outside of a circle (defined by body position and
* MIN_WALK_SQUARED).
*
* This can be solved easily if we first make the following assumption:
* For all values of x inside the rectangle, there is at least one value of
* y that lies outside of the circle.
*
* Based on this assumption we can generate a random point easily.
*/
// First, generate a random x value.
targetX = rnd.nextInt(rx1, rx2);
/* Now use the circle's equation:
* (x - a)^2 + (y - b)^2 = r^2
* => y = b + sqrt(r^2 - (x - a)^2)
*
* If r^2 is less than (x - a)^2, the root will become imaginary, thus all
* y values lies outside of the circle for this x.
*/
float tmp = ExtraMath.square(targetX - cx);
if (cr < tmp) {
// Circle is not intersecting our x here
targetY = rnd.nextFloat(ry1, ry2);
} else {
// Here we have to take the circle into account
int yRoot = (int) (Math.sqrt(cr - tmp));
// Top and bottom of the circle
int y1 = cy - yRoot;
int y2 = cy + yRoot + 1; // +1 so that we don't get point in the circle
// Note that portions of the circle could lie outside of the rectangle.
if (y2 < ry1 || y1 > ry2) {
// Entire circle is outside of the rectangle
targetY = rnd.nextInt(ry1, ry2);
} else if (y1 < ry1) {
// Top of circle is above the rectangle
targetY = rnd.nextInt(y2, ry2);
} else if (y2 > ry2) {
// Bottom of circle is below the rectangle
targetY = rnd.nextInt(ry1, y1);
} else {
// The part of the circle we're interested in is within the rectangle
// We now have two intervals, note that the size of the two intervals
// differ, we have to be careful so we get an uniform distribution.
int topSize = y1 - ry1;
int bottomSize = ry2 - y2;
int totalSize = topSize + bottomSize;
if (rnd.nextInt(totalSize) < topSize) {
// Upper
targetY = rnd.nextInt(ry1, y1);
} else {
// Lower
targetY = rnd.nextInt(y2, ry2);
}
}
}
return new Vector2(targetX, targetY);
}
public class Walking implements IBossState {
public static final int MIN_WALK = 100;
public static final int MIN_WALK_SQUARED = ExtraMath.square(MIN_WALK);
private final Rectangle body;
private final float speed;
private final Movement movement;
private final Rectangle movementRect;
private Vector2 currentTarget;
private int targetsLeft;
/**
* Create a new walk state for boss AI.
*
* @param body the boss body
* @param hand the boss hand
* @param movement the boss movement
* @param speed the speed of the boss
* @param movementRect the rectangle which the boss should move within
* @param targets the number of targets (positions the boss should walk to), greater than zero
* @param initialTarget the first target the boss should reach
*/
public Walking(
Rectangle body,
Hand hand,
Movement movement,
float speed,
Rectangle movementRect,
int targets,
Vector2 initialTarget) {
assert targets > 0;
assert initialTarget != null;
this.body = body;
this.speed = speed;
this.movement = movement;
this.targetsLeft = targets;
this.movementRect = movementRect;
this.currentTarget = initialTarget;
}
/**
* Create a new walk state for boss AI. Instead of specifying the initial target a random target
* will be chosen instead.
*
* @param entity the boss entity
* @param hand the boss hand
* @param movement the boss movement
* @param speed the speed of the boss
* @param movementRect the rectangle which the boss should move within
* @param targets the number of targets (positions the boss should walk to)
*/
public Walking(
Rectangle body,
Hand hand,
Movement movement,
float speed,
Rectangle movementRect,
int targets) {
this(
body,
hand,
movement,
speed,
movementRect,
targets,
newRandomTarget(
Locator.getRandom(),
(int) movementRect.getX1(),
(int) movementRect.getY1(),
(int) movementRect.getX2(),
(int) movementRect.getY2(),
(int) body.getCenter().x,
(int) body.getCenter().y,
MIN_WALK_SQUARED));
}
@Override
public void start(GameTime time) {
headFor(currentTarget);
}
@Override
public void update(GameTime time) {
if (targetsLeft > 0) {
Vector2 a = Vector2.subtract(body.getMin(), currentTarget);
if (Vector2.dot(a, movement.getVelocity()) >= 0) {
--targetsLeft;
// Target passed
if (targetsLeft > 0) {
currentTarget =
newRandomTarget(
Locator.getRandom(),
(int) movementRect.getX1(),
(int) movementRect.getY1(),
(int) movementRect.getX2(),
(int) movementRect.getY2(),
(int) body.getX1(),
(int) body.getY1(),
MIN_WALK_SQUARED);
headFor(currentTarget);
}
}
}
}
public Vector2 getTarget() {
return currentTarget;
}
@Override
public boolean isFinished() {
return targetsLeft == 0;
}
@Override
public BossState getState() {
return BossState.WALKING;
}
private void headFor(Vector2 target) {
assert Rectangle.contains(movementRect, target);
Vector2 delta = Vector2.subtract(target, body.getMin());
Vector2 direction = delta.normalize();
Vector2 velocity = Vector2.multiply(direction, speed);
movement.setVelocity(velocity);
}
/**
* Generate a random position that lies within a rectangle but outside of a circle.
*
* @param rnd the random generator to use
* @param rx1 top left x of the rectangle
* @param ry1 top left y of the rectangle
* @param rx2 bottom right x of the rectangle
* @param ry2 bottom right y of the rectangle
* @param cx x position of the circle
* @param cy y position of the circle
* @param cr the squared radius of the circle
* @return a vector specifying a random position
*/
public static Vector2 newRandomTarget(
Random rnd, int rx1, int ry1, int rx2, int ry2, int cx, int cy, int cr) {
assert cr < ExtraMath.square(ry2 - ry1);
float targetX, targetY;
/* The problem:
* We want to generate a random point within a rectangle (movementRect) but
* that lies outside of a circle (defined by body position and
* MIN_WALK_SQUARED).
*
* This can be solved easily if we first make the following assumption:
* For all values of x inside the rectangle, there is at least one value of
* y that lies outside of the circle.
*
* Based on this assumption we can generate a random point easily.
*/
// First, generate a random x value.
targetX = rnd.nextInt(rx1, rx2);
/* Now use the circle's equation:
* (x - a)^2 + (y - b)^2 = r^2
* => y = b + sqrt(r^2 - (x - a)^2)
*
* If r^2 is less than (x - a)^2, the root will become imaginary, thus all
* y values lies outside of the circle for this x.
*/
float tmp = ExtraMath.square(targetX - cx);
if (cr < tmp) {
// Circle is not intersecting our x here
targetY = rnd.nextFloat(ry1, ry2);
} else {
// Here we have to take the circle into account
int yRoot = (int) (Math.sqrt(cr - tmp));
// Top and bottom of the circle
int y1 = cy - yRoot;
int y2 = cy + yRoot + 1; // +1 so that we don't get point in the circle
// Note that portions of the circle could lie outside of the rectangle.
if (y2 < ry1 || y1 > ry2) {
// Entire circle is outside of the rectangle
targetY = rnd.nextInt(ry1, ry2);
} else if (y1 < ry1) {
// Top of circle is above the rectangle
targetY = rnd.nextInt(y2, ry2);
} else if (y2 > ry2) {
// Bottom of circle is below the rectangle
targetY = rnd.nextInt(ry1, y1);
} else {
// The part of the circle we're interested in is within the rectangle
// We now have two intervals, note that the size of the two intervals
// differ, we have to be careful so we get an uniform distribution.
int topSize = y1 - ry1;
int bottomSize = ry2 - y2;
int totalSize = topSize + bottomSize;
if (rnd.nextInt(totalSize) < topSize) {
// Upper
targetY = rnd.nextInt(ry1, y1);
} else {
// Lower
targetY = rnd.nextInt(y2, ry2);
}
}
}
return new Vector2(targetX, targetY);
}
}
