1. 行動 (Movement)
靜宜大學資工系
蔡奇偉 副教授

2. 大綱 The Basics of Movement Algorithms Kinematic Movement Algorithms
Steering Behaviors
Combining Steering Behaviors
Predicting Physics
Jumping
Coordinated Movement

3. 遊戲人工智慧的模型

4. The Movement algorithm Structure

5. Statics struct Static: position # a 2D vector
orientation # a single floating point value
The 2D movement axes and the 3D basis
The positions of characters in the level

6. 右手座標系統：
左手座標系統：

7. Kinematics struct Kinematic position # a 2 or 3D vector
orientation # a single floating point value
velocity # another 2 or 3D vector
rotation # a single floating point value
struct SteeringOutput:
linear # 加速度 a 2 or 3D vector
angular # 角加速度 a single floating point value

8. struct Kinematic:
... Member data as before ...
def update(steering, time):
# Update the position and orientation
position += velocity * time +
0.5 * steering.linear * time * time
orientation += rotation * time +
0.5 * steering.angular * time * time
# and the velocity and rotation
velocity += steering.linear * time
rotation += steering.angular * time

9. 簡化版（因為 time 值很小）
struct Kinematic:
... Member data as before ...
def update (steering, time):
# Update the position and orientation
position += velocity * time
orientation += rotation * time
# and the velocity and rotation
velocity += steering.linear * time
rotation += steering.angular * time

10. Kinematic Movement Algorithms
Seek
Flee
Arriving
Wandering

11. def getNewOrientation(currentOrientation, velocity):
# Make sure we have a velocity
if velocity.length() > 0:
# Calculate orientation using an arc tangent of
# the velocity components.
return atan2(-velocity.x, velocity.z)
# Otherwise use the current orientation
else: return currentOrientation

12. Kinematic Seek（尋找）
A kinematic seek behavior takes as input the character’s and their target’s static data. It calculates the direction from the character to the target and requests a velocity along this line.
target
character

13. struct KinematicSteeringOutput:
velocity
rotation
class KinematicSeek:
# Holds the static data for the character and target
character
target
# Holds the maximum speed the character can travel
maxSpeed

14. # Create the structure for output
target
character
def getSteering():
# Create the structure for output
steering = new KinematicSteeringOutput()
# Get the direction to the target
steering.velocity = target.position - character.position
# The velocity is along this direction, at full speed
steering.velocity.normalize()
steering.velocity *= maxSpeed
# Face in the direction we want to move
character.orientation =
getNewOrientation(character.orientation,steering.velocity)
# Output the steering
steering.rotation = 0
return steering

15. Kinematic Flee（逃跑）
If we want the character to run away from their target, we can simply reverse the second line of the getSteering method to give
# Get the direction away from the target
steering.velocity = character.position - target.position
The character will then move at maximum velocity in the opposite direction.
target
character

16. Arriving（抵達） (1) (2) (3) (4) 超過目標，須返回 target character target

17. 解決方法：
一、角色進入目標範圍圈內，即表示已抵達。
二、減速接近目標。
三、在目標範圍圈才減速接近目標。
target
character

18. Wandering（徘徊）
A kinematic wander behavior always moves in the direction of the character’s current orientation with maximum speed. The steering behavior modifies the character’s orientation, which allows the character to meander as it moves forward.

19. class KinematicWander:
character
maxSpeed
# Holds the maximum rotation speed we’d like, probably
# should be smaller than the maximum possible, to allow
# a leisurely change in direction
maxRotation
def getSteering():
# Create the structure for output
steering = new KinematicSteeringOutput()
# Get velocity from the vector form of the orientation
steering.velocity = maxSpeed * character.orientation.asVector()
# Change our orientation randomly
steering.rotation = randomBinomial() * maxRotation
# Output the steering
return steering
def randomBinomial():
return random() - random()

20. Steering Behaviors