Pro OpenGL ES for iOS

42 CHAPTER 2: All That Math Jazz^

spacecraft with a full six degrees of freedom: three translational components and three

rotational components. The rotational parts are usually referred to as roll, pitch, and yaw

(RPY). Roll would be rotations around the z-axis, pitch is around the x (in other words,

aiming the nose up or down), and yaw is rotation around the y-axis, moving the nose left

and right. Figure 2-6a, b, and c show this at work in the Apollo spacecraft from the

moon landings in the 1960s. The proper sequence would be yaw, pitch, and roll, or

rotation around y, x, and finally z. (This requires 12 multiplications and 6 additions, while

premultiplying the three rotation matrices could reduce that down to 9 multiplications

and 6 additions.) The transformations would be incremental, comprising the changes in

the RPY angles since the last update, not the total ones from the beginning. In the good

ol’ days, round-off errors could compound distorting the matrix, leading to very cool but

otherwise unanticipated results (but still cool nonetheless).

FOR TRAINING PURPOSES ONLY

+Z

D

C

B

A SM RCS MOTOR (4 SETS)

ENGINE LOCATION

S PS

+ YAW

+Y

+ ROLL

+ PITCH - ROLL

-Z

+ ROLL

• PITCH

+X

• ROLL
  
  
  • YAW
    
    
    • Y
    
    
    
    
  
  
  
  

(^6532)