Pro OpenGL ES for iOS

36 CHAPTER 2: All That Math Jazz^ Mathematicians are always fond of expressing things in the most compact form possible. So 2D r ...

CHAPTER 2: All That Math Jazz (^37) form is called homogeneous coordinates, and in this case it helps to create a 3x3 matrix tha ...

38 CHAPTER 2: All That Math Jazz^ With scaling, as with the other two transformations, the order is very important when applied ...

CHAPTER 2: All That Math Jazz (^39) Note Moving back and forth from one frame of reference to another is the quickest road to in ...

40 CHAPTER 2: All That Math Jazz^ matrix to express this, here is what we get (notice the new notation, where R(z,a) is used to ...

CHAPTER 2: All That Math Jazz (^41) ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − 0 0 0 1 sin( ) 0 cos( ) 0 0 1 0 0 cos( ) 0 sin( ) 0 ( , ) a a a a ...

42 CHAPTER 2: All That Math Jazz^ spacecraft with a full six degrees of freedom: three translational components and three rotati ...

CHAPTER 2: All That Math Jazz (^43) PUSH TO TALK SWITCH PARAMETERS ROTATION CONTROL ROTATION CONTROL PARAMETERS HARD STOP DIRECT ...

44 CHAPTER 2: All That Math Jazz^ he sketched the first mammoth on a cave wall. But it is actually quite easy to grasp, as oppos ...

CHAPTER 2: All That Math Jazz (^45) In perspective projection, the distance component, z, is used to scale what will ultimately ...

46 CHAPTER 2: All That Math Jazz^ With these boundaries established, the one final transformation is that to the viewport, OpenG ...

CHAPTER 2: All That Math Jazz (^47) Figure 2-12. Projecting x and y onto the device’s screen. You can visuallize this as either ...

48 CHAPTER 2: All That Math Jazz^ search through your object list to find which was the most likely target. Untransforming somet ...

CHAPTER 2: All That Math Jazz (^49) What About Quaternions? Quaternions are hyper-complex entities that can store the RPY inform ...

Chapter 3 Building a 3D World In the first two chapters, we covered the cool stuff and the math stuff (which could be either coo ...

52 CHAPTER 3: Building a 3D World^ math coordinates (although that can be adjusted as needed by using some of the Core Graphics ...

CHAPTER 3: Building a 3D World (^53) ModelView Matrix Object Coordinates Projection Matrix Eye Coordinates Divide by w Clip Coor ...

54 CHAPTER 3: Building a 3D World^ Eye Coordinates There is no magical viewpoint object in OpenGL. So, instead of moving your vi ...

CHAPTER 3: Building a 3D World (^55) within the frustum may eventually find their way to the screen (if not obscured by a closer ...

56 CHAPTER 3: Building a 3D World^ Back to the Fun Stuff: A Simpler Demo When Xcode 4.2 was released (along with the iOS5 SDK), ...