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n 2, we talked about 2D coordinate systems, including a special case of such systems: the screen coordinate system. When dealing with 3D coordinate systems, however, a lot more is involved with defining a 3D virtual object and transforming such an object into a 2D representation on the screen. This chapter covers the basics of creating 3D games. First, you ll learn the fundamental concepts, and then you ll see how to apply them in a simple XNA project. This will prepare you for creating a complete 3D game in the next chapters.

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Because the JavaMail API uses a static factory method to associate MIME message objects with the underlying e-mail transport (usually SMTP), we need to register a custom transport with JavaMail in the createMimeMessage() method. We omit the implementation of the version of createMimeMessage(InputStream) method entirely because it is not used by our implementation. But an appropriate exception is generated so that if refactoring causes the method to become part of the code path of a class under test, we will not flounder around trying to determine the cause of mysterious failures! The rest of the methods take the populated MimeMessage or SimpleMailMessage instances for transmission and instead store them in lists for later retrieval by the unit test. Additional utility methods are provided to access these lists, to obtain the count of messages contained within them, and to clear them of their contents upon test completion. Listing 10-19 shows the environment that our three mail DAO test methods will operate within. We establish standard parameters for the sender, recipient, and subject of the e-mails that will be applied to the e-mails to be transmitted. We establish the mock instance of the JavaMailSender to be supplied to the DAO implementations (shown in bold in Listing 10-19), and we create a suitable timesheet object that will be passed to the MailDao s sendTimesheetUpdate method for each case. We also provide a tearDown() method that will clear the mock JavaMailSender s message stores after each test has completed.

When dealing with three Cartesian dimensions, two types of coordinate systems are used: lefthanded and right-handed. These names refer to the z axis s position relative to the x and y axes. To determine this position, point the fingers of one hand to the x axis s positive direction and move them in a counterclockwise direction to the y axis s positive position. The z axis s direction is the direction your thumb points to. Figure 8-1 illustrates this concept. To put it a different way, in the left-handed coordinate system, the z value gets bigger (the positive direction) when you go from the screen to a point away from you (considering that the x axis and the y axis are on the computer screen). The right-handed 3D system is the opposite: the z values increase toward you from the screen. The XNA Framework works, by default, in a right-handed coordinate system (which, it s worth noting, is different from DirectX s default). This means that negative values for the z axis are visible, and the more negative they are for a given object, the farther the object is from the screen. Positive values are not shown, unless you change your camera position, as you ll see later in this chapter.

Figure 8-1. The Cartesian 3D coordinate systems Now that you understand 3D coordinate systems, the next step to explore is how you can map 3D objects from this system to your computer (or Xbox 360) 2D screen. Fortunately, XNA does all the hard mathematical work for this mapping, but you still need to understand the concept of projections and how they apply to XNA to issue the basic instructions for how to present the objects on the screen. Similarly to other gaming libraries, XNA supports two different types of projections: Perspective projection: The most common type of projection, perspective projection takes the z distance into account and adjusts the objects accordingly. This projection makes objects appear smaller when far from the screen. Depending on the position, the objects also appear deformed, as in the real world. For example, the sides of a cube that are closer to the screen seem bigger than the farther ones. Figure 8-2 shows a graphical representation of the perspective projection.