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instance of this type where there is no need to mention the type name when it is created To create a record, you place the field names followed by equal signs and the field values between braces ({}), as shown in the Rainbow identifier F# does not force field names to be unique, so sometimes the compiler cannot infer the type of a field from the field names alone In such a case, the compiler cannot infer the type of the record To create records with nonunique fields, the compiler needs to statically know the type of the record being created If the compiler cannot infer the type of the record, you need to use a type annotation, as described in the previous section Using a type annotation is illustrated by the types Organization2 and Organization3, and their instances thePlayers and wayneManor.

To follow along with the examples in Part 3 of this book, you need to create a Visual Studio solution named Northwind that contains four projects; DataLayer, BusinessLayer, NorthwindWeb, and TestLayer. Each of these projects contains logically separated classes associated with the database objects, business objects, web objects, and unit tests. This solution will host your entire application.

Listing 8-6. Function That Performs a Perspective Projection def perspective_project(vector3, d): x, y, z = vector3 return (x * d/z, y * d/z) There s a little more math involved in perspective projection than there is for a simple parallel projection. The perspective_project function multiplies the x and y coordinates by the d value (which we will discuss later), and divides by the z component. It also negates the y component ( y) since the y axis is in the opposite direction in 2D. The d value in perspective_project is the viewing distance, which is the distance from the camera to where units in the 3D world units correspond directly to the pixels on the screen. For instance, if we have an object at coordinate (10, 5, 100), projected with a viewing distance of 100, and we move it one unit to the right at (11, 5, 100), then it will appear to have moved exactly one pixel on screen. If its z value is anything but 100, it will move a different distance relative to the screen. Figure 8-6 shows how the viewing distance relates to the width and height of the screen. Assuming the player (indicated by the smiley face) is sitting directly in front of the screen, then the viewing distance would be approximately the distance, in pixel units, from the screen to the player s head.

You can see the type of the identifier given explicitly just after its name Accessing the fields in a record is fairly straightforward You simply use the syntax record identifier name, followed by a dot, followed by field name The following example illustrates this, showing how to access the chief field of the Organization record // define an organization type type Organization = { chief: string; indians: string list } // create an instance of this type let wayneManor = { chief = "Batman"; indians = ["Robin"; "Alfred"] } // access a field from this type printfn "wayneManorchief = %s" wayneManorchief Records are immutable by default To an imperative programmer, this may sound like records are not very useful, since there will inevitably be situations where you need to change a value in a field.

For this purpose, F# provides a simple syntax for creating a copy of a record with updated fields To create a copy of a record, place the name of that record between braces, followed by the keyword with, followed by a list of fields to be changed, with their updated values The advantage of this is that you don t need to retype the list of fields that have not changed The following example demonstrates this approach It creates an initial version of wayneManor and then creates wayneManor', in which "Robin" has been removed.

So how do we select a good value for the viewing distance (d) We could just experiment to find a value that makes the 3D scene look convincing, but we can take the guesswork out of it by calculating d from the field of view (fov), which is the angular range of the scene that is visible at one moment. For human beings, the fov is the range from the left eye to the right eye, which is about 180 degrees. Figure 8-7 shows the relationship between fov and viewing distance. When the fov angle increases (grows wider), the viewing distance decreases as more of the scene becomes visible. The opposite happens when the fov decreases (becomes narrower); viewing distance increases and less of the scene is visible.