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Output.TexCoord = inTexCoord; return Output; } Next, you need to add some code to your vertex shader that constructs the Tangent-toWorld matrix. As explained earlier, this transformation happens in two phases. First you transform the normal coordinates from tangent to object space and next from object to world space. Start by defining the tangentToObject matrix. To define a transformation matrix, you need to know the basic vectors of the coordinate system, which are the normal, tangent, and bitangent of the tangent space. Your vertex shader receives the normal and tangent of each vertex. As explained earlier, you can calculate the binormal by making their cross product, because it is the vector perpendicular to the normal and tangent: float3 Binormal = normalize(cross(inTangent,inNormal)); With your binormal calculated, you re ready to construct your Tangent-to-Object matrix, because the rows of a transformation matrix are nothing more than three vectors defining the new coordinate system. The vectors of an ideal coordinate systems are also normalized, so you take care of this: float3x3 tangentToObject; tangentToObject[0] = normalize(Binormal); tangentToObject[1] = normalize(inTangent); tangentToObject[2] = normalize(inNormal);

The language implicitly supplies a parameterless constructor for every struct. This constructor sets each of the struct s members to the default value for that type. Value members are set to their default values. Reference members are set to null. The predefined parameterless constructor exists for every struct and you cannot delete or redefine it. You can, however, create additional constructors, as long as they have parameters. Notice that this is different from classes. For classes, the compiler will only supply an implicit parameterless constructor if no other constructors are declared. To call a constructor, including the implicit parameterless constructor, use the new operator. Notice that the new operator is used even though the memory is not allocated from the heap. For example, the following code declares a simple struct with a constructor that takes two int parameters. Main creates two instances of the struct one using the implicit parameterless constructor, and the second with the declared two-parameter constructor. struct Simple { public int x; public int y; public Simple(int a, int b) { x = a; y = b; } } class Program { static void Main() { Call implicit constructor Simple s1 = new Simple(); Simple s2 = new Simple(5, 10); Call constructor Console.WriteLine("{0},{1}", s1.x, s1.y); Console.WriteLine("{0},{1}", s2.x, s2.y); } } // Constructor with parameters

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Tip By normalizing the rows of this matrix and because the three row vectors are perpendicular to each

Click the Libraries tab to view the Kupu Libraries panel, as shown in Figure 4-36.

other, the inverse of this matrix is the same as the transpose of this matrix. You can find the transpose of a matrix by mirroring the elements over the axis that runs from the top-left to the bottom-right over the elements, which is much easier to do than calculating the inverse of a matrix.

You can also create an instance of a struct without using the new operator. If you do this, however, there are several restrictions you cannot Use the value of a data member until you have explicitly set it Call any function member until all the data members have been assigned For example, the following code shows two instances of struct Simple created without using the new operator. When there is an attempt to access s1 without explicitly setting the data member values, the compiler produces an error message. There are no problems reading from s2 after assigning values to its members. struct Simple { public int x; public int y; } class Program { static void Main() { No constructor calls Simple s1, s2; Console.WriteLine("{0},{1}", s1.x, s1.y); Not yet assigned s2.x = 5; s2.y = 10; Console.WriteLine("{0},{1}", s2.x, s2.y); } }

All you should do now is combine the Tangent-to-Object transform with the Object-toWorld transform by multiplying their matrices, so you obtain the Tangent-to-World matrix. The Object-to-World matrix is nothing more than the (very common) World matrix (containing, for example, the rotation of your tower), so you end up with this code: float3x3 tangentToWorld = mul(tangentToObject, xWorld); Output.TTW = tangentToWorld; You pass this matrix on to your pixel shader. Now your pixel shader can easily transform any vector from tangent space to world space by multiplying the vector with this matrix!

Libraries are static or dynamic collections of resources, defined by the system at a deeper level; they provide abstract locations for objects of any type. For example, you usually use a library when you insert an image into a page content type: when you click the Insert image icon on the Kupu toolbar, a panel will appear, as shown in Figure 4-37; thanks to a specific library, this panel shows all the images already uploaded in the system that you can choose from.

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