ASP.NET Web PDF Document Viewer/Editor Control Library

You can achieve the same results by representing each vertex as a matrix with one row and four columns, with the vertex coordinates as the first three columns and 1 as the value in the last one. You then multiply this matrix to a special matrix, constructed to produce the translation transformation to the vertex matrix. Figure 8-12 presents the same operation applied to the first vertex.

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public void testSave() throws Exception { // Setup test data final MockParameterMap params = new MockParameterMap(); params.put("username", "example"); final MockRequestContext context = new MockRequestContext(params); action.bind(context); final UserAccount account = new UserAccount("example"); // Script the test final UserAccountService service = createMock(UserAccountService.class); action.setUserAccountService(service); service.createUser(matchesNamedAccount(account)); replay(service); // Carry out the action final Event event = action.save(context); // Verify success verify(service); final String successEventId = support.success(action).getId(); assertEquals(successEventId,event.getId()); } By using the provided MockRequestObject, we can avoid the need to know any of these details. And because the provider of the library has provided the mock implementation,

Figure 8-12. Applying a matrix multiplication to a 3D vertex A little explanation about multiplication for matrices is in order. To calculate the resulting matrix, you must take each value in the row of the first matrix, multiply it by each of the values in the corresponding column in the second matrix, and then sum all of the results. So, in the previous sample, the calculations are as follows: x = (50 1) + (10 0) + (0 0) + (1 0) = 50 y = (50 0) + (10 1) + (0 0) + (1 40) = 50 z = (50 0) + (10 0) + (0 1) + (1 0) = 0 Put simply, you can perform translations by putting the desired values for translation over the x, y, and z positions in the last row of the transformation matrix. You can perform scaling by replacing the 1s on the diagonal with fractional values (to shrink) or values bigger than 1 (to expand), and perform rotation around any axis using a combination of sine and cosine values in specific positions in the matrix. So, what s the big deal about using matrices One of the biggest benefits is that you can perform complex operations by multiplying their corresponding transformation matrices. You can then apply the resulting matrix over each vertex on the 3D model, so you can perform all operations on the model by multiplying its vertices for only one matrix, instead of calculating each transformation for each vertex. For example, usually you will need to rotate, scale, and translate an object to position it in your 3D scene, and then perform new operations according to the object s movement around the scene. In this situation, instead of calculating all operations

we can reasonably assume that changes in the implementation details of one will be reflected by appropriate changes to the other.

for each vertex, you multiply the transformation matrices and calculate only one operation per vertex: multiplying it by this resulting matrix. Even better, all graphics cards have built-in algorithms to multiply matrices, so this multiplication consumes little processing power. Considering that complex 3D objects may have thousands of vertices, doing the transformations with as low a processing cost as possible is a must, and matrices allow this. Fortunately, you don t need to understand all these mathematical details to use matrices and execute 3D transformations in your program. All game programming libraries (from OpenGL to DirectX) offer ready-to-use matrix manipulation functions, and XNA is no exception. Through the Matrix class, many matrix operations are available, such as the following: Matrix.CreateRotationX, Matrix.CreateRotationY, and Matrix.CreateRotationZ: Each of these creates a rotation matrix for each of the axes. Matrix.Translation: Creates a translation matrix (one or more axes). Matrix.Scale: Creates a scale matrix (one or more axes). Matrix.CreateLookAt: Creates a view matrix used to position the camera, by setting the 3D position of the camera, the 3D position it is facing, and which direction is up for the camera. Matrix.CreatePerspectiveFieldOfView: Creates a projection matrix that uses a perspective view, by setting the angle of viewing (field of view), the aspect ratio (the ratio used to map the 3D projection to screen coordinates, usually the width of the screen divided by the height of the screen), and the near and far planes, which limit which part of the 3D scene is drawn. See Figure 8-13 to better understand these concepts. Similarly, you have two extra methods, CreatePerspectiveOffCenter and CreatePerspective, which create matrices for perspective projection using different parameters.