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OpenGL does not require that u be passed in as a unit vector: OpenGL will automatically compute the normalization of u in order to compute the rotation matrix. 3. glScalef(float α1 , float α2 , float α3 ). This command scales the x-, y-, z-coordinates the matrix  α1 0 0  0 α2 0   0 0 α3 0 0 0 of points independently. That is to say, it sets M = M ◦ S, where S is  0 0 . 0 1 The matrix S will map x1 , x2 , x3 , 1 to α1 x1 , α2 x2 , α3 x3 , 1 , so it allows scaling independently in each of the x-, y-, and z-directions.

The vector v1 is v’s projection onto u. The vector v2 is the component of v orthogonal to u. The vector v3 is v2 rotated 90◦ around u. The dashed line segments in the figure all meet at right angles. First, the command glMatrixMode(GL_MODELVIEW); selects the model view matrix as the currently active matrix. Other matrices that can be selected with this command include the projection matrix. 5 explains the interaction between these two matrices. The following four commands provide simple ways to effect modeling transformations.

Displaying. In this stage, the scene is rendered onto the computer screen or other display medium such as a printed page or a film. A window on a computer screen consists of a rectangular array of pixels. Each pixel can be independently set to an individual color and brightness. For most 3-D graphics applications, it is desirable to not render parts of the scene that are not visible owing to obstructions of view. OpenGL and most other graphics display systems perform this hidden surface removal with the aid of depth (or distance) information stored with each pixel.

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