The transformation module has four state registers that the user can modify: the viewport, the viewing matrix, the world matrix, and the projection matrix. Whenever one of these parameters is modified, they are combined to form a new transformation matrix, which is also maintained by the transformation module. The transformation matrix defines the rotation and projection of a set of 3D vertices from their model coordinates to the 2D window.
Although the application can set the transformation matrix directly, it is not recommended. A number of matrix classifications take place in the combination phase that allow optimized transformation math to be used, but this is precluded if the application specifies the matrix directly.
A display list supports a number of different vertex types. For rasterization-only hardware, the application should use the D3DTLVERTEX structure, which is a transformed and lit vertex—that is, it contains screen coordinates and colors. If the hardware handles the transformations, the application should use a D3DLVERTEX structure. This structure contains only data and a color that would be filled by software lighting. The D3DHVERTEX structure defines a homogeneous vertex used when the application is supplying model-coordinate data that needs clipping. If the hardware supports lighting, the application simply uses a D3DVERTEX structure, because this type of vertex can be transformed and lit during rendering. The software emulation driver supports all of these vertex types.
There are two types of methods for the transformation module: those that set the state of the transformation module and those that use the transformation module directly to act on a set of vertices. Calling the transformation module directly is useful for testing bounding volumes or for transforming a set of vectors. These operations transform geometry by using the current transformation matrices. They can also perform clipping tests against the current viewing volume. The structure used for all the direct transformation functions is D3DTRANSFORMDATA.
You can find a general discussion of transformations in the section devoted to viewports in Retained Mode, Transformations. For a discussion of transformations in frames, see Transformations. Although each of these sections discusses Retained-Mode API, the architecture and mathematics of the transformations apply to both Retained and Immediate modes. For an overview of the mathematics of transformations, see 3D Transformations.