3-D Transformations

In programs that work with 3-D graphics, you can use geometrical transformations to:

• Express the location of an object relative to another object.
• Rotate, shear, and size objects.
• Change viewing positions, directions, and perspective.

You can transform any point into another point by using a 4×4 matrix. In the following example, a matrix is used to reinterpret the point (x, y, z), producing the new point (x^', y^', z^'):

You perform the following operations on (x, y, z) and the matrix to produce the point (x^', y^', z^'):

The most common transformations are translation, rotation, and scaling. You can combine the matrices that produce these effects into a single matrix to calculate several transformations at once. For example, you can build a single matrix to translate and rotate a series of points.

Matrices are specified in row order. For example, the following matrix could be represented by an array:

The array for this matrix would look like this:

D3DMATRIX scale = {
    D3DVAL(s),    0,            0,            0,
    0,            D3DVAL(s),    D3DVAL(t),    0,
    0,            0,            D3DVAL(s),    D3DVAL(v),
    0,            0,            0,            D3DVAL(1)
};
 

This section describes the 3-D transformations available to your applications through Direct3D:

• Translation
• Rotation
• Scaling

For more information about transformations in Direct3D Immediate Mode, see Viewports and Transformations.