About 3-D Transformations

DirectX SDK

About 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 and size objects.
Change viewing positions, directions, and perspectives.

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'):

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. For more information, see Matrix Concatenation.

Matrices are written in row-column order. A matrix that evenly scales vertices along each axis (known as uniform scaling) is represented by the following matrix (using mathematical notation):

[C++]

In C++, Direct3D Immediate Mode declares matrices as a two-dimensional array, using the D3DMATRIX structure. The following example shows how to initialize a D3DMATRIX structure to act as a uniform scaling matrix:

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

[Visual Basic]

In Visual Basic, Direct3D Immediate Mode uses matrices declared as a two-dimensional array, using the D3DMATRIX type. The following example shows how to initialize a variable of type D3DMATRIX to act as a uniform scaling matrix:

    Dim ScaleMatrix As D3DMATRIX
 
    ' In this example, s is a variable of type Single.
    With ScaleMatrix
        .rc11 = s
        .rc22 = s
        .rc33 = s
        .rc44 = 1
    End With