### Matrix Scaling

One
of the transformations you can apply to an object is scaling. Scaling
is the ability to shrink or grow an object by a certain factor. For
instance, if you have a square centered on the origin that was two units
wide and two units tall and you scaled it twice its size, you would
have a square that now went four units in each direction. Figure 1 shows an example of the scaling effect.

Remember the 1s that were placed into the identity
matrix? Those 1s control the scaling on each of the three axes. When
vertices are transformed using this matrix, their X, Y, and Z values are
altered based on the scaling values. By changing the X axis value to a 2
and the Y axis to a 3, the objects will be scaled twice their size in
the X direction and three times their size in the Y. An example ScaleMatrix array is shown next. The variables scaleX, scaleY, and scaleZ show where the appropriate scaling values would go.

float ScaleMatrix [4][4] = {
scaleX, 0.0f, 0.0f, 0.0f,
0.0f, scaleY, 0.0f, 0.0f,
0.0f, 0.0f, scaleZ, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
};

Direct3D has a function called D3DXMatrixScaling that will generate a matrix for you based on scaling values you pass in.

D3DXMATRIX * D3DXMatrixScaling (
D3DXMATRIX * pOut,
FLOAT sx,
FLOAT sy,
FLOAT sz
);

### Matrix Translation

The
act of moving an object is called translation. Translation allows for
an object to be moved along any of the three axes by specifying the
amount of movement needed. For example, if you want to move an object
right along the X axis, you would need to translate that object an
appropriate number of units in the positive X direction. To do so, you
would need to create a translation matrix. This matrix will then cause
any objects it affects to be moved to the right. Figure 2 shows an example of a square being translated.

Again,
I’ll start with the identity matrix and change it to add in the
variables that affect translation. Take a look at the following
translation matrix; the variables moveX, moveY, and moveZ show you where the translation values would go. If you wanted to translate an object 4 units to the right, you would replace moveX with the value 4.

float TranslationMatrix [4][4] = {
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
moveX, moveY, moveZ, 1.0f
};

The Direct3D function D3DXMatrixTranslation is used to easily create a translation matrix with any values you specify.

D3DXMATRIX* D3DXMatrixTranslation(
D3DXMATRIX *pOut,
FLOAT x,
FLOAT y,
FLOAT z
);