3D Graphics Basics - Game Coding Complete - page 461

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about that axis will make the teapot appear as if it is sitting on a potter s wheel. How

do you calculate the angle? Go back to your unit circle to figure it out. The angle you
want is 45 degrees, or

/4. We also know that the angle should be negative. Here ' s

π

why: If you were looking along the Y-axis, you ' d be underneath the teapot looking

straight up. The teapot s spout needs to twist clockwise to achieve the desired result,

so the angle is negative.
A rotation matrix for the Y-axis looks like this:

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2
4

3
5

cos ð Þ 0 sin ð Þ 0
0100
sin ð Þ 0 cos ð Þ 0
0001

Here ' s the code to create this matrix in DirectX:

float angle = -D3DX_PI / 4.0f;
D3DXMATRIX rotateY;
D3DXMatrixRotationY(&rotateY, angle);
Let ' s transform a vector with this matrix and see what happens. Since the teapot ' s

spout is pointing down the X-axis, let ' s transform (x=1, y=0, z=0):

D3DXVECTOR4 original(1, 0, 0, 1);
D3DXVECTOR4 result(0,0,0,0);
D3DXVec4Transform(&result, &original, &rotateY);
Here

' s the result:

result {...} D3DXVECTOR4

x 0.70710677 float

y 0.00000000 float

z 0.70710677 float

w 1.0000000 float

Excellent, that s exactly what we want. The new vector is sitting on the X-Z plane, and

both coordinates are in the positive. If we take that same transform, apply it to every
vertex of the teapot, and then redraw it, we

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ll get the picture shown in Figure 14.8.
This matrix will create a rotation about the X-axis:

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2
4

3
5

1 0 0 0

0 cos ð Þ sin ð Þ 0

0 sin ð Þ cos ð Þ 0

0 0 0 1