Graphics Programming in 3D - Essentials of Interactive Computer Graphics - page 443

class CXformInfoControl : public CDialog {
.

Source file.
XformInfoControl.h/cpp
files in the Controls folder
of the D3D _ RotateMatrix
project.

// current sldier bar setting

float m _ rx, m _ ry, m _ rz;
.

A:

void CXformInfoControl::OnHScroll( ... ) {
.
// new values from slider bar
float x=m _ XSlider.GetSliderValue();
.
switch (current _ control)
// when radio button is rotation
case IDC _ ROTATE: {
// compute the change in sldier bar position

float dx=x-m _ rx;
// remember current position
m _ rx = x;
// send change in position to set rotation
xform.UpdateRotationXByDegree(dx);

B:

V = ( v x , v y , v z )

θ

V b

.

V a

q = (V, θ)

Listing 16.11. Capturing rotation differentials.

Figure 16.6. The quater-
nion representation of rota-
tion.

UWBGL_D3D_Lib17

Change summary. See p. 533
for a summary of changes to
the library.

The cost of concatenating operations is the major shortcoming of representing
rotation by an explicit matrix. The quaternion offers a storage and computation-
ally efficient alternative to representing rotations. As illustrated in Figure 16.6, a
quaternion describes a rotation with 4 floating-point numbers:

Right-handed rotation di-
rection. With the right hand,
stick out the thumb and curl
the rest of the fingers into a
“thumbs up” sign. The thumb
direction is along the axis of
rotation, and the rest of the fin-
gers point in the positive direc-
tion of rotation.

V

q =( , θ )=( v x , v y , v z , θ ) , (16.4)

where V is the axis of rotation and is the angle to rotate. Notice the right-

handed rotation direction and that axes V a and V b are perpendicular to the axis
of rotation V . Just as we can describe a series of affine transformations by
concatenating corresponding matrices, a series of rotations can be described by

θ