Graphics Programming in 3D - Essentials of Interactive Computer Graphics - page 440

UWBGL_D3D_Lib16

Change summary. See p. 531
for a summary of changes to
the library.

To properly support the concatenation operations as described by Equation (16.2),
the Lib16 library defines an explicit rotation operator (matrix) in the XformInfo
class. This matrix replaces the three floating-point numbers that represented the
Euler angles. Listing 16.9 shows the updated XformInfo class where at label C
we define a 3 3 matrix to replace the previous three floating-point numbers. At

label A and label A1, we see that in this case, the matrix is initialized with the
identity matrix ( I 3 ). The function at label B is designed to allow the user to adjust
rotation in the x -axis by dx ( R x

×

( dx ) ). In this case we must compute

R x m _ rotation = ( dx ) × m _ rotation .

At label B1, we use the variable m to represent the rotation operator R x .Atla-
bel B2, we compute the content of the operator R x ( dx ) . At label B3, the new

rotation operation is concatenated with the XformInfo .
It is important to notice that the rotation matrix in XformInfo is an ordered
concatenation of all rotation requests. In this case, we do not know the individual
steps by which to arrive at this rotation. In addition, we do not have a simple user-

class UWB _ XformInfo {

Source file.
uwbgl _ XformInfo4.h/cpp
file in the Common Files/
XformInfo subfolder of the
UWBGL _ D3D _ Lib16 project.

public :

A:

void InitializeRotation(); // initialize rotation

.
B: void UpdateRotationXByDegree(dx); // update rotaion by dx about x axis
.
protected :
C: mat3 m _ rotation;

// A 3 x 3 matrix

.

void UWB _ XformInfo::InitializeRotation()
A1: makeIdentity(m _ rotation); // initialize to identity ( I 3 )

void UWB _ XformInfo::UpdateRotationXByRadian( float dx)
B1: mat3 m;

// a 3 x 3 matrix

// compute R x

( dx )

B2: m[1][1]=...; m[1][2]=...

B3: m _ rotation = m * m _ rotation; // concatenate R x ( dx ) with the 3 x 3 matrix

Listing 16.9. Supporting 3D rotation with explicit matrix representation.