MATRIXLF Structure

Of the nine fields in MATRIXLF, four are special 32-bit FIXED variables. The remaining five are 32-bit long integer variables.

The scaling, reflecting, and rotation constants, M11,M12,M21,M22, are the 32-bit, signed, FIXED variables, with an implied binary point between the second and third bytes. The translation constants, M31 and M32, and the three third-column variables, are 32-bit long integers.

A FIXED variable is a binary representation of a floating-point number. A FIXED variable has two parts:

• The high-order 16-bits, which contain a signed integer in the range -32768 through 32767.

• The low-order 16-bits, which contain the numerator of a fraction in the range 0 through 65535.

  The denominator for this fraction is 65536.

For example, to store the cosine of 60° (0.5) in a FIXED variable, an application would multiply 65536 by 0.5. The result, 32768, would be the value to assign to a field in the MATRIXLF structure.

To store a scaling factor of 3 in a FIXED variable, the application would multiply 65536 by 3. Again, the result, 196608, would be the value to assign to a field in the MATRIXLF structure.