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Transform
Current Version
0
Fields
Entity/Object
Variable
Description
integer
Version.
integer
d
Space dimension.
Boolean
1 if transformation is a unit transformation; 0 otherwise. If the value is 1, no more fields are present.
double [d+1][d+1]
M
Values in transformation matrix.
Boolean
1 if determinant is positive; 0 otherwise.
Boolean
1 if matrix is isotropic; 0 otherwise.
Description
The transformation class is defined by the transformation matrix, which operates as a premultiplier on column vectors containing homogeneous coordinates thus
where the conventional 3D coordinates are
The matrix thus consists of
where
R
is a nonsingular transformation matrix, containing the rotation, reflection, nonuniform scaling, and shearing components;
T
is a translation vector; and
S
is a global scaling factor greater than zero.
