COMSOL Multiphysics™

Transform
Transform
Supported Versions 1
Subtype of
Fields
Serializable
The class is
ENTITY/
OBJECT
VARIABLE
DESCRIPTION
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 M Values in transformation matrix
[d+1][d+1]
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, that operates as a
pre-multiplier on column vectors containing homogenous coordinates thus
x' y' z' s' = M ⋅ xyzs'
where the conventional 3D coordinates are
The matrix thus consists of
x
-- y s
-- z s -- s
R
T x
T y
T z
000 S
where R is a non singular transformation matrix, containing the rotation, reflection,
non-uniform scaling and shearing components, T is a translation vector and S is a
global scaling factor greater than zero.
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