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8.2 Coordinate Transformations
For precise set-up of the scan system relative to the
Image Field
(or, if the
Option "Second Scan Head
Control"
is enabled, two scan heads can be adjusted
relative to a common
Image
transformation can be defined (separately for the
first and second scan head connectors) for all x and
y output coordinates (x|y) defined by
Vector
Commands or
"Arc"
x'
M
=
y'
The (2 x 2) total matrix M is thereby automatically
calculated by the RTC6 PCIe Board as a product of a
scaling matrix M
, a rotation matrix M
S
transformation matrix M
:
T
M
=
M
T
The coefficients of the three matrices (M
M
) and the offset values (x
S
defined for the first and second scan head connector.
The offset (x
|y
) is set by
0
0
set_offset_list.
For 3-axis scan systems,
set_offset_xyz
set_offset_xyz_list
enables setting of an offset z
the z coordinate, too (z
has the opposite effect of
0
set_defocus
or set_defocus_list).
The following applies:
z'
=
RTC6 boards
Doc. Rev. 1.0.21 en-US
8 Advanced Functions for Scan Head Control and Laser Control
Field), a linear coordinate
Commands:
x
x
0
+
y
y
0
and a general
R
M
M
R
S
, M
, and
T
R
|y
) can be individually
0
0
set_offset
or
or
for
0
z
z
+
0
The coefficients of the scaling matrix M
set_scale
or
set_scale_list
that is common to both axes:
M
=
S
The coefficients of the rotation matrix M
set_angle
or
set_angle_list
angle (in accordance with mathematical
convention: positive angles produce
counterclockwise rotation):
cos
M
=
R
sin
The coefficients m
...m
11
22
transformation matrix M
T
set_matrix_list:
m
M
=
T
m
With the general transformation matrix M
above matrices (M
and M
S
as further transformations for scaling, rotating,
mirroring or skewing objects can be defined:
• Scaling by the factors k
M
=
T
• Rotation by the angle :
cos
M
=
T
sin
Example:
set_matrix( 1, 0.5, -0.866, 0.866, 0.5, 1 )
defines a rotation by 60° (counterclockwise)
around the center of the
scan head connector.
This can also be achieved by set_angle(1,60).
are set by
S
using a scaling factor k
k 0
0 k
are set by
R
by specifying a rotation
sin
–
cos
of the general
are set by
set_matrix
or
m
11
12
m
21
22
, the two
T
, as special case) as well
R
and k
:
x
y
k
0
x
0 k
y
sin
–
cos
Image Field
for the first
224
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