KUC711AE 3BHB004661R0001 ABB power supply control module
Technical data of product parameters
This KUC711AE 3BHB004661R0001 discusses the mathematics of transformation matrices. It is not
necessary to read this section to use the transformations described previously;
the information is presented for the benefit of readers who want to gain a deeper
understanding of the theoretical basis of coordinate transformations.
To understand the mathematics of coordinate transformations in PDF, it is vital
to remember two points:
• Transformations alter coordinate systems, not graphics objects. All objects painted before a transformation is applied are unaffected by the transformation. Objects painted after the transformation is applied are interpreted in theKUC711AE 3BHB004661R0001
transformed coordinate system.
• Transformation matrices specify the transformation from the new (transformed)
coordinate system to the original (untransformed) coordinate system. All coordinates used after the transformation are expressed in the transformed coordinate system. PDF applies the transformation matrix to find the equivalent
coordinates in the untransformed coordinate system.
Note: Many computer graphics textbooks consider transformations of graphics objects rather than of coordinate systems. Although either approach is correct and selfconsistent, some details of the calculations differ depending on which point of viewKUC711AE 3BHB004661R0001
is taken. If a series of transformations is carried out, the matrices representing each of the
individual transformations can be multiplied together to produce a single equivalent matrix representing the composite transformation.
Matrix multiplication is not commutative—the order in which matrices are multiplied is significant. Consider a sequence of two transformations: a scaling transformation applied to the user space coordinate system, followed by a conversionKUC711AE 3BHB004661R0001
from the resulting scaled user space to device space. Let MS be the matrix specifying the scaling and MC the current transformation matrix,
Product picture display
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Focus on DCS, PLC, robot control system and large servo system.
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