Therefore, the new homogeneous coordinate
of each node on fluid meshes can be calculated based on Eq.
However, DSD can cause destruction of the appearance characteristics of the model because it lacks complete homogeneous coordinate
The corresponding affine transformation can be represented by a 4 x 4 matrix T(v) in a homogeneous coordinate
system as follows:
proposed a linear homogeneous coordinate
transformation method .
Here we note that Kempf had proved (using different methods than those used in this paper) that the homogeneous coordinate
ring of a Grassmanian in its Plucker embedding is wonderful (see ).
Based on features of geometric error and homogeneous coordinate
transformation matrixes, coordinate transformation of the component of CNC machine tool in the local coordinate systems can be expressed with the product of homogeneous coordinate
0] is translation matrix from left camera to right camera; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the homogeneous coordinate
of the projection point position in left camera; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the homogeneous coordinate
of the projection point position in right camera; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the homogeneous coordinate
of a 3-D point.
Indeed, the homogeneous coordinates
of the point T in the W-frame can be written as a function of [beta]:
Points in homogeneous coordinates
can be written as [x'.
It is a nice illustration of a utilization of matrices in geometry, application of homogeneous coordinates
, homogeneous transformation matrices and matrix algebra (Many similar exercises can be found in [Cox, 1998], [Craig, 1986], [Tsai, 1999]).
where d and o are the homogeneous coordinates
of the distorted and original input images.
T] are the homogeneous coordinates
of point m and M , and P is a 3 x 4 is camera projection matrix.