Which of the following matrix equation is correct for 3D shearing in Z axis?
Posted: Thu Jul 14, 2022 8:45 am
a) \(\begin{matrix} x1 & 1 \; 0 \; 0 \; 0 & x0\\
[ y1 ] = &[ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\
z1 & Sh_x \; 0 \;1 \; 0 & z0\\
1 & Sh_y \; 0 \; 0 \; 1 & 1\end{matrix}
\)
b)\(\begin{matrix} x1 & 1 \; 0 \; Sh_x \;Sh_y & x0\\
[ y1 ] = &[ 0\; 1 \; 0 \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \;0 \; 0 \; 1 & 1\end{matrix}
\)
c) \(\begin{matrix}x1 & 1 \;0 \; Sh_x \;0 & x0\\
[ y1 ] = & [ 0 \; 1 \; Sh_y \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
0 & 0 \; 0 \; 0 \; 1 & 0\end{matrix}
\)
d)\(\begin{matrix}x1 & 1 \; 0\; Sh_x \; 0 & x0\\
[ y1 ] = &[ 0 \; 1 \; Sh_y \; 0 ] &[ y0 ]\\
z1 & 0\; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}\)
[ y1 ] = &[ 0 \; 1 \; 0 \; 0 ] &[ y0 ]\\
z1 & Sh_x \; 0 \;1 \; 0 & z0\\
1 & Sh_y \; 0 \; 0 \; 1 & 1\end{matrix}
\)
b)\(\begin{matrix} x1 & 1 \; 0 \; Sh_x \;Sh_y & x0\\
[ y1 ] = &[ 0\; 1 \; 0 \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
1 & 0 \;0 \; 0 \; 1 & 1\end{matrix}
\)
c) \(\begin{matrix}x1 & 1 \;0 \; Sh_x \;0 & x0\\
[ y1 ] = & [ 0 \; 1 \; Sh_y \; 0 ]& [ y0 ]\\
z1 & 0 \; 0 \; 1 \; 0 & z0\\
0 & 0 \; 0 \; 0 \; 1 & 0\end{matrix}
\)
d)\(\begin{matrix}x1 & 1 \; 0\; Sh_x \; 0 & x0\\
[ y1 ] = &[ 0 \; 1 \; Sh_y \; 0 ] &[ y0 ]\\
z1 & 0\; 0 \; 1 \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1\end{matrix}\)