Which of the following matrix equation is correct for 3 D scaling of an object?
Posted: Thu Jul 14, 2022 8:45 am
a) \(\begin{matrix}
x1 & Sx \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; Sy \; 0 \; 0 ] & [ y0 ]\\
z1 & 0 \; 0 \; Sz \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1
\end{matrix}
\)
b) \(\begin{matrix}
x1 & Sx \; 0 \; 0 \; 1 & x0\\
[ y1 ] = & [ 0 \; Sy \; 1 \; 0 ] & [ y0 ]\\
z1 & 0 \; 1 \; Sz \; 0 & z0\\
1 & 1 \; 0 \; 0 \; 0 & 1
\end{matrix}
\)
c) \(\begin{matrix}
x1 & Sx \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; Sy \; 0 \; 0 ] & [ y0 ]\\
z1 & 0 \; 0 \; Sz \; 0 & z0\\
0 & 0 \; 0 \; 0 \; 1 & 0
\end{matrix}
\)
d) \(\begin{matrix}
x1 & 0 \; 0 \; 0 \; Sx & x0\\
[ y1 ] = & [ 0 \; 0 \; Sy \; 0 ] & [ y0 ]\\
z1 & 0 \; Sz \; 0 \; 0 & z0\\
1 & 1 \; 0 \; 0 \; 0 & 1
\end{matrix}
\)
x1 & Sx \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; Sy \; 0 \; 0 ] & [ y0 ]\\
z1 & 0 \; 0 \; Sz \; 0 & z0\\
1 & 0 \; 0 \; 0 \; 1 & 1
\end{matrix}
\)
b) \(\begin{matrix}
x1 & Sx \; 0 \; 0 \; 1 & x0\\
[ y1 ] = & [ 0 \; Sy \; 1 \; 0 ] & [ y0 ]\\
z1 & 0 \; 1 \; Sz \; 0 & z0\\
1 & 1 \; 0 \; 0 \; 0 & 1
\end{matrix}
\)
c) \(\begin{matrix}
x1 & Sx \; 0 \; 0 \; 0 & x0\\
[ y1 ] = & [ 0 \; Sy \; 0 \; 0 ] & [ y0 ]\\
z1 & 0 \; 0 \; Sz \; 0 & z0\\
0 & 0 \; 0 \; 0 \; 1 & 0
\end{matrix}
\)
d) \(\begin{matrix}
x1 & 0 \; 0 \; 0 \; Sx & x0\\
[ y1 ] = & [ 0 \; 0 \; Sy \; 0 ] & [ y0 ]\\
z1 & 0 \; Sz \; 0 \; 0 & z0\\
1 & 1 \; 0 \; 0 \; 0 & 1
\end{matrix}
\)