[cig-commits] r7005 - cs/cigma/trunk/doc/manual

[sue at geodynamics.org]

Author: sue
Date: 2007-05-30 14:04:00 -0700 (Wed, 30 May 2007)
New Revision: 7005

Modified:
   cs/cigma/trunk/doc/manual/cigma.lyx
Log:
rework equation format

Modified: cs/cigma/trunk/doc/manual/cigma.lyx
===================================================================
--- cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-30 20:04:41 UTC (rev 7004)
+++ cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-30 21:04:00 UTC (rev 7005)
@@ -465,7 +465,16 @@
 
 \begin_layout Standard
 \begin_inset Formula \[
-\]
+\begin{array}{cc}
+x\left(\xi\eta\zeta\right) & =\alpha_{0}+\alpha_{1}\xi+\alpha_{2}\eta+\alpha_{3}\zeta+\alpha_{4}\xi\eta+\alpha_{5}\xi\zeta+\alpha_{6}\eta\zeta+\alpha_{7}\xi\eta\zeta\\
+ & =\frac{1}{8}\left[x_{0}\cdot\left(1-\xi-\eta-\zeta+\xi\eta+\xi\zeta+\eta\zeta-\xi\eta\zeta\right)\right.\\
+ & +x_{1}\cdot\left(1+\xi-\eta-\zeta-\xi\eta-\xi\zeta+\eta\zeta+\xi\eta\zeta\right)\\
+ & +x_{2}\cdot\left(1-\xi+\eta-\zeta-\xi\eta+\xi\zeta-\eta\zeta+\xi\eta\zeta\right)\\
+ & +x_{3}\cdot\left(1+\xi+\eta-\zeta+\xi\eta-\xi\zeta-\eta\zeta-\xi\eta\zeta\right)\\
+ & +x_{4}\cdot\left(1-\xi-\eta+\zeta+\xi\eta-\xi\zeta-\eta\zeta+\xi\eta\zeta\right)\\
+ & +x_{5}\cdot\left(1+\xi-\eta+\zeta-\xi\eta+\xi\zeta-\eta\zeta-\xi\eta\zeta\right)\\
+ & +x_{6}\cdot\left(1-\xi+\eta+\zeta-\xi\eta-\xi\zeta+\eta\zeta-\xi\eta\zeta\right)\\
+ & \left.+x_{7}\cdot\left(1+\xi+\eta+\zeta+\xi\eta+\xi\zeta+\eta\zeta+\xi\eta\zeta\right)\right]\end{array}\]
 
 \end_inset
 
@@ -474,7 +483,15 @@
 
 \begin_layout LyX-Code
 \begin_inset Formula \[
-x\left(\xi\eta\zeta\right)=\alpha_{0}+\alpha_{1}\xi+\alpha_{2}\eta+\alpha_{3}\zeta+\alpha_{4}\xi\eta+\alpha_{5}\xi\zeta+\alpha_{6}\eta\zeta+\alpha_{7}\xi\eta\zeta\]
+\begin{array}{c}
+=\left[\frac{1}{8}\left(1-\xi\right)\left(1-\eta\right)\left(1-\zeta\right)\right]\cdot x_{0}\,\,\,\,\,\,\,\,\,\,\left(-1,-1,-1\right)\\
++\left[\frac{1}{8}\left(1+\xi\right)\left(1-\eta\right)\left(1-\zeta\right)\right]\cdot x_{1}\,\,\,\,\,\,\,\,\,\,\left(+1,-1,-1\right)\\
++\left[\frac{1}{8}\left(1-\xi\right)\left(1+\eta\right)\left(1-\zeta\right)\right]\cdot x_{2}\,\,\,\,\,\,\,\,\,\,\left(-1,+1,-1\right)\\
++\left[\frac{1}{8}\left(1+\xi\right)\left(1+\eta\right)\left(1-\zeta\right)\right]\cdot x_{3}\,\,\,\,\,\,\,\,\,\,\left(+1,+1,-1\right)\\
++\left[\frac{1}{8}\left(1-\xi\right)\left(1-\eta\right)\left(1+\zeta\right)\right]\cdot x_{4}\,\,\,\,\,\,\,\,\,\,\left(-1,-1,+1\right)\\
++\left[\frac{1}{8}\left(1+\xi\right)\left(1-\eta\right)\left(1+\zeta\right)\right]\cdot x_{5}\,\,\,\,\,\,\,\,\,\,\left(+1,-1,+1\right)\\
++\left[\frac{1}{8}\left(1-\xi\right)\left(1+\eta\right)\left(1+\zeta\right)\right]\cdot x_{6}\,\,\,\,\,\,\,\,\,\,\left(-1,+1,+1\right)\\
++\left[\frac{1}{8}\left(1+\xi\right)\left(1+\eta\right)\left(1+\zeta\right)\right]\cdot x_{7}\,\,\,\,\,\,\,\,\,\,\left(+1,+1,+1\right)\end{array}\]
 
 \end_inset
 
@@ -482,155 +499,11 @@
 \end_layout
 
 \begin_layout LyX-Code
-\begin_inset Formula \[
-=\frac{1}{8}\left[x_{0}\cdot\left(1-\xi-\eta-\zeta+\xi\eta+\xi\zeta+\eta\zeta-\xi\eta\zeta\right)\right.\]
 
-\end_inset
-
-
 \end_layout
 
 \begin_layout LyX-Code
 \begin_inset Formula \[
-+x_{1}\cdot\left(1+\xi-\eta-\zeta-\xi\eta-\xi\zeta+\eta\zeta+\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+x_{2}\cdot\left(1-\xi+\eta-\zeta-\xi\eta+\xi\zeta-\eta\zeta+\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+x_{3}\cdot\left(1+\xi+\eta-\zeta+\xi\eta-\xi\zeta-\eta\zeta-\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+x_{4}\cdot\left(1-\xi-\eta+\zeta+\xi\eta-\xi\zeta-\eta\zeta+\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+x_{5}\cdot\left(1+\xi-\eta+\zeta-\xi\eta+\xi\zeta-\eta\zeta-\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+x_{6}\cdot\left(1-\xi+\eta+\zeta-\xi\eta-\xi\zeta+\eta\zeta-\xi\eta\zeta\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-\left.+x_{7}\cdot\left(1+\xi+\eta+\zeta+\xi\eta+\xi\zeta+\eta\zeta+\xi\eta\zeta\right)\right]\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-=\left[\frac{1}{8}\left(1-\xi\right)\left(1-\eta\right)\left(1-\zeta\right)\right]\cdot x_{0}\,\,\,\,\,\,\,\,\,\,\left(-1,-1,-1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1+\xi\right)\left(1-\eta\right)\left(1-\zeta\right)\right]\cdot x_{1}\,\,\,\,\,\,\,\,\,\,\left(+1,-1,-1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1-\xi\right)\left(1+\eta\right)\left(1-\zeta\right)\right]\cdot x_{2}\,\,\,\,\,\,\,\,\,\,\left(-1,+1,-1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1+\xi\right)\left(1+\eta\right)\left(1-\zeta\right)\right]\cdot x_{3}\,\,\,\,\,\,\,\,\,\,\left(+1,+1,-1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1-\xi\right)\left(1-\eta\right)\left(1+\zeta\right)\right]\cdot x_{4}\,\,\,\,\,\,\,\,\,\,\left(-1,-1,+1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1+\xi\right)\left(1-\eta\right)\left(1+\zeta\right)\right]\cdot x_{5}\,\,\,\,\,\,\,\,\,\,\left(+1,-1,+1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1-\xi\right)\left(1+\eta\right)\left(1+\zeta\right)\right]\cdot x_{6}\,\,\,\,\,\,\,\,\,\,\left(-1,+1,+1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
-+\left[\frac{1}{8}\left(1+\xi\right)\left(1+\eta\right)\left(1+\zeta\right)\right]\cdot x_{7}\,\,\,\,\,\,\,\,\,\,\left(+1,+1,+1\right)\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-\begin_inset Formula \[
 \begin{array}{cc}
 = & N_{0}\left(\vec{\xi}\right)\cdot x_{0}+N_{1}\left(\vec{\xi}\right)\cdot x_{1}+N_{2}\left(\vec{\xi}\right)\cdot x_{2}+N_{3}\left(\vec{\xi}\right)\cdot x_{3}+N_{4}\left(\vec{\xi}\right)\cdot x_{4}+...\\
 =\end{array}\]
@@ -650,6 +523,8 @@
 \end_layout
 
 \begin_layout Standard
+\noindent
+\align center
 where 
 \begin_inset Formula $\xi_{a}=\pm1,\,\eta_{b}=\pm1,\,\zeta_{c}\pm1$
 \end_inset
@@ -658,6 +533,18 @@
 \end_layout
 
 \begin_layout LyX-Code
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="1" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
 \begin_inset Formula \[
 x\left(\vec{\xi}\right)=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)x_{i}\]
 
@@ -666,7 +553,7 @@
 
 \end_layout
 
-\begin_layout LyX-Code
+\begin_layout Standard
 \begin_inset Formula \[
 y\left(\vec{\xi}\right)=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)y_{i}\]
 
@@ -675,7 +562,7 @@
 
 \end_layout
 
-\begin_layout LyX-Code
+\begin_layout Standard
 \begin_inset Formula \[
 z\left(\vec{\xi}\right)=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)z_{i}\]
 
@@ -684,33 +571,40 @@
 
 \end_layout
 
-\begin_layout LyX-Code
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
-\end_layout
+\begin_layout Standard
+\begin_inset Formula $\vec{x}=x\hat{x}+y\hat{y}+z\hat{z}$
+\end_inset
 
-\begin_layout LyX-Code
 
 \end_layout
 
-\begin_layout LyX-Code
-\begin_inset Formula $\vec{x}=x\hat{x}+y\hat{y}+z\hat{z}$
+\begin_layout Standard
+\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\left(x_{i}\hat{x}+y_{i}\hat{y}+z_{i}\hat{z}\right)$
 \end_inset
 
 
 \end_layout
 
-\begin_layout LyX-Code
-\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\left(x_{i}\hat{x}+y_{i}\hat{y}+z_{i}\hat{z}\right)$
+\begin_layout Standard
+\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\vec{x}_{i}\,\,\,\,\,\mathrm{tabulate\, the}\, N_{i}\left(\vec{\xi}\right)\mathrm{'s\, for\, each\, required}\,\vec{\xi}$
 \end_inset
 
 
 \end_layout
 
-\begin_layout LyX-Code
-\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\vec{x}_{i}\,\,\,\,\,\mathrm{tabulate\, the}\, N_{i}\left(\vec{\xi}\right)\mathrm{'s\, for\, each\, required}\,\vec{\xi}$
 \end_inset
+</cell>
+</row>
+</lyxtabular>
 
+\end_inset
 
+
 \end_layout
 
 \begin_layout LyX-Code