From 0c36375d1eab3dce03405f44cbd62860c21558d7 Mon Sep 17 00:00:00 2001
From: Ralf Hielscher <ralfHielscher@users.noreply.github.com>
Date: Thu, 7 Nov 2024 16:14:46 +0100
Subject: [PATCH] docu

---
 doc/ODFAnalysis/SigmaSections.m | 16 ++++++++--------
 doc/Tutorials/GrainTutorial.m   | 27 ++++++++++++---------------
 2 files changed, 20 insertions(+), 23 deletions(-)

diff --git a/doc/ODFAnalysis/SigmaSections.m b/doc/ODFAnalysis/SigmaSections.m
index e79b76766..7ff728346 100644
--- a/doc/ODFAnalysis/SigmaSections.m
+++ b/doc/ODFAnalysis/SigmaSections.m
@@ -4,7 +4,7 @@
 % Although $\varphi_2$ sections are most common to represent orientation
 % distribution functions they heavily suffer from geometrical distortions
 % of the orientation space. Lets illustrate this at a simple example.
-% The following $\varphi_2$ sections represent a hexagonal ODF composod
+% The following $\varphi_2$ sections represent a hexagonal ODF composed
 % from several unimodal components
 
 % the ODF is defined at the bottom of this script to be secret during the first read :)
@@ -124,8 +124,8 @@
 
 %%
 
-% They can be seen as the (001) pole figure splitted according to rotations
-% about the (001) axis. Lets have a look at the 001 pole figure
+% They can be seen as the (001) pole figure split according to rotations
+% about the (001) axis. Lets have a look at the (001) pole figure
 
 plotPDF(odf,Miller(0,0,0,1,cs))
 
@@ -137,12 +137,12 @@
 
 %%
 % we can clearly distinguish the two spots in the middle indicating two
-% radial symmetric portions. On the other hand the spots at 001 appear in
-% every section indicating a fibre at position [001](100). Knowing that
-% sigma sections are nothing else then the split 001 pole figure they
-% are much more simple to interpret then usual phi2 sections.
+% radial symmetric portions. On the other hand the spots at (001) appear in
+% every section indicating a fiber at position [001](100). Knowing that
+% sigma sections are nothing else then the split (001) pole figure they are
+% much more simple to interpret than usual $\phi_2$ sections.
 
-%% Customizations
+%% Customization
 
 oS = sigmaSections(odf.CS,odf.SS);
 
diff --git a/doc/Tutorials/GrainTutorial.m b/doc/Tutorials/GrainTutorial.m
index 4ca2e58e9..b682c77d1 100644
--- a/doc/Tutorials/GrainTutorial.m
+++ b/doc/Tutorials/GrainTutorial.m
@@ -14,9 +14,10 @@
 plot(ebsd)
 
 %%
-% The phase map shows a multi-phase rock specimen with Andesina, Quartz,
-% Biotite and Orthoclase. Lets restrict it to a smaller region of interest.
-% The rectangle is defined by [xmin, ymin, xmax-xmin, ymax-ymin].
+% The phase map displays a multi-phase rock specimen with phases such as
+% Andesine, Quartz, Biotite, and Orthoclase. We will now focus on a smaller
+% rectangular region of interest defined by the coordinates |[xmin, ymin,
+% xmax - xmin, ymax - ymin]|.
 
 region = [19000 1500 4000 1500];
 % overlay the selected region on the phase map
@@ -58,31 +59,27 @@
 hold off
 
 %%
-% For the map created, most of the phases are colored based on where they
-% exist, while only the Quartz phase is colored according to the
-% orientation. The quartz orientations are colored using the following ipf
-% color key
+% In this visualization most phases are displayed in uniform colors, while
+% Quartz is colored according to the ipf color key
 
 close all
 ipfKey = ipfColorKey(ebsd_region('Quartz'));
 plot(ipfKey)
 
-
 %%
-% Alternatively, we may colorize each quartz grain according to its mean
-% orientation.  Again, the other phases are colored based on where they
-% exist.
+% Alternatively, we can display each quartz grain according to its mean
+% orientation.
 
 plot(grains({'Andesina','Biotite','Orthoclase'}),'FaceAlpha',0.4)
 hold on
 plot(grains('Quartz'),grains('Quartz').meanOrientation)
 legend off
 
-
 %% Highlight specific boundaries
-% We can create a phase map with certain grain boundaries highlighted.  In
-% this case, we highlight where adjacent grains of Andesina and Orthoclase
-% have a misorientation with rotational axis close to the c-axis.
+% We can create a phase map with certain grain boundaries highlighted. In
+% this phase map, we highlight grain boundaries where neighboring grains of
+% Andesine and Orthoclase exhibit a misorientation with a rotational axis
+% close to the c-axis.
 
 close all
 % copy all boundaries between Andesina, Orthoclase to a new variable