Calculating shape preferred orientation

[Andrew Cross]

Hi,

Is there an MTEX function for extracting the orientation of the long axis of a grain? I want to make a plot of shape preferred orientation in a mylonite by showing the alignment of grain long axes with the foliation plane.

Thanks in advance

[David Mainprice]

Suggestions for grain shape and orientation analysis are as follows;

1) 10-15 degrees for grain segmentation angle

2) use a minimum of 10 indexed points per grain

you need to make some tests to see if keeping the non-index points gives better representation of your grains or not.

For an over view here is a list of possible parameters for grains with 2D EBSD data

%%

%**************************************************************************

% Determine all MTEX standard Grain Size and Shape parameters

%**************************************************************************

% calculate all parameters

% area (with holes = non-indexed points)

g_area = area(grains);

% aspect ratio is the ratio between the two principal components

g_aspectratio = aspectratio(grains);

% centroid = barycenter of the grain-polygon, with respect to its holes

% note that the barycenter can be outside the grain for some complex shapes

g_centroid = centroid(grains);

% equivalent radius er = sqrt(area/pi)

g_equivalentradius = equivalentradius(grains);

% equivalent diameter ed = 2*sqrt(area/pi)

g_equivalentdiameter = 2 * equivalentradius(grains);

% equivalent perimeter ep = 2*pi*equivalent radius

g_equivalentperimeter =  equivalentperimeter(grains);

% calculates the perimeter (p) of a grain, with holes

g_perimeter = perimeter(grains);          

% shapefactor = perimeter/equivalent perimeter = p/ep

g_shapefactor = shapefactor(grains);

%

There are two functions for grain shape; aspect ratio and shape factor, I prefer aspect ratio 

of course can make tests with both.  To get the orientation of the grain long axis associated with aspect ratio

There used to be a function for plotting the ellipse of the grain on EBSD map, but this was withdrawn from MTEX several years ago, it might be nice to have back.

%%

%**************************************************************************

% Determine angle of long axis of grain from EBSD map X-axis

%**************************************************************************

% Principle components using SVD analysis

% Eigen-vectors (ev) Eigen-values (ew)

[ev,ew]= principalcomponents(grains,'Hull');

% Angle from X-axis using Eigen-vectors (ev)

Theta = atan2(ev(1,2,:),ev(1,1,:))/degree;

% Remove unwanted singleton dimensions

Theta=squeeze(Theta);

% keep angles in the range 0-180 degrees from X-axis

for i=1:length(Theta)

    if(Theta(i)<0)

       Theta(i) = 180 + Theta(i);

    end

end

%%

%**************************************************************************

% Plot classical Rose diagram frequency vs angle

%**************************************************************************

figure

Rad_Theta = Theta * pi/180;

% bin width = 5 degrees (360/5 = 72)

n_angle_bins_Rose = 72;

rose(Rad_Theta,n_angle_bins_Rose)

% plot title

title('Angle from X=0 degrees Radius = counts','FontSize’,14)

% save plot

savefigure('/MatLab_Programs/Rose_diagram_angle_vs_aspect_ratio.png’)

There are other presentations of data you could make, this is simplest.

all the best David

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