determining planar boundaries

[Saoussen-ouhiba]

Hello,

I would like to determine the planar portion of a grain boundary as indicated by an ellipse in the figure below

Could you help me to do such an operation please? My objective is to calculate the misorientation axis and angle of these planar boundaries.

Thank you a lot for your help,

Saoussen

[kilir]

Hi,
there are several ways to discriminate a "planar" part of the boundary, e.g. via a curvature threshold or an angular threshold between (higher order) grain boundary segments. However, it seems you have also drawn your ellipse based on the scale/size of this part of the grain boundary.

How would you exactly or at least in some more detail define the "planar portion of a grain boundary" without having to draw it?

Cheers,
Rüdiger

[Saoussen-ouhiba]

Thank you for your reply. The ellipse was drawn manually so that you can see what I mean by a "planar" part of a boundary.

I would define a "planar portion of a grain boundary" as a part having a mean curvature equal to zero.

Thanks again,

Saoussen

[kilir]

Hi Saoussen,
in that case, you need to make at least some decisions.

1. how much smoothing does your data need
2. what would you consider as the "mean curvature"; how many neighboring segments you'd consider (and this will most likely depend on a number of factors)
3. what is close enough to zero for the threshold of curvature

EDIT: handle triple junctions. Curvature isn't computed correctly for larger number of neighbors (alternatively, go grain by grain)

Try this one:

mtexdata titanium
grains = ebsd.calcGrains;
%%
% 1) decide how much smoothing is required

smooth_iter = 5;

grainsS = smooth(grains,smooth_iter); 

% % remove tripe points since curvature uisn't computed the right way
tpi = unique(grainsS.boundary.triplePoints.boundaryId);
gbind = ones(length(grainsS.boundary),1);
gbind(tpi) = 0;
gbi=grainsS.boundary(logical(gbind));
gbi =gbi('indexed');

% 2) determine how many neighbours you'd like to consider determining the
% curvature

n_neighbours = 3;

curv = gbi.curvature(n_neighbours);

% 3) decide below which threshold your gb is considered "planar" 
plGb= curv <= 0.001;

gbplanar = gbi(plGb);

% only take a certain length
gbplanar = gbplanar(gbplanar.componentSize > 5);

plot(gbi,curv)
hold on
plot(gbplanar,'linewidth',2,'linecolor','r')
hold off

Cheers,
Rüdiger