%% Boundary Curvature
%
%%
% The curvature of a curve is defined by fitting localy a circle and taking
% one over its radius. Hence, a straight line will have curvature 0 and a
% circle of radius $2$ will have constant curvature $1/2$ everywhere.
% Hence, the unit of the curvature computed in MTEX is one over the unit of
% the EBSD coordinates which is usually $\mu m$. Let us demonstrate
% boundary curvature use some artifical grain shapes

% import the artificial grain shapes
mtexdata testgrains silent

% select and smooth a few interesting grains
grains = smooth(grains('id',[2 3 9 11 15 16 18 23 31 33 38 40]),10);

plotx2east

%%
% Therefore, we first extract all boundary segments and colorize them
% according to their curvature.

% extract boundary segments
gB = grains.boundary;

% plot some dark background
plot(gB,'linewidth',10,'micronbar','off');  

% colorize boundaries by curvature
hold on
plot(gB,gB.curvature,'linewidth',6);
hold off

% set a specific colormap
mtexColorMap('blue2red')
setColorRange(0.25*[-1,1])
mtexColorbar

%%
% Note that all the curvature values are positive. This allways happens if
% the curvature is computed for multiple grains at one. If we consider
% single grains and compute the curvature of single grain boundaries the
% sign of the values indicates whether the grain boundary is convex for
% concav with respect to the specifc grain.

for k = 1:length(grains)
  
  gB = grains(k).boundary;
  plot(gB,'linewidth',10,'micronbar','off');
  hold on
  plot(gB,gB.curvature,'linewidth',6);
  
end
hold off

mtexColorMap('blue2red')
setColorRange(0.25*[-1,1])
drawNow(gcm,'figSize',getMTEXpref('figSize'))

%%
% Finally we illustrate the ussage of the <grainBoundary.curvature.html
% curvature> command at a real EBSD map.

% import data and reconstruct grains
mtexdata titanium silent
[grains,ebsd.grainId] = calcGrains(ebsd('indexed'));
grains = smooth(grains,5);

% plot an ipf map
plot(ebsd('indexed'),ebsd('indexed').orientations)

hold on

% plot grain boundaries
plot(grains.boundary,'linewidth',4)

% colorize the grain boundaries of grain 42 according to curvature
plot(grains(42).boundary,grains(42).boundary.curvature(5),'linewidth',6)
hold off
mtexColorMap('blue2red')
setColorRange(0.1*[-1,1])
mtexColorbar

mtex-toolbox
github-repos/MATLAB/mtex-toolbox-mtex/mtex-f0ce46a720935e9ae8106ef919340534bca1adcb/doc/GrainBoundaries/BoundaryCurvature.m
mtex
github-repos/MATLAB/mtex-toolbox-mtex
f0ce46a720935e9ae8106ef919340534bca1adcb