ODF Shapes (The class kernel)

standard distributions on SO(3)

Class Description

The class kernel is needed in MTEX to define the specific form of unimodal and fibre symmetric ODFs. It has to be passed as an argument when calling the methods uniformODF and fibreODF.

Defining a kernel function

A kernel is defined by specifying its name and its free parameter. Alternatively one can also specify the halfwidth of the kernel. Below you find a list of all kernel functions supported by MTEX.

psi{1} = AbelPoissonKernel(0.79);
psi{2} = deLaValleePoussinKernel(13);
psi{3} = vonMisesFisherKernel(7.5);
psi{4} = bumpKernel(35*degree);
psi{5} = DirichletKernel(3);
psi{6} = GaussWeierstrassKernel(0.07);
psi{7} = fibreVonMisesFisherKernel(7.2);
psi{8} = SquareSingularityKernel(0.72);

Plotting the kernel

Using the plot command you can plot the kernel as a function on SO(3) as well as the corresponding PDF, or its Fourier coefficients

% the kernel on SO(3)
close; figure('position',[100,100,700,450])
hold all
for i = 1:numel(psi)
  plot(psi{i},'DisplayName',class(psi{i}));
end
hold off
legend(gca,'show')

the corresponding PDF

close; figure('position',[100,100,700,450])
hold all
for i = 1:numel(psi)
  plotPDF(psi{i},'RK','DisplayName',class(psi{i}));
end
hold off

ylim([-1,20])

legend(gca,'show')

the Fourier coefficients of the kernels

close; figure('position',[100,100,500,450])
hold all
for i = 1:numel(psi)
  plotFourier(psi{i},'bandwidth',32,'DisplayName',class(psi{i}));
end
hold off
legend(gca,'show')

Complete Function list

psi = kernel(A)