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projfacet2hyperplane.m
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projfacet2hyperplane.m
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function newvertices = projfacet2hyperplane(nvec,vertices)
% PROJFACET2HYPERPLANE project facet vertices onto a hyperplane defined by nvec
% Take a list of vertices defining a facet with vertices on
% the unit hypersphere and project them onto a tangent hyperplane at a
% user-defined point, nvec. Useful for computing spherical barycentric
% coordinates (sphbary.m).
%--------------------------------------------------------------------------
% Author: Sterling Baird
%
% Date: 2020-07-03
%
% Inputs:
% nvec === normalized normal to desired tangent hyperplane (i.e.
% point on unit hypersphere)
%
% vertices === rows of vertices of facet to project from
% hypersphere to tangent hyperplane @ nvec
%
% Outputs:
% newvertices === new vertices of facet (projected from hypersphere to
% tangent hyperplane @ nvec)
%
% Dependencies:
% projray2hyperplane.m
%
% References:
% https://math.stackexchange.com/q/1256236/798661
%--------------------------------------------------------------------------
%% project vertices onto hyperplane
%initialize
newvertices = zeros(size(vertices));
nvertices = size(vertices,1);
for i = 1:nvertices
vtx = vertices(i,:); %vertex
newvertices(i,:) = projray2hyperplane(nvec,vtx);
end
end %projfacet2hyperplane