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findconvexcone_simple.m
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findconvexcone_simple.m
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function [idx,weights] = findconvexcone_simple(x0,xs)
%This is a simplified version of the function findconvexcone() that is contained
%in the Sound Field Synthesis Toolbox, see description and license below. The
%simplification was realised to make it more efficient when used together with an
%implementation of the image source model for selection of HRTF directions, but as
%a consequence the function now only works for full-spherical point clouds (which
%is also sensible when using it for the image source model).
%
%FINDCONVEXCONE selects up to 3 points from x0 with xs in their conic span
%
% Usage: [idx,weights] = findconvexcone(x0,xs)
%
% Input parameters:
% x0 - point cloud on a sphere around the origin / m [nx3]
% xs - desired direction as point in R^3 / m [1x3]
%
% Output parameters:
% idx - row indices of N points in x0 [Nx1]
% where N is 1,2 or 3
% weights - weights [Nx1]
%
% FINDCONVEXCONE(x0,xs) returns 1,2 or 3 row indices into x0 and non-negative
% weights w1, ..., w3 such that w1*x1 + w2*x2 + w3*x3 with
% [x1; x2; x3] == x0(idx,:) composes the point inside the triangle spanned
% by x1, x2, x3.
%
% x1...x3 are selected from the convex hull in R3.
% Various precautions are taken to make this well-behaved in most cases.
%
% (If all x0 and xs have unit norm this is VBAP.)
%
% See also: findnearestneighbour, test_interpolation_point_idx
%*****************************************************************************
% The MIT License (MIT) *
% *
% Copyright (c) 2010-2019 SFS Toolbox Developers *
% *
% Permission is hereby granted, free of charge, to any person obtaining a *
% copy of this software and associated documentation files (the "Software"), *
% to deal in the Software without restriction, including without limitation *
% the rights to use, copy, modify, merge, publish, distribute, sublicense, *
% and/or sell copies of the Software, and to permit persons to whom the *
% Software is furnished to do so, subject to the following conditions: *
% *
% The above copyright notice and this permission notice shall be included in *
% all copies or substantial portions of the Software. *
% *
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL *
% THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING *
% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER *
% DEALINGS IN THE SOFTWARE. *
% *
% The SFS Toolbox allows to simulate and investigate sound field synthesis *
% methods like wave field synthesis or higher order ambisonics. *
% *
% https://sfs.readthedocs.io [email protected] *
%*****************************************************************************
%% ===== Prepare Grid (see local functions below) ========================
% Normalise x0 and xs to lie on unit sphere as only direction is relevant
xs = xs./norm(xs,2);
radii = vector_norm(x0,2);
x0 = x0./repmat(radii,[1,size(x0,2)]);
%% ===== Computation =====================================================
% Delaunay triangulation of convex hull
simplices = convhulln(x0);
% Find x0 with smallest angle to xs
[~,most_aligned_point] = ...
max(vector_product(x0,repmat(xs,size(x0,1),1),2));
% The simplices at "most aligned point" are the most likely candidates,
% put them at the beginning of the list
mask = logical(sum(simplices==most_aligned_point,2));
simplices = [simplices(mask,:); simplices(~mask,:) ];
% One of these simplices contains xs
for n = 1:size(simplices,1);
A = x0(simplices(n,:),:);
weights = xs/A;
weights(abs(weights)<1e-10) = 0;
if all(weights >= 0) % non-negative weights == convex combination
idx = simplices(n,:);
break;
end
end
% Normalise weights
weights = weights/sum(weights);
[weights,order] = sort(weights.','descend');
idx = idx(order).';