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renderSH_helper_mat.m
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renderSH_helper_mat.m
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% Copyright ©2013. The Regents of the University of California (Regents).
% All Rights Reserved. Permission to use, copy, modify, and distribute
% this software and its documentation for educational, research, and
% not-for-profit purposes, without fee and without a signed licensing
% agreement, is hereby granted, provided that the above copyright notice,
% this paragraph and the following two paragraphs appear in all copies,
% modifications, and distributions. Contact The Office of Technology
% Licensing, UC Berkeley, 2150 Shattuck Avenue, Suite 510, Berkeley, CA
% 94720-1620, (510) 643-7201, for commercial licensing opportunities.
%
% Created by Jonathan T Barron and Jitendra Malik, Electrical Engineering
% and Computer Science, University of California, Berkeley.
%
% IN NO EVENT SHALL REGENTS BE LIABLE TO ANY PARTY FOR DIRECT, INDIRECT,
% SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, INCLUDING LOST PROFITS,
% ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF
% REGENTS HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
%
% REGENTS SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING, BUT NOT
% LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
% PARTICULAR PURPOSE. THE SOFTWARE AND ACCOMPANYING DOCUMENTATION, IF ANY,
% PROVIDED HEREUNDER IS PROVIDED "AS IS". REGENTS HAS NO OBLIGATION TO
% PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
function [E, dS_dN, dS_dL] = renderSH_helper(N, L, NO_SHADOW)
RETURN_DE = nargout >= 2;
RETURN_DL = nargout >= 3;
ORDER = 2;
if ORDER == 1
L(5:end) = 0;
end
c1 = 0.429043;
c2 = 0.511664;
c3 = 0.743125;
c4 = 0.886227;
c5 = 0.247708;
M = [ c1 * L(9), c1 * L(5), c1 * L(8), c2 * L(4);
c1 * L(5), -c1 * L(9), c1 * L(6), c2 * L(2);
c1 * L(8), c1 * L(6), c3 * L(7), c2 * L(3);
c2 * L(4), c2 * L(2), c2 * L(3), c4 * L(1) - c5 * L(7)];
assert(size(N,2) == 3)
I = ones(size(N,1), 1);
Na = [N, I];
NM = Na * M;
E = sum(NM .* Na,2);
% if (nargin < 3) || NO_SHADOW
% E = max(0, E);
% end
%
% iszero = E == 0;
if RETURN_DL
dS_dL = [c4 * I, (2*c2)*N(:,2), (2*c2)*N(:,3), (2*c2)*N(:,1), (2*c1)*(N(:,1).*N(:,2)), (2*c1)*(N(:,2).*N(:,3)), c3*(N(:,3).^2) - c5, (2*c1)*(N(:,1).*N(:,3)), c1*(N(:,1).^2 - N(:,2).^2)];
% dS_dL(iszero,:) = 0;
end
if RETURN_DE
dS_dN = 2*NM(:,1:3);
% dS_dN(iszero,:) = 0;
end
% function [E, dS_dL, dS_dN] = renderSH_helper(N, L)
%
% RETURN_DL = nargout >= 2;
% RETURN_DE = nargout >= 3;
%
% c1 = 0.429043;
% c2 = 0.511664;
% c3 = 0.743125;
% c4 = 0.886227;
% c5 = 0.247708;
%
% M = [ c1 * L(9), c1 * L(5), c1 * L(8), c2 * L(4);
% c1 * L(5), -c1 * L(9), c1 * L(6), c2 * L(2);
% c1 * L(8), c1 * L(6), c3 * L(7), c2 * L(3);
% c2 * L(4), c2 * L(2), c2 * L(3), c4 * L(1) - c5 * L(7)];
%
%
% assert(size(N,2) == 3)
%
% I = ones(size(N,1), 1);
% Na = [N, I];
% NM = Na * M;
% E = max(0, sum(NM .* Na,2));
%
% % Mrep = repmat(M(end,:), size(N,1),1);
% % NM = N * M(1:3,:) + Mrep;
% % E = max(0, sum(NM(:,1:3) .* N,2) + NM(:,4));
%
%
% % E = sum(NM .* Na,2);
% iszero = E == 0;
%
% if RETURN_DL
% dS_dL = [c4 * I, (2*c2)*N(:,2), (2*c2)*N(:,3), (2*c2)*N(:,1), (2*c1)*(N(:,1).*N(:,2)), (2*c1)*(N(:,2).*N(:,3)), c3*(N(:,3).^2) - c5, (2*c1)*(N(:,1).*N(:,3)), c1*(N(:,1).^2 - N(:,2).^2)];
% % E = max(0, dS_dL * L);
% dS_dL(iszero,:) = 0;
% end
%
% if RETURN_DE
% dS_dN = 2*NM(:,1:3);
% % dS_dN = N * M(:,1:3);
% dS_dN(iszero,:) = 0;
% end
%
%
% % NORMALIZE = false;
% %
% % if NORMALIZE
% % % Divide by the max
% %
% % E_unsigned = sum((N * M) .* N,2);
% % E = max(0, E_unsigned);
% % nonzero = E > 0;
% %
% % Z_idx = find(E == max(E), 1, 'first');
% % Z = max(eps, E(Z_idx));
% %
% % % Z2 = (4.*(c2.*L(3)+c1.*(L(6).^2+L(8).^2).^(1/2)).^2+(2.*c2.*(L(2).^2+L(4).^2).^(1/2)+c1.*(L(5).^2+L(9).^2).^(1/2)).^2).^(1/2)+(1/2).*(2.*c4.*L(1)+(c3+(-2).*c5).*L(7)+abs(c3.*L(7)));
% % % [Z2/Z]
% %
% % if RETURN_DL
% % dL = [c4 * (N(:,4).^2), (2*c2)*(N(:,2).*N(:,4)), (2*c2)*(N(:,3).*N(:,4)), (2*c2)*(N(:,1).*N(:,4)), (2*c1)*(N(:,1).*N(:,2)), (2*c1)*(N(:,2).*N(:,3)), c3*(N(:,3).^2) - c5*(N(:,4).^2), (2*c1)*(N(:,1).*N(:,3)), c1.*(N(:,1).^2+(-1).*N(:,2).^2)];
% % dL = dL/Z - E * (dL(Z_idx,:)/(Z^2));
% % dL = repmat(nonzero, 1, size(dL,2)) .* dL;
% % end
% %
% % if RETURN_DE
% % dE = (2/Z)*(N * M(:, 1:3));
% % dE = repmat(nonzero, 1, size(dE,2)) .* dE;
% % end
% %
% % E = E/Z;
% %