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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function kappa = surfaceCurvature(kappa1, kappa2, theta)
%SURFACECURVATURE Curvature on a surface from angle and principal curvatures.
%
% usage:
% KAPPA = surfaceCurvature(KAPPA1, KAPPA2, THETA)
% return the curvature KAPPA of surface with respect to direction THETA.
% KAPPA1 and KAPPA2 are the principal curvatures of the surface at the
% considered point. THETA is angle of direction relative to angle of
% first principal curvature KAPPA1.
%
% Examples:
% K = surfaceCurvature(KAPPA1, KAPPA2, 0) returns KAPPA1.
% K = surfaceCurvature(KAPPA1, KAPPA2, pi/2) returns KAPPA2.
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-04-07
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
kappa = kappa1 * cos(theta).^2 + kappa2 * sin(theta).^2;
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