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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 [vertices, faces] = curveToMesh(curve, varargin)
%CURVETOMESH Create a mesh surrounding a 3D curve.
%
% [V, F] = curveToMesh(CURVE)
% Computes the vertices and the faces of the mesh surrounding the
% specified 3D curve.
%
% [V, F] = curveToMesh(CURVE, THICKNESS)
% Specifies the thickness of the mesh (distance between mesh vertices and
% curve vertices). Default is 0.5.
%
% [V, F] = curveToMesh(CURVE, THICKNESS, NCORNERS)
% Also specifies the number of mesh vertices around each curve vertex.
% Default is 8.
%
%
% Example
% % Creates a tubular mesh around a trefoil knot curve
% t = linspace(0, 2*pi, 200)';
% x = sin(t) + 2 * sin(2 * t);
% y = cos(t) - 2 * cos(2 * t);
% z = -sin(3 * t);
% curve = [x, y, z];
% [v2, f2] = curveToMesh(curve, .5, 16);
% figure;
% drawMesh(v2, f2);
% axis equal; view(3);
% axis([-4 4 -4 4 -2 2]);
%
% See also
% meshes3d, torusMesh, surfToMesh
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2015-01-07, using Matlab 8.4.0.150421 (R2014b)
% Copyright 2015-2023 INRA - Cepia Software Platform
radius = .1;
if nargin > 1
radius = varargin{1};
end
nCorners = 8;
if nargin > 2
nCorners = varargin{2};
end
nNodes = size(curve, 1);
nVerts = nNodes * nCorners;
vertices = zeros(nVerts, 3);
% create reference corners, that will be rotated and translated
t = linspace(0, 2*pi, nCorners + 1)';
t(end) = [];
baseCorners = radius * [cos(t) sin(t) zeros(size(t))];
for iNode = 1:nNodes
% coordinate of current node
node = curve(iNode, :);
% compute local tangent vector
iNext = mod(iNode, nNodes) + 1;
tangentVector = normalizeVector3d(curve(iNext, :) - node);
% convert to spherical coordinates
[theta, phi, rho] = cart2sph2(tangentVector); %#ok<ASGLU>
% apply transformation to place corners around current node
rotY = createRotationOy(theta);
rotZ = createRotationOz(phi);
trans = createTranslation3d(node);
transformMatrix = trans * rotZ * rotY;
corners = transformPoint3d(baseCorners, transformMatrix);
% concatenate with other corners
vertices( (1:nCorners) + (iNode - 1) * nCorners, :) = corners;
end
% indices of vertices
inds = (1:nVerts)';
add1 = repmat([ones(nCorners-1, 1) ; 1-nCorners], nNodes, 1);
% generate faces
faces = [inds ...
mod(inds + add1 - 1, nVerts) + 1 ...
mod(inds + nCorners + add1 - 1, nVerts) + 1 ...
mod(inds + nCorners - 1, nVerts) + 1];
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