1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
|
## 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, facets] = triangulateCurvePair(curve1, curve2)
%TRIANGULATECURVEPAIR Compute triangulation between a pair of 3D open curves.
%
% [V, F] = testTriangulateCurvePair(CURVE1, CURVE2)
%
% Example
% % triangulate a surface patch between two open curves
% % create two sample curves
% t = linspace(0, 2*pi, 100);
% curve1 = [linspace(0, 10, 100)' 5 * sin(t') zeros(100,1)];
% curve2 = [linspace(0, 10, 100)' 2 * sin(t') 2*ones(100,1)];
% figure; hold on;
% drawPolyline3d(curve1, 'b');
% drawPolyline3d(curve2, 'g');
% view(3); axis equal;
% [v, f] = triangulateCurvePair(curve1, curve2);
% figure; drawMesh(v, f, 'linestyle', 'none');
% view(3); axis equal
%
% See also
% meshes3D, triangulatePolygonPair, meshSurfaceArea
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2017-05-18, using Matlab 9.1.0.441655 (R2016b)
% Copyright 2017-2023 INRA - Cepia Software Platform
%% Memory allocation
% number of vertices on each curve
n1 = size(curve1, 1);
n2 = size(curve2, 1);
% allocate the array of facets (each edge of each curve provides a facet)
nFacets = n1 + n2 - 2;
facets = zeros(nFacets, 3);
% look for the closest ends of two curves and reverse the second curve if
% needed
p1 = curve1(1, :);
if distancePoints(p1, curve2(1,:)) > distancePoints(p1, curve2(end,:))
curve2 = curve2(end:-1:1,:);
end
currentIndex1 = 1;
currentIndex2 = 1;
% concatenate vertex coordinates for creating mesh
vertices = [curve1 ; curve2];
%% Main iteration
% For each diagonal, consider the two possible facets (one for each 'next'
% vertex on each curve), each create current facet according to the closest
% one.
% Then update current diagonal for next iteration.
for i = 1:nFacets
nextIndex1 = mod(currentIndex1, n1) + 1;
nextIndex2 = mod(currentIndex2, n2) + 1;
% compute lengths of diagonals
dist1 = distancePoints(curve1(currentIndex1, :), curve2(nextIndex2,:));
dist2 = distancePoints(curve1(nextIndex1, :), curve2(currentIndex2,:));
if dist1 < dist2
% keep current vertex of curve1, use next vertex on curve2
facet = [currentIndex1 currentIndex2+n1 nextIndex2+n1];
currentIndex2 = nextIndex2;
else
% keep current vertex of curve2, use next vertex on curve1
facet = [currentIndex1 currentIndex2+n1 nextIndex1];
currentIndex1 = nextIndex1;
end
% create the facet
facets(i, :) = facet;
end
|
