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
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
|
## 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 varargout = revolutionSurface(varargin)
%REVOLUTIONSURFACE Create a surface of revolution from a planar curve.
%
% usage
% [X Y Z] = revolutionSurface(C1, C2, N);
% create the surface of revolution of parametrized function (xt, yt),
% with N+1 equally spaced slices, around the Oz axis.
% It assumed that C1 corresponds to the x coordinate, and that C2
% corresponds to the Oz coordinate.
%
% [X Y Z] = revolutionSurface(CURVE, N);
% is the same, but generating curve is given in a single parameter CURVE,
% which is a [Nx2] array of 2D points.
%
% [X Y Z] = revolutionSurface(..., THETA)
% where THETA is a vector, uses values of THETA for computing revolution
% angles.
%
% [X Y Z] = revolutionSurface(..., LINE);
% where LINE is a 1x4 array, specifes the revolution axis in the
% coordinate system of the curve. LINE is a row vector of 4 parameters,
% containing [x0 y0 dx dy], where (x0,y0) is the origin of the line and
% (dx,dy) is a direction vector of the line.
% The resulting revolution surface still has Oz axis as symmetry axis. It
% can be transformed using transformPoint3d function.
% Surface can be displayed using :
% H = surf(X, Y, Z);
% H is a handle to the created patch.
%
% revolutionSurface(...);
% by itself, directly shows the created patch.
%
% Example
% % draws a piece of torus
% circle = circleAsPolygon([10 0 3], 50);
% [x y z] = revolutionSurface(circle, linspace(0, 4*pi/3, 50));
% surf(x, y, z);
% axis equal;
%
% See also
% surf, transformPoint3d, drawSphere, drawTorus, drawEllipsoid
% surfature (on Matlab File Exchange)
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-04-09
% Copyright 2004-2023 INRA - CEPIA Nantes - MIAJ Jouy-en-Josas
%% Initialisations
% default values
% use revolution using the full unit circle, decomposed into 24 angular
% segments (thus, some vertices correspond to particular angles 30°,
% 45°...)
theta = linspace(0, 2*pi, 25);
% use planar vertical axis as default revolution axis
revol = [0 0 0 1];
% extract the generating curve
var = varargin{1};
if size(var, 2)==1
xt = var;
yt = varargin{2};
varargin(1:2) = [];
else
xt = var(:,1);
yt = var(:,2);
varargin(1) = [];
end
% extract optional parameters: angles, axis of revolution
% parameters are identified from their length
while ~isempty(varargin)
var = varargin{1};
if length(var) == 4
% axis of rotation in the base plane
revol = var;
elseif length(var) == 1
% number of points -> create row vector of angles
theta = linspace(0, 2*pi, var);
else
% use all specified angle values
theta = var(:)';
end
varargin(1) = [];
end
%% Create revolution surface
% ensure length is enough
m = length(xt);
if m==1
xt = [xt xt];
end
% ensure x and y are vertical vectors
xt = xt(:);
yt = yt(:);
% transform xt and yt to replace in the reference of the revolution axis
tra = createTranslation(-revol(1:2));
rot = createRotation(pi/2 - lineAngle(revol));
[xt, yt] = transformPoint(xt, yt, tra*rot);
% compute surface vertices
x = xt * cos(theta);
y = xt * sin(theta);
z = yt * ones(size(theta));
%% Process output arguments
% format output depending on how many output parameters are required
if nargout == 0
% draw the revolution surface
surf(x, y, z);
elseif nargout == 1
% draw the surface and return a handle to the shown structure
h = surf(x, y, z);
varargout{1} = h;
elseif nargout == 3
% return computed mesh
varargout = {x, y, z};
end
|
