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
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
<!DOCTYPE html>
<html>
<!-- Created by GNU Texinfo 7.1.1, https://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Coordinate Transformations (GNU Octave (version 10.3.0))</title>
<meta name="description" content="Coordinate Transformations (GNU Octave (version 10.3.0))">
<meta name="keywords" content="Coordinate Transformations (GNU Octave (version 10.3.0))">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta name="viewport" content="width=device-width,initial-scale=1">
<link href="index.html" rel="start" title="Top">
<link href="Concept-Index.html" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="Arithmetic.html" rel="up" title="Arithmetic">
<link href="Mathematical-Constants.html" rel="next" title="Mathematical Constants">
<link href="Rational-Approximations.html" rel="prev" title="Rational Approximations">
<style type="text/css">
<!--
a.copiable-link {visibility: hidden; text-decoration: none; line-height: 0em}
div.example {margin-left: 3.2em}
span:hover a.copiable-link {visibility: visible}
strong.def-name {font-family: monospace; font-weight: bold; font-size: larger}
-->
</style>
<link rel="stylesheet" type="text/css" href="octave.css">
</head>
<body lang="en">
<div class="section-level-extent" id="Coordinate-Transformations">
<div class="nav-panel">
<p>
Next: <a href="Mathematical-Constants.html" accesskey="n" rel="next">Mathematical Constants</a>, Previous: <a href="Rational-Approximations.html" accesskey="p" rel="prev">Rational Approximations</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<h3 class="section" id="Coordinate-Transformations-1"><span>17.8 Coordinate Transformations<a class="copiable-link" href="#Coordinate-Transformations-1"> ¶</a></span></h3>
<a class="anchor" id="XREFcart2pol"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-cart2pol"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">r</var>] =</code> <strong class="def-name">cart2pol</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">y</var>)</code><a class="copiable-link" href="#index-cart2pol"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-cart2pol-1"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">r</var>, <var class="var">z</var>] =</code> <strong class="def-name">cart2pol</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>)</code><a class="copiable-link" href="#index-cart2pol-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-cart2pol-2"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">r</var>] =</code> <strong class="def-name">cart2pol</strong> <code class="def-code-arguments">(<var class="var">C</var>)</code><a class="copiable-link" href="#index-cart2pol-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-cart2pol-3"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">r</var>, <var class="var">z</var>] =</code> <strong class="def-name">cart2pol</strong> <code class="def-code-arguments">(<var class="var">C</var>)</code><a class="copiable-link" href="#index-cart2pol-3"> ¶</a></span></dt>
<dd>
<p>Transform Cartesian coordinates to polar or cylindrical coordinates.
</p>
<p>The inputs <var class="var">x</var>, <var class="var">y</var> (, and <var class="var">z</var>) must be the same shape, or
scalar. If called with a single matrix argument then each row of <var class="var">C</var>
represents the Cartesian coordinate pair (<var class="var">x</var>, <var class="var">y</var>) or triplet
(<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>).
</p>
<p>The outputs <var class="var">theta</var>, <var class="var">r</var> (, and <var class="var">z</var>) match the shape of the
inputs. For a matrix input <var class="var">C</var> the outputs will be column vectors with
rows corresponding to the rows of the input matrix.
</p>
<p><var class="var">theta</var> describes the angle relative to the positive x-axis measured in
the xy-plane.
</p>
<p><var class="var">r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
</p>
<p><var class="var">z</var>, if present, is unchanged by the transformation.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">theta</var> = arctan (<var class="var">y</var> / <var class="var">x</var>)
<var class="var">r</var> = sqrt (<var class="var">x</var>^2 + <var class="var">y</var>^2)
<var class="var">z</var> = <var class="var">z</var>
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFpol2cart">pol2cart</a>, <a class="ref" href="#XREFcart2sph">cart2sph</a>, <a class="ref" href="#XREFsph2cart">sph2cart</a>.
</p></dd></dl>
<a class="anchor" id="XREFpol2cart"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-pol2cart"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>] =</code> <strong class="def-name">pol2cart</strong> <code class="def-code-arguments">(<var class="var">theta</var>, <var class="var">r</var>)</code><a class="copiable-link" href="#index-pol2cart"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-pol2cart-1"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>] =</code> <strong class="def-name">pol2cart</strong> <code class="def-code-arguments">(<var class="var">theta</var>, <var class="var">r</var>, <var class="var">z</var>)</code><a class="copiable-link" href="#index-pol2cart-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-pol2cart-2"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>] =</code> <strong class="def-name">pol2cart</strong> <code class="def-code-arguments">(<var class="var">P</var>)</code><a class="copiable-link" href="#index-pol2cart-2"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-pol2cart-3"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>] =</code> <strong class="def-name">pol2cart</strong> <code class="def-code-arguments">(<var class="var">P</var>)</code><a class="copiable-link" href="#index-pol2cart-3"> ¶</a></span></dt>
<dd><p>Transform polar or cylindrical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var class="var">theta</var>, <var class="var">r</var>, (and <var class="var">z</var>) must be the same shape, or
scalar. If called with a single matrix argument then each row of <var class="var">P</var>
represents the polar coordinate pair (<var class="var">theta</var>, <var class="var">r</var>) or the
cylindrical triplet (<var class="var">theta</var>, <var class="var">r</var>, <var class="var">z</var>).
</p>
<p>The outputs <var class="var">x</var>, <var class="var">y</var> (, and <var class="var">z</var>) match the shape of the inputs.
For a matrix input <var class="var">P</var> the outputs will be column vectors with rows
corresponding to the rows of the input matrix.
</p>
<p><var class="var">theta</var> describes the angle relative to the positive x-axis measured in
the xy-plane.
</p>
<p><var class="var">r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
</p>
<p><var class="var">z</var>, if present, is unchanged by the transformation.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">x</var> = <var class="var">r</var> * cos (<var class="var">theta</var>)
<var class="var">y</var> = <var class="var">r</var> * sin (<var class="var">theta</var>)
<var class="var">z</var> = <var class="var">z</var>
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFcart2pol">cart2pol</a>, <a class="ref" href="#XREFsph2cart">sph2cart</a>, <a class="ref" href="#XREFcart2sph">cart2sph</a>.
</p></dd></dl>
<a class="anchor" id="XREFcart2sph"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-cart2sph"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">phi</var>, <var class="var">r</var>] =</code> <strong class="def-name">cart2sph</strong> <code class="def-code-arguments">(<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>)</code><a class="copiable-link" href="#index-cart2sph"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-cart2sph-1"><span><code class="def-type">[<var class="var">theta</var>, <var class="var">phi</var>, <var class="var">r</var>] =</code> <strong class="def-name">cart2sph</strong> <code class="def-code-arguments">(<var class="var">C</var>)</code><a class="copiable-link" href="#index-cart2sph-1"> ¶</a></span></dt>
<dd><p>Transform Cartesian coordinates to spherical coordinates.
</p>
<p>The inputs <var class="var">x</var>, <var class="var">y</var>, and <var class="var">z</var> must be the same shape, or scalar.
If called with a single matrix argument then each row of <var class="var">C</var> must
represent a Cartesian coordinate triplet (<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>).
</p>
<p>The outputs <var class="var">theta</var>, <var class="var">phi</var>, <var class="var">r</var> match the shape of the inputs.
For a matrix input <var class="var">C</var> the outputs will be column vectors with rows
corresponding to the rows of the input matrix.
</p>
<p><var class="var">theta</var> describes the azimuth angle relative to the positive x-axis
measured in the xy-plane.
</p>
<p><var class="var">phi</var> is the elevation angle measured relative to the xy-plane.
</p>
<p><var class="var">r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">theta</var> = arctan (<var class="var">y</var> / <var class="var">x</var>)
<var class="var">phi</var> = arctan (<var class="var">z</var> / sqrt (<var class="var">x</var>^2 + <var class="var">y</var>^2))
<var class="var">r</var> = sqrt (<var class="var">x</var>^2 + <var class="var">y</var>^2 + <var class="var">z</var>^2)
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFsph2cart">sph2cart</a>, <a class="ref" href="#XREFcart2pol">cart2pol</a>, <a class="ref" href="#XREFpol2cart">pol2cart</a>.
</p></dd></dl>
<a class="anchor" id="XREFsph2cart"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-sph2cart"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>] =</code> <strong class="def-name">sph2cart</strong> <code class="def-code-arguments">(<var class="var">theta</var>, <var class="var">phi</var>, <var class="var">r</var>)</code><a class="copiable-link" href="#index-sph2cart"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-sph2cart-1"><span><code class="def-type">[<var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var>] =</code> <strong class="def-name">sph2cart</strong> <code class="def-code-arguments">(<var class="var">S</var>)</code><a class="copiable-link" href="#index-sph2cart-1"> ¶</a></span></dt>
<dd><p>Transform spherical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var class="var">theta</var>, <var class="var">phi</var>, and <var class="var">r</var> must be the same shape, or
scalar. If called with a single matrix argument then each row of <var class="var">S</var>
must represent a spherical coordinate triplet (<var class="var">theta</var>, <var class="var">phi</var>,
<var class="var">r</var>).
</p>
<p>The outputs <var class="var">x</var>, <var class="var">y</var>, <var class="var">z</var> match the shape of the inputs. For a
matrix input <var class="var">S</var> the outputs are column vectors with rows corresponding
to the rows of the input matrix.
</p>
<p><var class="var">theta</var> describes the azimuth angle relative to the positive x-axis
measured in the xy-plane.
</p>
<p><var class="var">phi</var> is the elevation angle measured relative to the xy-plane.
</p>
<p><var class="var">r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>The coordinate transformation is computed using:
</p>
<div class="example">
<div class="group"><pre class="example-preformatted"><var class="var">x</var> = r * cos (<var class="var">phi</var>) * cos (<var class="var">theta</var>)
<var class="var">y</var> = r * cos (<var class="var">phi</var>) * sin (<var class="var">theta</var>)
<var class="var">z</var> = r * sin (<var class="var">phi</var>)
</pre></div></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFcart2sph">cart2sph</a>, <a class="ref" href="#XREFpol2cart">pol2cart</a>, <a class="ref" href="#XREFcart2pol">cart2pol</a>.
</p></dd></dl>
</div>
<hr>
<div class="nav-panel">
<p>
Next: <a href="Mathematical-Constants.html">Mathematical Constants</a>, Previous: <a href="Rational-Approximations.html">Rational Approximations</a>, Up: <a href="Arithmetic.html">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
