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
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 6.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Octave: Coordinate Transformations</title>
<meta name="description" content="GNU Octave: Coordinate Transformations">
<meta name="keywords" content="GNU Octave: Coordinate Transformations">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="Arithmetic.html#Arithmetic" rel="up" title="Arithmetic">
<link href="Mathematical-Constants.html#Mathematical-Constants" rel="next" title="Mathematical Constants">
<link href="Rational-Approximations.html#Rational-Approximations" rel="prev" title="Rational Approximations">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smalllisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en">
<a name="Coordinate-Transformations"></a>
<div class="header">
<p>
Next: <a href="Mathematical-Constants.html#Mathematical-Constants" accesskey="n" rel="next">Mathematical Constants</a>, Previous: <a href="Rational-Approximations.html#Rational-Approximations" accesskey="p" rel="prev">Rational Approximations</a>, Up: <a href="Arithmetic.html#Arithmetic" 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#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Coordinate-Transformations-1"></a>
<h3 class="section">17.8 Coordinate Transformations</h3>
<a name="XREFcart2pol"></a><dl>
<dt><a name="index-cart2pol"></a>Function File: <em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dt><a name="index-cart2pol-1"></a>Function File: <em>[<var>theta</var>, <var>r</var>, <var>z</var>] =</em> <strong>cart2pol</strong> <em>(<var>x</var>, <var>y</var>, <var>z</var>)</em></dt>
<dt><a name="index-cart2pol-2"></a>Function File: <em>[<var>theta</var>, <var>r</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2pol-3"></a>Function File: <em>[<var>theta</var>, <var>r</var>, <var>z</var>] =</em> <strong>cart2pol</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2pol-4"></a>Function File: <em><var>P</var> =</em> <strong>cart2pol</strong> <em>(…)</em></dt>
<dd>
<p>Transform Cartesian coordinates to polar or cylindrical coordinates.
</p>
<p>The inputs <var>x</var>, <var>y</var> (, and <var>z</var>) must be the same shape, or
scalar. If called with a single matrix argument then each row of <var>C</var>
represents the Cartesian coordinate (<var>x</var>, <var>y</var> (, <var>z</var>)).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>r</var> is the distance to the z-axis (0, 0, z)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>P</var>
where each row represents one polar/(cylindrical) coordinate
(<var>theta</var>, <var>phi</var> (, <var>z</var>)).
</p>
<p><strong>See also:</strong> <a href="#XREFpol2cart">pol2cart</a>, <a href="#XREFcart2sph">cart2sph</a>, <a href="#XREFsph2cart">sph2cart</a>.
</p></dd></dl>
<a name="XREFpol2cart"></a><dl>
<dt><a name="index-pol2cart"></a>Function File: <em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>theta</var>, <var>r</var>)</em></dt>
<dt><a name="index-pol2cart-1"></a>Function File: <em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>pol2cart</strong> <em>(<var>theta</var>, <var>r</var>, <var>z</var>)</em></dt>
<dt><a name="index-pol2cart-2"></a>Function File: <em>[<var>x</var>, <var>y</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em></dt>
<dt><a name="index-pol2cart-3"></a>Function File: <em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>pol2cart</strong> <em>(<var>P</var>)</em></dt>
<dt><a name="index-pol2cart-4"></a>Function File: <em><var>C</var> =</em> <strong>pol2cart</strong> <em>(…)</em></dt>
<dd><p>Transform polar or cylindrical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var>theta</var>, <var>r</var>, (and <var>z</var>) must be the same shape, or
scalar. If called with a single matrix argument then each row of <var>P</var>
represents the polar/(cylindrical) coordinate (<var>theta</var>, <var>r</var>
(, <var>z</var>)).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>r</var> is the distance to the z-axis (0, 0, z).
</p>
<p>If only a single return argument is requested then return a matrix <var>C</var>
where each row represents one Cartesian coordinate
(<var>x</var>, <var>y</var> (, <var>z</var>)).
</p>
<p><strong>See also:</strong> <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2sph">cart2sph</a>.
</p></dd></dl>
<a name="XREFcart2sph"></a><dl>
<dt><a name="index-cart2sph"></a>Function File: <em>[<var>theta</var>, <var>phi</var>, <var>r</var>] =</em> <strong>cart2sph</strong> <em>(<var>x</var>, <var>y</var>, <var>z</var>)</em></dt>
<dt><a name="index-cart2sph-1"></a>Function File: <em>[<var>theta</var>, <var>phi</var>, <var>r</var>] =</em> <strong>cart2sph</strong> <em>(<var>C</var>)</em></dt>
<dt><a name="index-cart2sph-2"></a>Function File: <em><var>S</var> =</em> <strong>cart2sph</strong> <em>(…)</em></dt>
<dd><p>Transform Cartesian coordinates to spherical coordinates.
</p>
<p>The inputs <var>x</var>, <var>y</var>, and <var>z</var> must be the same shape, or scalar.
If called with a single matrix argument then each row of <var>C</var> represents
the Cartesian coordinate (<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>phi</var> is the angle relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>S</var>
where each row represents one spherical coordinate
(<var>theta</var>, <var>phi</var>, <var>r</var>).
</p>
<p><strong>See also:</strong> <a href="#XREFsph2cart">sph2cart</a>, <a href="#XREFcart2pol">cart2pol</a>, <a href="#XREFpol2cart">pol2cart</a>.
</p></dd></dl>
<a name="XREFsph2cart"></a><dl>
<dt><a name="index-sph2cart"></a>Function File: <em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>sph2cart</strong> <em>(<var>theta</var>, <var>phi</var>, <var>r</var>)</em></dt>
<dt><a name="index-sph2cart-1"></a>Function File: <em>[<var>x</var>, <var>y</var>, <var>z</var>] =</em> <strong>sph2cart</strong> <em>(<var>S</var>)</em></dt>
<dt><a name="index-sph2cart-2"></a>Function File: <em><var>C</var> =</em> <strong>sph2cart</strong> <em>(…)</em></dt>
<dd><p>Transform spherical coordinates to Cartesian coordinates.
</p>
<p>The inputs <var>theta</var>, <var>phi</var>, and <var>r</var> must be the same shape, or
scalar. If called with a single matrix argument then each row of <var>S</var>
represents the spherical coordinate (<var>theta</var>, <var>phi</var>, <var>r</var>).
</p>
<p><var>theta</var> describes the angle relative to the positive x-axis.
</p>
<p><var>phi</var> is the angle relative to the xy-plane.
</p>
<p><var>r</var> is the distance to the origin (0, 0, 0)<!-- /@w -->.
</p>
<p>If only a single return argument is requested then return a matrix <var>C</var>
where each row represents one Cartesian coordinate
(<var>x</var>, <var>y</var>, <var>z</var>).
</p>
<p><strong>See also:</strong> <a href="#XREFcart2sph">cart2sph</a>, <a href="#XREFpol2cart">pol2cart</a>, <a href="#XREFcart2pol">cart2pol</a>.
</p></dd></dl>
<hr>
<div class="header">
<p>
Next: <a href="Mathematical-Constants.html#Mathematical-Constants" accesskey="n" rel="next">Mathematical Constants</a>, Previous: <a href="Rational-Approximations.html#Rational-Approximations" accesskey="p" rel="prev">Rational Approximations</a>, Up: <a href="Arithmetic.html#Arithmetic" 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#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
