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
|
---
title: <transform-function>
slug: Web/CSS/transform-function
tags:
- CSS
- CSS Data Type
- CSS Transforms
- Layout
- NeedsTranslation
- Reference
- TopicStub
translation_of: Web/CSS/transform-function
---
<div>{{CSSRef}}</div>
<p>The <strong><code><transform-function></code></strong> <a href="/en-US/docs/Web/CSS">CSS</a> <a href="/en-US/docs/Web/CSS/CSS_Types">data type</a> represents a transformation that affects an element's appearance. Transformation functions can rotate, resize, distort, or move an element in 2D or 3D space. It is used in the {{cssxref("transform")}} property.</p>
<h2 id="Describing_transformations_mathematically">Describing transformations mathematically</h2>
<p>Various coordinate models can be used to describe an HTML element's size and shape, as well as any transformations applied to it. The most common is the <a href="https://en.wikipedia.org/wiki/Cartesian_coordinate_system">Cartesian coordinate system</a>, although <a href="https://en.wikipedia.org/wiki/Homogeneous_coordinates">homogeneous coordinates</a> are also sometimes used.</p>
<h3 id="Cartesian_coordinates"><a href="/@api/deki/files/5796/=coord_in_R2.png"><img src="/files/3438/coord_in_R2.png" style="float: right; width: 171px;"></a>Cartesian coordinates</h3>
<p>In the Cartesian coordinate system, a two-dimensional point is described using two values: an x coordinate (abscissa) and a y coordinate (ordinate). This is represented by the vector notation <code>(x, y)</code>.</p>
<p>In CSS (and most computer graphics), the origin <code>(0, 0)</code> represents the<em> top-left</em> corner of any element. Positive coordinates are down and to the right of the origin, while negative ones are up and to the left. Thus, a point that's 2 units to the right and 5 units down would be <code>(2, 5)</code>, while a point 3 units to the left and 12 units up would be <code>(-3, -12)</code>.</p>
<h3 id="Transformation_functions">Transformation functions</h3>
<p>Transformation functions alter the appearance of an element by manipulating the values of its coordinates. A linear transformation function is described using a 2x2 matrix, like this:</p>
<div style="text-align: center;">
<p><math> <mfenced> <mtable> <mtr><mtd>a</mtd><mtd>c</mtd></mtr> <mtr><mtd>b</mtd><mtd>d</mtd></mtr> </mtable> </mfenced> </math></p>
</div>
<p>The function is applied to an element by using matrix multiplication. Thus, each coordinate changes based on the values in the matrix:</p>
<div style="text-align: center;"><a href="/@api/deki/files/5799/=transform_functions_generic_transformation_cart.png"><img src="/@api/deki/files/5799/=transform_functions_generic_transformation_cart.png?size=webview" style="height: 32px; width: 189px;"></a></div>
<p><br>
It is even possible to apply several transformations in a row:</p>
<div style="text-align: center;"><a href="/@api/deki/files/5800/=transform_functions_transform_composition_cart.png"><img src="/@api/deki/files/5800/=transform_functions_transform_composition_cart.png?size=webview" style="height: 32px; width: 313px;"></a></div>
<p><br>
With this notation, it is possible to describe, and therefore compose, most common transformations: rotations, scaling, or skewing. (In fact, all transformations that are linear functions can be described.) Composite transformations are effectively applied in order from right to left.</p>
<p>However, one major transformation is not linear, and therefore must be special-cased when using this notation: translation. The translation vector <code>(tx, ty)</code> must be expressed separately, as two additional parameters.</p>
<div class="note">
<p><strong>Note:</strong> Though trickier than Cartesian coordinates, <a class="external" href="https://en.wikipedia.org/wiki/Homogeneous_coordinates">homogeneous coordinates</a> in <a class="external" href="https://en.wikipedia.org/wiki/Projective_geometry">projective geometry</a> lead to 3x3 transformation matrices, and can simply express translations as linear functions.</p>
</div>
<h2 id="Syntax">Syntax</h2>
<p>The <code><transform-function></code> data type is specified using one of the transformation functions listed below. Each function applies a geometric operation in either 2D or 3D.</p>
<h3 id="Matrix_transformation">Matrix transformation</h3>
<dl>
<dt>{{cssxref("transform-function/matrix","matrix()")}}</dt>
<dd>Describes a homogeneous 2D transformation matrix.</dd>
<dt>{{cssxref("transform-function/matrix3d","matrix3d()")}}</dt>
<dd>Describes a 3D transformation as a 4x4 homogeneous matrix.</dd>
</dl>
<h3 id="Perspective">Perspective</h3>
<dl>
<dt>{{cssxref("transform-function/perspective","perspective()")}}</dt>
<dd>Sets the distance between the user and the z=0 plane.</dd>
</dl>
<h3 id="Rotation">Rotation</h3>
<dl>
<dt>{{cssxref("transform-function/rotate","rotate()")}}</dt>
<dd>Rotates an element around a fixed point on the 2D plane.</dd>
<dt>{{cssxref("transform-function/rotate3d","rotate3d()")}}</dt>
<dd>Rotates an element around a fixed axis in 3D space.</dd>
<dt>{{cssxref("transform-function/rotateX","rotateX()")}}</dt>
<dd>Rotates an element around the horizontal axis.</dd>
<dt>{{cssxref("transform-function/rotateY","rotateY()")}}</dt>
<dd>Rotates an element around the vertical axis.</dd>
<dt>{{cssxref("transform-function/rotateZ","rotateZ()")}}</dt>
<dd>Rotates an element around the z-axis.</dd>
</dl>
<h3 id="Scaling_(resizing)">Scaling (resizing)</h3>
<dl>
<dt>{{cssxref("transform-function/scale","scale()")}}</dt>
<dd>Scales an element up or down on the 2D plane.</dd>
<dt>{{cssxref("transform-function/scale3d","scale3d()")}}</dt>
<dd>Scales an element up or down in 3D space.</dd>
<dt>{{cssxref("transform-function/scaleX","scaleX()")}}</dt>
<dd>Scales an element up or down horizontally.</dd>
<dt>{{cssxref("transform-function/scaleY","scaleY()")}}</dt>
<dd>Scales an element up or down vertically.</dd>
<dt>{{cssxref("transform-function/scaleZ","scaleZ()")}}</dt>
<dd>Scales an element up or down along the z-axis.</dd>
</dl>
<h3 id="Skewing_(distortion)">Skewing (distortion)</h3>
<dl>
<dt>{{cssxref("transform-function/skew","skew()")}}</dt>
<dd>Skews an element on the 2D plane.</dd>
<dt>{{cssxref("transform-function/skewX","skewX()")}}</dt>
<dd>Skews an element in the horizontal direction.</dd>
<dt>{{cssxref("transform-function/skewY","skewY()")}}</dt>
<dd>Skews an element in the vertical direction.</dd>
</dl>
<h3 id="Translation_(moving)">Translation (moving)</h3>
<dl>
<dt>{{cssxref("transform-function/translate","translate()")}}</dt>
<dd>Translates an element on the 2D plane.</dd>
<dt>{{cssxref("transform-function/translate3d","translate3d()")}}</dt>
<dd>Translates an element in 3D space.</dd>
<dt>{{cssxref("transform-function/translateX","translateX()")}}</dt>
<dd>Translates an element horizontally.</dd>
<dt>{{cssxref("transform-function/translateY","translateY()")}}</dt>
<dd>Translates an element vertically.</dd>
<dt>{{cssxref("transform-function/translateZ","translateZ()")}}</dt>
<dd>Translates an element along the z-axis.</dd>
</dl>
<h2 id="Specifications">Specifications</h2>
<table class="standard-table">
<thead>
<tr>
<th scope="col">Specification</th>
<th scope="col">Status</th>
<th scope="col">Comment</th>
</tr>
</thead>
<tbody>
<tr>
<td>{{SpecName('CSS3 Transforms', '#transform-property', 'transform')}}</td>
<td>{{Spec2('CSS3 Transforms')}}</td>
<td>Initial definition.</td>
</tr>
</tbody>
</table>
<h2 id="Browser_compatibility">Browser compatibility</h2>
<p> </p>
<p>{{Compat("css.types.transform-function")}}</p>
<p> </p>
<h2 id="See_also">See also</h2>
<ul>
<li>CSS {{cssxref("transform")}} property</li>
</ul>
|
