|
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> |
|
|
<html> |
|
|
<head> |
|
|
|
|
|
|
|
|
<meta name="Description" content="KLayout layout viewer and editor project page" /> |
|
|
<meta name="Keywords" content="KLayout OASIS GDS2 viewer editor layout semiconductor mask chip design" /> |
|
|
<meta name="abstract" content="KLayout is a free layout viewer and editor for several formats commonly used in the semiconductor industry to transfer layout data" /> |
|
|
<meta name="URL" content="https://www.klayout.de/" /> |
|
|
<meta name="Author" content="Matthias Koefferlein" /> |
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/> |
|
|
<meta http-equiv="Content-Script-Type" content="text/javascript" /> |
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> |
|
|
|
|
|
<title>KLayout Layout Viewer And Editor</title> |
|
|
|
|
|
|
|
|
<link rel="alternate" type="application/rss+xml" title="RSS" href="http://www.klayout.de/news.xml"/> |
|
|
<link rel="stylesheet" type="text/css" href="https://www.klayout.de/format.css?v2.0"/> |
|
|
<link rel="shortcut icon" href="https://www.klayout.de/favicon.ico"/> |
|
|
|
|
|
|
|
|
<link rel="stylesheet" type="text/css" href="https://www.klayout.de/fonts.css"/> |
|
|
|
|
|
|
|
|
<script src="https://www.klayout.de/jquery-3.4.1.min.js"></script> |
|
|
|
|
|
|
|
|
<link href="https://www.klayout.de/bootstrap-4.3.1-dist/css/bootstrap.min.css" rel="stylesheet"> |
|
|
<script src="https://www.klayout.de/bootstrap-4.3.1-dist/js/bootstrap.min.js"></script> |
|
|
|
|
|
|
|
|
|
|
|
</head> |
|
|
|
|
|
<body> |
|
|
|
|
|
<div class="klayout-header"> |
|
|
|
|
|
<div class="container mb-5"> |
|
|
|
|
|
<nav class="navbar navbar-dark navbar-expand-lg"> |
|
|
|
|
|
<a class="navbar-brand" href="https://www.klayout.de"><img src="https://www.klayout.de/klayout.png" srcset="https://www.klayout.de/klayout-x2.png 2x" alt="KLayout"></a> |
|
|
|
|
|
<div class="collapse navbar-collapse" id="navbarToggleExternalContent"> |
|
|
|
|
|
<ul class="navbar-nav ml-auto mr-auto"> |
|
|
|
|
|
<li class="nav-item dropdown active mr-4"> |
|
|
<a class="nav-link dropdown-toggle klayout-menu" href="#" id="navbarDropdown" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> |
|
|
About |
|
|
</a> |
|
|
<div class="dropdown-menu" aria-labelledby="navbarDropdown"> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/intro.html">KLayout Project</a> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/doc.html">Documentation</a> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/galleries.html">Galleries</a> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/credits.html">Credits</a> |
|
|
<div class="dropdown-divider"></div> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/contact.html">Contact</a> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/impressum.html">Impressum / Imprint</a> |
|
|
<a class="dropdown-item" href="https://www.klayout.de/privacy_policy.html">Datenschutz / Privacy Policy</a> |
|
|
</div> |
|
|
</li> |
|
|
<li class="nav-item active mr-4"> |
|
|
<a class="nav-link klayout-menu" href="https://www.klayout.de/build.html">Get KLayout</a> |
|
|
</li> |
|
|
<li class="nav-item active mr-4"> |
|
|
<a class="nav-link klayout-menu" href="https://sami.klayout.org">Package Index</a> |
|
|
</li> |
|
|
<li class="nav-item active mr-5"> |
|
|
<a class="nav-link klayout-menu" href="https://www.klayout.de/forum">Forum</a> |
|
|
</li> |
|
|
<li class="nav-item active"> |
|
|
<span class="nav-link klayout-menu"> |
|
|
<a href="https://f-si.org"><img src="https://www.klayout.de/f-si_logo_32h_w.png" border="0" title="Free Silicon Foundation" alt="F-Si"/></a> |
|
|
<a class="ml-4" href="https://github.com/KLayout"><img src="https://www.klayout.de/GitHub-Mark-32px-white.png" border="0" title="KLayout on GitHub" alt="GitHub"/></a> |
|
|
</span> |
|
|
</li> |
|
|
|
|
|
</ul> |
|
|
|
|
|
</div> |
|
|
|
|
|
|
|
|
<button class="navbar-toggler" type="button" data-toggle="collapse" data-target="#navbarToggleExternalContent" aria-controls="navbarToggleExternalContent" aria-expanded="false" aria-label="Toggle navigation"> |
|
|
<span class="navbar-toggler-icon"></span> |
|
|
</button> |
|
|
|
|
|
</nav> |
|
|
|
|
|
</div> |
|
|
|
|
|
</div> |
|
|
|
|
|
<div class="container"> |
|
|
|
|
|
<h1>Transformations in KLayout</h1> |
|
|
|
|
|
<p> |
|
|
KLayout supports a subset of affine transformations with the following contributions: |
|
|
</p> |
|
|
|
|
|
<ul> |
|
|
<li><b>Rotation and/or mirroring:</b> rotation by a given angle or mirroring at a given axis.</li> |
|
|
<li><b>Scaling:</b> magnification by the given factor.</li> |
|
|
<li><b>Translation:</b> a displacement by the given vector.</li> |
|
|
</ul> |
|
|
|
|
|
<p> |
|
|
The execution order is "displacement after rotation, mirroring and scaling". |
|
|
Transformations are used for example to describe the instantiation of a cell. The content of |
|
|
a cell appears in the parent cell after the given transformation has been applied to the |
|
|
content of the cell. |
|
|
</p> |
|
|
|
|
|
<p> |
|
|
The transformations supported by KLayout cover the transformations employed within GDS2, OASIS and |
|
|
other layout formats. KLayout does not support shearing currently. |
|
|
</p> |
|
|
|
|
|
<p> |
|
|
The following figure illustrates the effect of the transformation "r90 *2 7,9". This notation |
|
|
specifies a transformation composed of a rotation by 90 degree, a scaling with factor 2 and |
|
|
a displacement by 7 units in x- and 9 units in y-direction. In that example, the "F" shape is |
|
|
first rotated by 90 degree around the origin. Because the "F" is already displaced from the origin, |
|
|
this will also move the "F" shape. The shape then is scaled. Again it will move because |
|
|
every point of the polygon moves away from the origin. Finally it is displaced by the |
|
|
given displacement vector. |
|
|
</p> |
|
|
|
|
|
<img src="images/transformation_overview.svg"/> |
|
|
|
|
|
<p> |
|
|
The notation shown here is used in many places within KLayout. It is basically composed of the following parts |
|
|
which are combined putting one or more blanks in between. The order the parts are specified |
|
|
is arbitrary: the displacement is always applied after the rotation. |
|
|
</p> |
|
|
|
|
|
<ul> |
|
|
<li><x><b>,</b><y>: A displacement (applied after rotation and scaling) in micron units. If no displacement is specified, "0,0" is assumed.</li> |
|
|
<li><b>r</b><a> or <b>m</b><a>: A rotation by angle "a" (in degrees) or mirroring at the "a" axis (the x axis rotated by "a" degree). If no rotation or mirroring is specified, no rotation is assumed.</li> |
|
|
<li><b>*</b><s>: A scaling by the factor "s". If no scaling is specified, no scaling is assumed.</li> |
|
|
</ul> |
|
|
|
|
|
<p> |
|
|
Here are some examples: |
|
|
</p> |
|
|
|
|
|
<ul> |
|
|
<li><b>0,100</b>: shift 100 units up.</li> |
|
|
<li><b>r90</b>: rotation by 90 degree counterclockwise (positive in the mathematical sense).</li> |
|
|
<li><b>m0</b>: mirroring at the x-axis.</li> |
|
|
<li><b>m45 100,-200</b>: swap x and y (mirror at 45 degree axis), shift 100 units to the right and 200 units down.</li> |
|
|
<li><b>r22.5 *1.25</b>: rotate by 22.5 degree and scale by factor 1.25.</li> |
|
|
</ul> |
|
|
|
|
|
<p> |
|
|
The distance units are usually micron. In some cases (i.e. transformations inside a database), |
|
|
the unit is database units and dx and dy are integer values. |
|
|
</p> |
|
|
|
|
|
<p> |
|
|
Mirroring and rotation are exclusive and mirroring includes a rotation. In fact, a mirror operation at a certain axis is |
|
|
identical to a mirror operation at the x-axis, followed by a rotation by twice the angle "a". |
|
|
The following figure illustrates rotation and mirroring with the eight basic transformations involving rotations by |
|
|
multiples of 90 degree: |
|
|
</p> |
|
|
|
|
|
<img src="images/transformation_basic.svg"/> |
|
|
|
|
|
<p> |
|
|
KLayout is not restricted to these basic operations. Arbitrary angles are supported (i.e. "r45" or "m22.5"). Usually however, |
|
|
this implies grid snapping and other issues. This also is true for arbitrary scaling values. KLayout is also more effective when using |
|
|
simple transformations involving only rotations by multiples of 90 degree and do not use scaling. |
|
|
</p> |
|
|
|
|
|
|
|
|
|
|
|
</div> |
|
|
</body> |
|
|
</html> |
|
|
|
|
|
|
