Tiling in InkScape
The tiles are in reality just clones of the source tile or object. Thus the same methods that apply to clones apply to tiles. (See the section called Clones in Chapter 4, Editing Basics.)
While random use of the Tile Clones dialog can produce exquisite patterns, it is useful to understand the fundamentals of tessellation in order to have more control over the final design.
To construct a tiling, open up the Create Tiled Clones dialog (Edit → Clone → Create Tiled Clones... ).
At the bottom of the dialog is a fixed section where you can choose the size of the tiling either by the number of rows and columns or by the width and height of the area you wish to cover. The terms Rows and Columns are only really appropriate for tiling of rectangular tiles (see below). Checking the “Used saved size and position of the tile” forces the tiling to use the size and position of the base tile at the last time the tile was used in a tiling. This preserves the spacing between tiles if the bounding box has changed due to editing the base tile. Clicking on the Reset button resets most of the entries under the tabs to their default values. The Remove button can be used to undo a tiling when the base tile is selected. The Unclump button can be used to spread out the clones in a somewhat random fashion (can be repeated). And, finally, the Create button creates the tiling.
With a circle and the default values (P1 symmetry, two rows and two columns), you will get the following tiling:
The circle has been replicated four times in two rows and two columns. The original circle is still there, under the top-left cloned circle. The bounding box of the circle has been used as the base tile size.
This example is not so interesting, but there are many options under the dialog’s tabs that can produce many interesting effects. Each tab will be covered in turn in the following sections.
The Symmetry tab is at the heart of the tiling process. Understanding the different symmetries is necessary to have full control over the outcome of a tiling. The symmetry of the tiling is selected from the pull-down menu under the Symmetry tab (see previous figure).
There are three regular geometric shapes that can be replicated to cover a surface completely (without gaps or overlaps). These shapes are: triangles, rectangles (parallelograms), and hexagons. A complete set of tiling symmetries requires taking these shapes and adding rotations and reflections. It is known that there are 17 such tiling symmetries. (See: Wikipedia entry [http://en.wikipedia.org/wiki/Wallpaper_group].) All 17 symmetries are included in the Inkscape Create Tiled Clones dialog. The symmetries are shown next.
Tilings based on a rectangle tile (or 45-45-90 degree triangle). The outlined dark blue tile is the basic unit. Red and yellow dots show the reflection and rotation symmetries. Points of twofold and fourfold rotational symmetry are shown by pink diamonds and green squares, respectively. The P1 and P2 symmetries also work with parallelograms.
Tiling based on regular subdivisions of a hexagonal. The outlined dark blue tile is the basic unit. All tilings have points of threefold rotational symmetry (orange triangles). Two also have twofold and sixfold rotational symmetries (pink diamonds and purple hexagons). The pairs of numbers indicate the row and column numbers.
The basic tile for each of the 17 symmetries is shown in dark blue in the preceding figures. Inkscape uses the bounding box of an object to determine the basic tile size. For rectangular base tiles, the bounding box corresponds to the base tile. However, for triangular base tiles, the base tile covers only part of the bounding box area. This can result in tiles “overlapping” if an object extends outside the base tile shape (but is still within the bounding box) as in the tiling in the introduction to this chapter. Overlapping can also occur if the base tile is altered after the tiles are positioned.
On the left is a triangle and circle that are grouped together. The triangle corresponds to the base tile for a P6M symmetry. Note that the red circle is outside the base triangle but is still within the bounding box of the group (and triangle). On the right is a P6M tiling with the triangle and circle. Note how the red circle ends up above some but below other triangles as determined by the order in which the tiling is made.
Inkscape always uses the Geometric bounding box to determine the tile size. This avoids problems when creating a triangular tile with a Stroke where the Visual bounding box doesn’t have the same width to height ratio as the Geometric bounding box.
If you need to adjust the base tile size after having created a tiling, you can use the XML Editor dialog to change the parameters “inkscape:tile-h” and “inkscape:tile-w” (these will appear after you have cloned the object and are used only if the Use saved size and position of the tile button is checked).