Rev 02 (author © Richard Ashbery)
In order to create such masterpieces as seen in architecture like 'The Mezquita Cathedral in Cordoba, Southern Spain' (figure 1) the pattern designers had to possess a good knowledge of geometry. The designs contain endless repetition of patterns based on a geometric grid. Templates had to be hand drawn by draughtsmen making it a laborious and labour intensive process. With a good computer drawing package it is not difficult to create some effective designs of your own.
Fig 1 One of the doorways in the Mezquita Cathedral in Cordoba, Spain
Only hexagon based designs are covered in this introductory tutorial. Once the basic principals have been understood designs using other polygons can be undertaken.
Look closely at the grid in figure 2. It consists of equilateral triangles. Six of these form a hexagon.
Fig 2 Isometric grid showing a hexagon
Please note: for clarity grids are shown having vertical or angled dotted lines. In practice drawing software displays these as dots.
Enables a user to position a shape exactly aligning with the grid. Ensure this is switched on before attempting examples.
A method of copying a shape in exactly the same position as the original.
An important facility to aggregate shapes so that they can be dragged en-masse.
Enables user to draw any regular polygon.
Term used by the author to describe a complete page of shapes (containing hexagons, diamonds, triangles etc.).
The result is a simple hexagon tessellation where all shapes are joined together without gaps. Interestingly only one side of a hexagon is shared by its neighbour.
Before continuing delete rows of hexagons 3, 4, 5, and 6. Drag the second row of hexagons to position shown in diagram below on the left in figure 4. Simply moving position of second hexagon group now reveals a diamond. Use a line tool to trace around the diamond allowing it to be coloured. The four corner points will automatically lock to the grid making the process quite easy. Hint - the path must be closed in order to fill the shape with colour. Clone diamond and drag to the right as shown. Repeat.
Move the hexagons to give the pattern shown in figure 4 (diagram on the right) - equilateral triangles will be revealed.
Fig 4 Revealing diamonds (left) and equilateral triangles (right)
How would you arrange the hexagons to form a star shape?
If hexagons are overlapped some new patterns can be constructed. We can divide any side of a hexagon (since all are identical in length) into numerical sections. The diagram on the left (figure 5) shows one of its sides divided into three equal parts. For simplicity lets divide the side by 1/2 and look at what happens when two hexagons overlap by this amount - a diamond is clearly visible.
Fig 5 Division of a side of a hexagon
By adding a third hexagon two further diamonds will be created (figure 6). Clone and drag the group of three diamonds to new positions shown in the diagram and repeat a number of times until you create a pattern matrix. Another shape is revealed - a star.
The left hand picture in figure 16 under the heading, Examples shows how a finished design will look.
Fig 6 1/2 side of hexagon overlap
Four diamonds and an equilateral triangle are created when three hexagons overlap by 1/3 of a side (figure 7).
Fig 7 Hexagons overlapped (1/3 of a side)
Duplicate the hexagons (becomes the new grid) and fill the diamonds and equilateral triangles as shown below (left diagram). By removing the grid and hexagons a clear and regular pattern is revealed (figure 8 - right diagram).
Alternatively by filling the shape inside the hexagon appears to create another pattern. The 3 diamonds and equilateral triangle arrangement can still be clearly seen (figure 9).
Figure 10 shows a 2/3 overlap. The obvious shapes are the 6 diamonds and a star.
Fig 10 Overlap - 2/3 of a side
Start to build a pattern by following the instructions in figure 11. Repeat until a row is formed. Group the row, clone them and drag to form another row below. Hint: it is important to ensure that the top diamonds in the second row precisely overlap the bottom diamonds in the first row to achieve the required pattern.
Repeat until a complete pattern matrix is constructed as shown in figure 12. Can you see another shape?
Fig 11 Start to build a pattern
Fig 13 shows another way of linking the six diamonds to the original group of six.
If the diamond group above is formed into a pattern matrix (illustrated in figure 14) then hexagons and new shape can be visualised (highlighted by the red dotted lines).
As already mentioned this tutorial only covers the hexagon. Armed with this knowledge you will discover many other polygon designs. Examples shown in figure 15 are drawings that feature hexagons having no overlap and therefore easier to draw.
The drawing - bottom right contains a knot pattern requiring a unique 'cutting tool' to perform the interlacing effect. In ArtWorks2 it is called 'ClipView' and uses a path to clip a view of another path. Quality drawing software packages all contain a method for doing this.
Fig 15 Hexagon examples - without overlap
Figure 16 illustrates two slightly more advanced designs using overlapping hexagons. Look at the drawing on the right - can you see the shape that makes this design work so effectively?
Fig 16 Hexagon examples - with overlap
RISC OS Computer Systems:
Windows PC Computer Systems:
To get the most out of these complex software packages expect a steep learning curve. I'm recommending Xara Photo and Graphic Designer because it can be considered as a 'two-in-one' package - it has numerous drawing effects but also has significant photo manipulation facilities.
Some of the very best with excellent step-by-step instructions: http://www.xaraxone.com/html/tutorials.html. All tutorials are created using Xara Photo and Graphic Designer.
Tutsplus have some good tutorials mainly created with Adobe Illustrator but there is a fee to pay for the best: http://design.tutsplus.com
The graphic designer, David Wade specialises in geometric art. He has published a lot of books, some containing excellent construction techniques. The little pocket book series is worth investigating... http://www.woodenbooks.com
Each month I update my website to show some of the designs that are possible: