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Monday, December 14, 2015

11a) Drawing "Automatic" Pattern Repeats (Part 1)

It's been a while since I've written a tutorial about Inkscape, and I think it's time to talk about my favorite trick with the software. This is a method I use to automatically place pattern repeats in a diagram. It can be used for any diagram that has symmetry: from a butterfly all the way up to a doily. Even if you already know how to use Inkscape, I encourage you to read on to see if this is something that would be useful to you.

Here is an example of a finished diagram (the Frauberger Doily) using this method. All rings, chains, and picots have been duplicated and rotated around a central axis. Only the first pattern repeat is placed by hand. All others are generated by the computer:


It's a little difficult to explain the entire process in one post, so I am breaking this tutorial into two posts. For the first post, I will talk about how to move the center of rotation and how to calculate the degree of rotation.



Before you begin, you will need to know how to draw rings, chains, and picots. You should also be familiar with duplicating objects (CTRL+D) and with rotating objects using the Inkscape menu (Object > Transform > Rotate). If you need to brush up on any of these topics, you can to go my Tutorials tab and read through some of the Inkscape posts listed there.

Let's start by drawing a ring. I've copy/pasted this one from my Free Diagramming Template:


Click on the ring a second time, and notice how the arrows on the edges change. Crosshairs will also appear in the middle of the ring. These crosshairs represent the ring's center of rotation, and will be our focal point for much of the tutorial.


With your mouse, click and drag the crosshairs to a new location. This will change the ring's center of rotation to a point of your choosing. I've placed my crosshairs below the ring so that I can make a six ring flower. Each new ring that I make through duplication (CTRL+D) will rotate around this new central point:


The next step is to duplicate the ring by pressing CTRL+D on your keyboard. After you have duplicated the ring, open up the rotation menu by going to Object > Transform at the top of the screen:


Now click on the Rotation tab, and enter the angle at which you would like to rotate. For a 6 ring flower, I have entered 60 degrees. 


Click apply and the rotated ring will fall into place:


Keep pressing CTRL+D on your keyboard and "Apply" on the rotation menu to fill in the rest of the diagram. Here is my 6 ring flower:


If you want to learn more about the math that I used to calculate the 60 degree rotation, read the following two paragraphs. If you already know how to do this, skip ahead to the next section about working with grouped objects.

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To calculate the degree of rotation we need to use some basic geometry. This math applies to tatting designs that rotate around a central axis, such as squares, snowflakes, and doilies. (For butterflies and hearts, we will use something different called a horizontal flip).

A circle is made up of 360 degrees. To calculate the degree of rotation for different shapes in tatting, we need to divide 360 by the number of sides in our shape. A square, for example, will have 90 degrees of rotation for each side (360 divided by 4 sides). A snowflake will have 60 degrees of rotation for each side (360 divided by 6 sides). The last round of the Frauberger Doily has 16 sides, so each pattern repeat had to be rotated by 22.5 degrees (360 divided by 16). It's often helpful to have a calculator handy!

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Working with Grouped Objects

In addition to rotating single objects, we can also change the center of rotation for objects in a group. For the next example, I'm going to use a Trefoil, which is three rings grouped together into one element. This trefoil has also been copy/pasted from my Free Diagramming Template:


If you are working with something that you have drawn on your own, make sure to highlight the part of the drawing that you want to group and press CTRL+G on your keyboard. (To read more about Grouping click here). 

After the object has been grouped, click on it again to bring up the rotation arrows and crosshairs. Just like the first example, the rotation center (crosshairs) can be moved anywhere on the screen:


For this example I'm going to duplicate the trefoil and rotate it by 90 degrees. I don't have to use the rotation menu because there is a hotkey at the top of the screen to do this:


This is what it looks like after duplicating and rotating a few times:


You can see the start of a simple diagram. We could add chains in between the trefoils to make a cohesive pattern, but this would be very hard to do without guides. Guides help us to match up the rotation centers of each new piece of the drawing, and I will be talking about how to use them in the next post.


Flipping Horizontally and Vertically

If you have a pattern that is symmetrical down the center, you can use a horizontal or vertical flip to place a pattern repeat. This can be used for hearts, butterflies, earrings, and bookmarks. There are also instances in doilies, snowflakes, and other patterns where horizontal or vertical flips come in handy for placing picots and rings. 

The horizontal and vertical flip hotkeys can be found at the top of the screen, next to the 90 degree rotation hotkeys:


As with the previous examples, I have relocated the center of rotation to another point on the screen. This time I'm working with a diagonally facing trefoil:


 Duplicating the trefoil and making a horizontal flip will look like this:


A vertical flip will look like this:


Horizontal and vertical flips are a newer feature in Inkscape, and I found a small glitch when working with them. You must make sure that the object is in rotation mode (i.e. crosshairs will be visible as well as rotation arrows) before making the flip. If the resize arrows are present, the object will always flip on its central axis (and not on the new rotation point set by you).

That is all for this post. In tomorrow's post I will talk about how to use guides so that the exact center of rotation can be pinpointed and matched among various elements in the diagram.

9 comments:

  1. I draw my diagrams in Paint. :(
    I have to learn Inkscape!

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    Replies
    1. Yes, although it is simpler to use, Paint has a lot of limitations when compared to Inkscape. Inkscape can be frustrating to learn, but gets much easier with practice!

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  2. complimenti informatica anche io uso inskape ed ho insegnato matematica, fisica ed informata grazie ciao

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  3. Thank you for these great explanations, and all your hard work at making designing easier for everyone!

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  4. This process looks so time consuming and difficult! I think I'll continue to let you do the designing, and I will purchase and tat your patterns... much easier!

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  5. Ah great !!! So the key is to have that crosshair. Fairly simple thereafter... I missed the rotation part of your tutorials & have struggled to maintain the shape when angled. Thanks again for this wonderful explanation :-)

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  6. Amazing what can be done on a computer,
    Margaret

    ReplyDelete