How to Make a Push Pin Art in An Arrangement of Equilateral Triangles

The pictures below show the original image and the final result of the push pin work, it looks cool, doesn’t it? With only a few colors of push pins, my colleagues in Esri(Beijing) R&D Center and I created this push pin work, it’s really interesting!

original and final work

perspective view

This article talks about how to convert an image into a push pin image, and I’ll assume that you are familiar with Adobe Photoshop. OK, let’s get started!

Step 1. Select your image.

Select an image which you want to use for your push pin work, the entire work will be based on this image. Then open this image in Adobe Photoshop, you should be able to see it in the Layers panel.

Layers Panel

Step 2. Resize the image.

The original image which I choose is 5100 * 3000 pixels in size, it’s too large because each pixel represents a push pin, I will adjust the image to a smaller size, for me, 510 * 300 is a good choice. In adobe photoshop, you can select menu Image -> Image Size… to resize an image. But if you insist on using large images, you will need lots of time and a wall which is big enough for all the push pins.

Resize Image

Step 3. Transform the image.

Actually, make a push pin image in a rectangular arrangement is easier than in an equilateral triangular arrangement, but you may notice that if we arrange push pins in equilateral triangles, we could make the push pins arranged more closely and increase space utilization, of course, the effect will also be better. In my view, it is quite a valuable part during the whole making process.

At the moment, the images cannot be transformed yet, we should first unlock the image layer(also called making layer), what you need to do is hold down option(alt) key and double click the image layer in Layers panel. After this, the lock icon should disappear which indicates the image could be transformed. To transform the image, select menu Edit -> Free Transform (shortcut key is Command + T), set the value of H(horizontal skew) to -30 degrees, then press enter to apply the transformation.

transformation skew horizontal -30

Next, the image need another horizontal scale transformation,  select menu Edit -> Free Transform again, set the value of W(horizontal scale) to 86.60254 percents and do not check maintain aspect ratio option, then apply the transformation.

transformation scale width 86.60254

If you are interested in how the number 86.60254 come out, please read this section, if not, just ignore it.
Because all angles in an equilateral triangle are equal to 60 degrees, that's why we skew the image by -30 degrees horizontally, after skewing, the square shape becomes a parallelogram which has two angles equal to 60 degrees and two angles equal to 120 degrees.
change square shapeHere comes the secret, 0.8660254(86.60254 percents) is equal to the value of sine 60 degrees, and you will see number 115.47005 percents(1.1547005) later, it's the inverse of 0.8660254.

Do make sure that you do these two transformations separately, otherwise, you will not be able to recover the distorted image later. The following image shows the effect after the two transformations.

after first two transformations

Step 4. Enlarge canvas size.

After completing the previous step, part of the image is beyond the boundary of the canvas. In order not to affect the follow-up actions, we should enlarge the size of the canvas. Select menu Image -> Canvas Size…, set the value of Width to 125 percents, then press OK.

enlarge canvas

Now you could see the hidden part of the image.

after enlarge canvas

Step 5. Set image to indexed color mode.

Indexed color use limited colors to display an image. Now I have push pins in six different colors, these colors are  red(#FF0000), green(#119911), blue(#0088DD), yellow(#FFEE00)white(#FFFFFF) and black(#000000). I will use these six colors to index my image.

Push Pin

In photoshop, select menu Image -> Mode -> Indexed Color….

Indexed Color

In the opened dialog, set the value of Colors to the count of the colors you have, for me, the value is 6 because I have push pins in six colors. Next, you need to specify these colors, choose Custom… in the Forced drop-down list, then another dialog will open, add all the six colors to the palette, click OK.

Forced Colors

Here is the look of the image in indexed color mode, you can see each pixel has been converted into one of those six colors.

indexed color mode image

Step 6. Enlarge each pixel.

Now each pixel in our image has a corresponding color, but when you want to print this image, you will realize that the space for a push pin marker is too narrow, so it’s better to enlarge all the pixels. Another advantage of this step is that later you can replace each push pin marker with a customized pattern which could helps you find the center points of the push pin markers area much easier. To enlarge pixels, select menu Image -> Image Size…, I set 3200 percents for both width and height in Pixel Dimensions options, this will make each push pin marker area 32 * 32 pixels in size. In Resample Image option, remember to select Nearest Neighbor, this method will keep the number of colors to remain constant.

Enlarge Pixels

Now you could see that each pixel is magnified by 32 times.

Enlarged Pixels 32 Times

Step 7.  Transform the image back.

In step 3, we have transformed the image twice, now we need to recover the distorted image. But images in indexed color mode cannot be transformed, so first we need to change the image back into RGB mode by selecting menu Image -> Mode -> RGB Color, then hold down option(alt) key and double click the image layer in Layers panel to unlock the layer again. To recover image, the image need another two transformations, and these two should also be applied separately. The first is to scale the width of the image, select menu Edit -> Free Transform, set the value of W(horizontal scale) to 115.47005 percents, then apply the transformation.

transformation scale width 115.47005

Next, we will apply another skew transformation, select menu Edit -> Free Transform, set the value of H(horizontal skew) to 30 degrees, then press enter to apply the transformation.

transformation skew horizontal 30

Zoom in the image, you can see the shapes for push pin markers become into parallelograms.

diamond shape push pin area

Actually, now you can print this image and start pushing push pins on the wall. Although the push pin marker areas are already in an equilateral triangular arrangement, but these markers are still not clear enough, especially when marker areas in the same color are connected, and it’s difficult to find centers of these areas. To improve the usability of the push pin image, we could replace these areas with customized patterns, I’ll talk about this in the next few steps.

Step 8. Create patterns.

The purpose of creating patterns is to make the push pin markers more clearly, we could make patterns into circular shapes with obvious central markers. Since each push pin marker area is in 32 * 32 pixels, the patterns should be in the same size. I have push pins in six colors, it means that I will create six different patterns.

I will take the red pattern for example.

  • Creating patterns is as easy as creating images, just select menu File -> New…, set both Width and Height to 32 pixels and give it a name, then click OK.create new pattern
  • After this, use your imagination and photoshop skills to create the red pattern that you would like. This is the red pattern created by me.red pattern
  • The red pattern needs two separate transformations, you could do the same procedure as step 3 to apply these two transformations. First,  select menu Edit -> Free Transform, set the value of H(horizontal skew) to -30 degrees, then press enter to apply the transformation. Next, select menu Edit -> Free Transform again, set the value of W(horizontal scale) to 86.60254 percents and apply the transformation. The red pattern will be distorted like the image below.red distorted pattern
  • After you creating the red pattern, you should save it for later use. To save patterns, select menu Edit -> Define Pattern…, give your pattern a name, then click OK.define pattern

You should repeat this process for every pattern you want to create. These are the six patterns created by me.

before transformation

six patterns

after transformation

six distorted patterns

You can download the pattern psd file from this link: https://www.dropbox.com/s/vemot5gshvie6n7/patterns.psd

You can also download the adobe photoshop pattern format(.pat) file from this link: https://www.dropbox.com/s/3x0tqb6t1g9vdl1/push%20pin%20patterns.pat

Step 9. Create new layers filled up with the new patterns.

I will take the red pattern as an example in this step. Go back to the push pin image psd file, add a new layer in Layers panel, then select menu Edit -> Fill…, in the opened dialog, use Pattern as the fill source and choose the red pattern that you created in step 8, click OK.

fill pattern

The new layer will be filled with the red pattern.

filled with red patern

But for now, the pattern layer is not arranged in equilateral triangles, we need do two more transformations! Gosh, how many transformations have we applied? These two transformations are same as the two in step 7. First transformation is to scale the width of the layer, select menu Edit -> Free Transform, set the value of W(horizontal scale) to 115.47005 percents, then apply the transformation. Second transformation is to skew the layer,  select menu Edit -> Free Transform again, set the value of H(horizontal skew) to 30 degrees and apply the transformation. Now the patterns should be in the arrangement as we expect.

patterns arranged as expected

Maybe the pattern layer is not aligned to the push pin image layer right now, then you just need to move the pattern layer a few pixels in horizontal and vertical directions, make sure that the center of a pattern shape and the center of its related push pin marker are at the same point. The image below shows the result.

align patterns layer

Step 10. Replace push pin markers with patterns.

To replace the red push pin marker areas, we should find those red marker areas first. Select Magic Wand tool, set Tolerance to 50 and do not check Contiguous option.

magic wand tool

Then select push pin layer in Layers panel, click mouse on any red push pin marker area, it will generate a selection which contains all the red push pin marker areas for you. After this, select red pattern layer in Layers pattern, click Add layer mask button at the bottom of the panel.

add layer mask

You can find that all the red pattern shapes have disappear expect those which are within the red push pin marker areas.

red patterns within red push pin marker areas

Step 11. Process the rest patterns.

Repeat step 9 and step 10 for the rest color patterns. Once all the pattern layers have been done, the result would be like the following image.

six patterns layers

Almost done, but there is still a little problem: there are useless space on left and right sides because we have enlarged canvas size in step 4, we need to make sure that the canvas is the same size as the push pin image. Select menu Image -> Canvas Size…, set the value of Width to 80 percents, then press OK.

reduce canvas size

After reducing the size of the canvas, we get the final effect at last.

final effect

Step 12. Push the push pins!

Congratulations! Now you have the push pin image, print it out and put it on a wall, and start pushing! Be sure to get enough rest. Here is the final work done by my colleagues in the office.

final work

Hope you enjoy this!

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20 thoughts on “How to Make a Push Pin Art in An Arrangement of Equilateral Triangles

  1. LD

    Hi,
    Thanks for the directions. They are awesome! I got to step 8 and then I am lost. Could you explain how you created those 6 patters? Thanks again.

    Reply
  2. Jeffri

    Hey
    I want to know why did u choose the pattern size of 32 pixels?
    and why did u enlarge the image size 3200 percent “i know the purpose of it but i need to know why did u choose this exact number?”

    PS
    i have a pushpins with 9mm diameter so if u can help me to choose the right values

    THANKS A BUNCH FOR THIS GREAT TUTORIAL !!!

    Reply
    1. Jeffri

      and could you please include a download link for your patterns “psd file”
      you can upload them using dropbox and post the share link here

      Reply
    2. CCPalettes Post author

      1. 32 is a multiple of 2, it’s convenient to create symmetric figures for customized patterns.
      2. If the number is too large, 64 for example, the psd file will cost too much memory.
      3. If the number is too small, 8 for example, customized patterns will not be clear, it’s not suitable for recognition and printing.
      4. So I choose 32, it’s a power of 2. I think there are a lot of numbers you can use, like 24, 28, 36, etc.

      About choosing the right values, suppose that you want to print image on a page which is 1000 * 1000 square millimeters in size. Before printing the image, you could set ‘scale the print media to fit print size’, the page will fill with the image and the patterns will also be scaled automatically. So you can choose any number you like, the printer will help you do the rest work.

      Reply
  3. LD

    Hi CC Palettes, no matter what I try to do I can get the damn picture to work with the patterns after step 8. No idea what I am doing wrong. Would it be possible to do a screen video (where the screen activity is recorded) and post on youtube. Sorry for the trouble, it’s a huge frustrating learning curve. You are awesome!!

    Reply
      1. Gabriella

        I got an activation email. Can I send you and image to convert for me. I can send you a payment through paypal.

  4. Ali Almutawaa

    Hi,
    I am struggling to buy the pins, the above mentioned chines site is only in Chinese language and can’t use it. is there any site that can provide me with the 5 colors I am looking for. I have contacted so many sites in the far east and India to buy them, but no joy.

    Ali

    Reply

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