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Using the Polar Coordinates Effect:
"Digital Ikebana"
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Using the Polar Coordinates Effect:
"Digital Ikebana"
Created by: Brian


Converting rectangular (or x and y) coordinates to polar (distance and angle) coordinates can produce some interesting images. We will explore some of the possibilities using sample images and also the variations produced by positioning an image on a larger canvas. It is always a challenge to try and anticipate the general result of an effect rather than just accept what "rolling the dice" gives you.

We will use the effect to produce some digital images.

Download File Download File
Here you can download the images I used but use any you like.

Open Image

Reset to Default

Open any image, e.g. "/tutorial/html/tut8eff/santa.jpg", and go to Effects || Distortion Effects || Polar Coordinates. Click on the Reset-to-Default button; the settings should now be as follows:
– Rectangular to polar = selected
– Edge mode = Color

These values will be used all the time for this tutorial. The Edge Mode decides what fills in spare areas around the distorted image. Note that the Transparent Edge Mode is only available if you are not working on a background layer.

We will now use the Polar Coordinates effect on a few images to see the resuts and then develop some guidelines for using it.

As an example, starting with an image of Santa Claus (/tutorial/html/tut8eff/santa.jpg), which has a lot of white space around the subject, and using the above (default) settings in Effects || Distortion Effects || Polar Coordinates you produce the middle image on the left. The spare space is filled with black in this case.

Try repeating the effect – press Ctrl+Y – and you get the bottom image on the left.

Try repeating the action a few more times.

The results might look attractive but I find them very unpredictable and not useful.


Using a scene with most detail at the sides gives an abrupt join at the top centre.

Open "/tutorial/html/tut8eff/scene.jpg" and go to Effects || Distortion Effects || Polar Coordinates with the default settings we used above to get the bottom image on the left.

Again, try repeating the effect – press Ctrl+Y – and repeat the action a few more times.


This scene has more detail in the centre but still gives a definite join at the top.

Open "/tutorial/html/tut8eff/trees.jpg" and go to Effects || Distortion Effects || Polar Coordinates again with the default settings; repeat the action again to see the results.


Applying the effect to a symmetrical pattern gives a symmetrical result.

Try filling a square image with the "Shadow dot" pattern in the Pattern list of the Pattern tab in the Materials Properties dialog (click into the Materials box to get this dialog) and then go to Effects || Distortion Effects || Polar Coordinates.

See the variations possible just by altering the scale of the pattern.

Open Image     Copy     Move Tool

A symmetrical image made by mirroring and combining gives an image that could be used as a special effect. For example this composite rectangular photo could be made into an acceptable oval tray with a decorated bottom. A square image can produce a circular design for a plate.

Open "/tutorial/html/tut8eff/trees.jpg" again. The image is 200x267 pixels. Copy it to the clipboard (Edit || Copy or Ctrl+C).

Now make the image bigger: Go to Image || Canvas Size:
– Width = 400
– Height = 267
– Top / Bottom / Left = 0
– Right = 200

Paste the contents of the clipboard as a new layer into your image (Edit || Paste || Paste As New Layer or Ctrl+L). Then go to Image || Mirror. With the Move tool, position the pasted image to join up in the middle (see top image on the left). The Arrow keys give fine movement if needed. Then go to Effects || Distortion Effects || Polar Coordinates to get the bottom image on the left.

Save this image as "/tutorial/html/tut8eff/polar_trees.jpg" since we'll need it again later on.


Try using a simple image with detail confined to one edge and leave a lot of white space and also experiment with the effect of the detail confined to different areas.

In the screenshots on the left, the image on the left becomes the image on the right when the Polar Coordinates effect is applied (Effects || Distortion Effects || Polar Coordinates).

Open a new square image and either paint a strip along an edge or try some images from the Picture Tubes tool. Keep it simple and confined to an edge.


Here the image detail is confined to part of the bottom edge only.

Try the effects obtained using part of the other edges.


To me, more useful results seem to come if there is a lot of white space or non-detail area in the image and if the detail is confined to one edge, particularly the bottom edge.

Symetrical images produce a symetrical result and square or rectangtular images produce circular or oval images.

Try using this effect by applying some of these guide lines so that you have some chance of getting a predictable result.

Now let us try some examples: first a simple wreath, then a tray, and last some "Digital Ikebana".


A Simple Wreath

Some Holly Leaves tubes were sprayed across the bottom of a square image, and then the Polar Coordinates effect applied (Effects || Distortion Effects || Polar Coordinates).

For the final wreath, the join at the top was covered and some more sprigs were added.

Try other leaves and objects as well.


Deform Tool

A Tray

The symmetrical image we saved as polar_trees.jpg made by mirroring and combining a scene was used as the basis for this tray with some clipart handles added (handles.jpg).

Make and save this image as tray.jpg – we will use it later on.

Using the Deform tool, reduce the height of the image by about 2/3. This will give a passable side on view of a tray for our floral display. Save it as tray_a.jpg.


Ikebana - the Japanese Art of Flower Arrangement

This is where you can let your imagination run riot and design a digital flower arrangement using the Polar Coordinates effect.

Open Image     Magic Wand Tool     Copy     New Image

Open image flower.jpg from your download. The JPG image has a white background and we want the flower on a transparent background.

Using the Magic Wand tool with a Tolerance = 15, select the white background. With the Shift key down click on any white areas that are not included. Invert the selection (Selections || Invert or Ctrl+Shift+I) and copy it (Edit || Copy or Ctrl+C).

Create a new image of 200 x 200 pixels with a transparent background. Paste the flower as a new layer into this image (Edit || Paste || Paste A New Layer or Ctrl+L) and save it as "Polar_1.psp". We will use this single image of the flower on a transparent background as the basis for creating our floral arrangement using the Polar Coordinates effect.


Duplicate image "Polar_1.psp" by pressing Shift+D (Window || Duplicate).

With the Deform tool, rotate and size the flower so that it lies along the bottom edge and has a length of about 90% of the image width (see top left image).

Duplicate this image and rotate it by 90 degrees (2nd left image).

Again, duplicate this new image and rotate it by 90 degrees (3rd left image).

And duplicate this image and rotate it by 90 degrees to the right (bottom left image).

You now have four images with the flower aligned along the four edges.

Now on each of the four images you obtained by duplication, apply the Polar Coordinates effect (Effects || Distortion Effects || Polar Coordinates) with the default settings.

You will now have the original flower and these four variations open on your workspace.

New Image Open a new image of 400 x 400 pixels with transparent background.
Magic Wand Tool     Move Tool

On the images above we want to select just the flower image. This can be done by using the Magic Wand tool: Click on the transparent area of an image, hold the Shift key down and click on the black areas, then invert the selection with Selections || Invert and copy with Edit || Copy (Ctrl+C). This puts that flower image into the clipboard.

Activate the new 400 x 400 transparent image and paste the clipboard as a new layer (Edit || Paste || Paste As New Layer or Ctrt+L).

Repeat this until you have all 5 images pasted. They will be on top of each other in the center of the image but can be separated visually: Open the Layer palette and with a layer activated use the Move tool to make it easier to see what is there.


Layer Visibility Off

Deform Tool

We are starting to arrange the elements of the arrangement with the circular image rotated.

Now you can show your creative skills.

Select a flower layer in the Layer palette and perhaps turn off the visibility of the other flowers.

You might want to change the layer order by draging a layer name up or down in the Layer palette.

Remember the different modes available with the Deform tool as you rotate, distort and position each flower.

This is "digital", not real-life art, so arrange and alter things to please yourself.

You could also alter colours and introduce other clipart features and other flowers if you wish but this exercise is about the Polar Coordinates effect.


Finally, increase the canvas size (Image || Canvas Size), use the tray we made above as a base, and add a background and a frame.

"Move over, Picasso – you are sitting in my chair!"

There must be more applicatiions of the Polar Coordinates effect – explore, enjoy and have some fun.