An Impossible Triangle
With PaintShop Pro

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An impossible triangle (also known as the Penrose Triangle or a Tribar) is just what the name says - it appears to be something that cannot exist in reality.  It can also be described as an optical illusion and it's surprisingly easy to draw with PaintShop Pro (see the top left corner for an example)

The first one was created by the Swedish artist Oscar Reutersvard in 1934. 

In the 1950's a mathematician named Roger Penrose independently devised and popularized the figure.  It's also featured quite prominently in the work of artist M.C. Escher.

The thing that seems to make drawings such as this so popular is the disconnect between the two dimensional drawing we see and our attempt to see it in three dimensions.  As a simple, one dimensional drawing, the triangle is perfectly logical.

When our brains try to represent this two dimensional figure in three dimensions (length, height and depth) - well that causes some problems because our brains are telling us it's a figure that cannot exist.  Surprisingly, while it appears to be something impossible to create in the real world, there are numerous impossible sculptures throughout the world.

Like the research for the Celtic Knot, figuring out how to draw the Impossible Triangle with PaintShop Pro took a lot of time researching different methods on You Tube and a lot of different websites.

So I said it is easy to create with PaintShop - let's take a look ...! 

The Impossible Triangle Process

Drawing the Impossible Triangle with PaintShop Pro really is quite easy.  What we're going to do is stack three triangles, one on top of the other, erase some lines, add some other lines and the Impossible Triangle will be a beautiful piece of art you'll be proud of!

The Shape Tool

Click on the Shape Tool Icon
to reveal the Option bar.

The Option Bar - drop down the
menu and select the triangle.


Step One

The first step, of course, is to create a new file.  My file is 7" X 5" landscape with a white background at 300 pixels per inch.

Nice and simple, right ...?

Step Two

The Shape Tool is used to make three equilateral triangles (that is, the sides are all equal length and the three angles are 60 degrees) - the first triangle is the largest, the second smaller and the third one is the smallest.  

When you drag out a triangle with the Shape Tool it's not an equilateral triangle unless you hold down the Shift Key when you're dragging out the triangle.

If your triangle is upside down when you draw it, you can flip it over by moving your cursor close to one of the angles and spinning the triangle.

It may be helpful to place a guide on the canvas and align the base of the triangle to the guide.

Make the first triangle large and make sure the triangle is vertical.  Move it to the center of the document.

Draw out another triangle (with the Shift Key held down) and make it smaller than the first one and orient it the same way as the first triangle.  Move the cursor over the center point and drag the second triangle inside the first one so that the sides of the second are equal in distance from the sides of the first one.

Now do the exact same thing with a third triangle - make it smaller than the second, orient it the same and move it inside the second triangle.

When you've done all of these steps this is what you'll have - three equilateral triangles with the sides equal distance from each other.

Another thing - when you draw the triangles the lines may be very faint - don't worry about that, we'll fix it up soon enough (I did an extreme Levels adjustment to make sure these three can be seen),

The guides I used to align the base and the apex of the three triangles are also visible.

Step Three

The next step is to go over the lines of the triangle using the Point to Point Pen Tool (you can use the Brush Tool if you wish, but the Pen Tool is faster and more accurate in this situation).

For each new line I drew with the Pen Tool I added a new Vector layer.  The following is the progression of the lines ... 

First Line
From bottom right of middle triangle
to the outside line of the large triangle. 

Second Line
Same as the first but starts at the
bottom left corner of the middle triangle. 

Third Line
Carry on from the the first two lines. 

Fourth Line
Now do the same thing with the small triangle. 

Fifth Line
Second side of the small triangle. 

Sixth Line
The small triangle is complete. 

The Impossible Triangle is starting to appear.

To get it complete all we need to do is erase a few short lines and then add some shading and or color. 

Seventh Line
Now outline of the largest triangle. 

Step Four 

The final step is to take out the pointy parts of the three corners so they look like this.

It's a simple erasing job, especially on the top point bit the bottom two point can be a bit of a challenge.

And that, my friends, is why we make use of the guides in PaintShop Pro.

So this is how to get that nice flat top on each of the corners.  As I mentioned, the top corner is simple.

The first thing to do is to delete the layer with the three triangles that you first made - you don't need 'em anymore, and then merge all of the layers into one layer.

Now drag a guide down from the ruler so that it's positioned like this ...

This gives a nice guideline to add the flat part to the top corner.

Get out the Pen Tool again and set it for Point to Point as before,.  Draw a line from the left arm of the big triangle to the right arm following the guide.  When it's exactly where you want it click on the check mark in the Options Bar.

Select the Eraser Tool and erase everything above the line that you just drew.

You'll end up with a nice flat top on your drawing and that's what you want.

The challenge is doing the exact same thing to the other points of the triangle because the guides will only be horizontal or vertical so we need to do some image rotating. 

Rotating the Image
 
There are two ways to rotate the figure - you can simply go to Image > Free Rotate, make sure that Free is selected and enter 240 into the box.  This will cause your figure to rotate 240 degrees and the next pointy tip should be at the top and available for fixing.

If all goes well then you can move a  guide  (like this) and draw a line with the Pen Tool.  Now erase everything above the line you just drew - that's two of them done.

Now two of the points are done.  To finish up just go back to Free Rotate and do it over again.

This is what you should have when you're finished - a nice impossible triangle!

Erasing 

Now there's a bit of erasing to do and then the impossible triangle will be completed.

There are three short little lines that need to be removed.

The three little lines that are highlighted in the striking  purple color are the ones that need to go.

You can paint them over with white or grab the eraser and erase the three short little pieces


Once you do that - this is what you'll have. 

You can leave it as it is or add some shading or coloring or other embellishments. 

Shading

Now for some fun - shading and coloring your impossible triangle. 


The easiest way to start is to make sure the white background is removed, leaving only the black outlines.

To do this just grab the Magic Wand, make sure that Contiguous is not checked, click on the white and press delete on your keyboard.  This is the result you should have ...


Now you can do whatever you wish!

Underlying color or gradient

Add a new layer and then drag it below the triangle layer.  If the triangle layer is still the Background layer then double click on it and click OK - this makes the Background a full layer.

With the new layer below the triangle layer add a color or gradient with the Flood Fill tool.

With a blank layer below the transparent triangle ...

Select a color from the Materials Palette, select the Flood Fill Tool and click on the layer.

I chose this nice blue-purply color for no particular reason.  It's a simple matter to confine the color outside the triangle.

Take the Magic Wand, select the color layer and click inside of the triangles arms until the inside of the triangle is completely selected.

After hitting the delete key, leave the selection active.  Decide on the color you want for the triangle and set it as the foreground color in the Materials Palette (I selected yellow because it's a complimentary color to the blue-purply color I selected earlier.

Get the Flood Fill tool and fill in the arms of the triangle.  Looking good so far!

Now the question is how will the triangle be colored and shaded?

The shading can be done with a brush and probably the only way to make it look right is to use an Intuos tablet with the pen set to change Opacity with pressure.

The easiest method is to make a selection (using the Freehand Selection tool set to Point to Point in the Options Bar) where you want the shading to be, promote the selection to a new layer and add a foreground to transparent gradient.

The gradient needs to be oriented in the direction of the selection.

This is how the impossible triangle looks colored and shaded ...


Other possibilities

There are lots of things you can do with your completed impossible triangle.  At its most basic, it's simply an interesting optical illusion.

I saved a copy of the triangle with only the lines visible and saved it as a .png file. 

This makes it easy to select the arms and add different colors and gradients and even some textures.

The key is to eliminate everything except the black lines and then save it for future use as the .png file.

How about using the impossible triangle as a tattoo? 

Starting with the .png file it's a simple matter to add some color and gradients.

Then make a copy and paste it as a new layer into an image.

Use the Pick Tool to resize (make sure it's set to scale), move the tattoo into position and then spin it around to the correct position.

Experiment with different layer blend modes to find the one that looks most natural.

The blend mode for this example is Overlay, which totally changed the colors and that's OK.

You can also make a Favicon with the impossible triangle.

Let your imagination run wild and have fun making your own Impossible Triangle!

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