affinity designer How to create a Reuleaux Triangle

[GarryP]

Designer was used in the video and I’m pretty sure that the same workflow can be followed in all the Affinity applications but you will have to use the relevant menu choices for the Geometry operations instead of the Designer toolbar buttons.

https://en.wikipedia.org/wiki/Reuleaux_triangle

Here’s how you can create a Reuleaux Triangle, see attached image and video below. (Apologies for the non-technical imprecise language.)
1. Make sure you have Snapping ON (you may need to put more snapping options ON than you normally have).
2. Draw a line which will be the bottom two points of the triangle.
3. Draw a circle with CTRL+SHIFT from a centre at one end of the line so that the edge of the circle meets the other end of the line.
4. Draw another circle the same way but from the other end of the line.
5. Draw a line from where the two circles intersect at the top to one end of the line.
6. Use the Move Tool (with SHIFT pressed) to resize the new line so it crosses the circle completely.
7. Draw a new circle with a centre at the intersection of the two circles at the top until the side of the new circle snaps to the same horizontal position as the end of the new line.
8. Delete both of the lines.
9. Select two circles and use Geometry Intersect.
10. Select both remaining shapes and use Geometry Intersect again.

The attached image shows some examples of using the corner tool on the shape and some effects (Martin’s “Golden boy”).

[Move Along People]

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[GarryP]

That’s a nice quick way of getting a shape that’s similar to a Reulaeux Triangle but it might not be a good way to get an exact decent (see note) Reulaeux Triangle. A Reulaeux Triangle is a very specific geometric shape that I think would be difficult to create precisely using the polygon tool and would require some experimentation and/or mathematical calculations by the user.
As you can see in my attached image, using the in-built functionality gives me an approximation of a Reulaeux Triangle (filled in orange) but the curves are wrong and I have had to manually scale the shape to fit by eye and it’s still not exact. (A curve of 46% is much closer but I still don’t know if it’s exactly right.)
It’s good to have a way of doing something similar that’s quick but constructing it properly will get you the real thing.
Also, learning to construct shapes, rather than letting the software do it, is good practice for when you need to create your own shapes that the software can’t create itself (which was sort of the point of the tutorial).

Note: As explained below, this probably isn’t an exact Reulaeux Triangle but, I think, it’s probably close enough for most purposes.

Edited March 7, 2020 by GarryP
Added note.

[lepr]

On 3/4/2020 at 8:33 AM, GarryP said:

A Reulaeux Triangle is a very specific geometric shape

Current Affinity apps cannot draw true ellipses/circles/arcs, so your method in the opening post does not produce an exact Reuleaux Triangle.

[GarryP]

An interesting statement.
Do you have any proof and/or reasoning to support it?

[walt.farrell]

3 hours ago, GarryP said:

An interesting statement.
Do you have any proof and/or reasoning to support it?

Try a Google search for

site:forum.affinity.serif.com true circle

One result that shows up at the top is this one:

There are probably others of interest in the list, or possibly earlier in that thread (but other parts of that thread are confusing given anon2's prior deletion of much of their site content.)

[GarryP]

Please forgive my ignorance but, for example, what is the difference between a circle drawn via the Ellipse Tool and a “true circle”?
In other words, if I drew a circle with the Ellipse Tool and then draw a “true circle” on top of it, what difference(s) would I see?

Edited March 6, 2020 by GarryP

[lepr]

7 hours ago, GarryP said:

Please forgive my ignorance but, for example, what is the difference between a circle drawn via the Ellipse Tool and a “true circle”?
In other words, if I drew a circle with the Ellipse Tool and then draw a “true circle” on top of it, what difference(s) would I see?

Unless you zoom in extremely closely, you won't see the Ellipse Tool's deviation from a true ellipse. 

To see for yourself that an Affinity "circle" isn't a true circle:

1. use Designer for its Outline view mode for the clearest comparison of the curves
2. draw a "circle" with Ellipse Tool
3. press cmd+j to duplicate it
4. zoom in as much as you want and see that the two curves overlap perfectly
5. rotate the duplicate about its centre by 45 degrees
6. now see that the curves deviate and cross each other at eight points

 

[Pšenda]

1 hour ago, anon2 said:

at eight points

Just add, that this corresponds to the fact that if you convert a circle / ellipse to a curve, it has four nodes (the resulting curve is composed of four Bezier curves). 

[GarryP]

Ah, now that is interesting.
I’ve attached a screen grab which shows two circles at 45 degrees rotation from each other at 40,000,001.1% zoom (I typed 40000000 but that’s the number the software came up with).
The amount of deviation between any set of two points on the circles seems to be way less than 0.0001 of a millimetre but it’s there nonetheless. Whether someone may need to take this into account will be up to them I suppose.
It’s good to learn new stuff. Thanks all for the explanations. (I’ve edited my earlier post accordingly.)

[Pšenda]

1 hour ago, GarryP said:

I’ve attached a screen grab which shows two circles at 45 degrees rotation from each other at 40,000,001.1% zoom (I typed 40000000 but that’s the number the software came up with).
The amount of deviation between any set of two points on the circles seems to be way less than 0.0001 of a millimetre but it’s there nonetheless. Whether someone may need to take this into account will be up to them I suppose.

I think the deviation is bigger.
It should be noted that the Affinity circle is not a "circle", but rather a square with a lot of rounded corners (for illustration only 🙂
Thus, the greatest deviation between these shapes is at the breaking point, that is, the node location. In other places the deviation may be smaller or even zero.

Here you can calculate / display the maximum deviation quite accurately.

Edited March 7, 2020 by Pšenda

[GarryP]

I didn’t see that much deviation myself but I didn’t look at every point on the circles.
Either way, the amount of deviation looks to be small enough that most people probably won’t notice a difference, but there could be times where any small difference may cause unexpected issues, Geometry functions for example.

Maybe this should be noted in the Help just so users are made aware of potential problems. After all, the website does say that Designer “<maintains> 100 percent accurate geometry”.

[Pšenda]

6 minutes ago, GarryP said:

but I didn’t look at every point on the circles.

Then you should not claim this.

1 hour ago, GarryP said:

The amount of deviation between any set of two points on the circles

You should be more careful about using the terms "exactly" and "any" :-)

However, this does not change the fact that for an ordinary user this accuracy is more than sufficient.

[GarryP]

If you read what I said above, the text says “The amount of deviation between any set of two points on the circles seems to be way less...”
This suggests that I didn’t make a complete and thorough survey and also allows for refutation.

I think that’s a quite reasonable thing for me to be saying in the circumstances where I was zoomed in to 40,000,001.1% and checking every single part of the curves would have been quite a chore to undertake.

I also think it should be noted that duplicating a circle and rotating the duplicate by 45 degrees clockwise does leave a shape, as per the attached image. I don’t think most users would expect this.

[Gazpacho]

Thanks for the post, this really helps me a lot.

[Mr. Doodlezz]

Hey guys,

thanks, I learned something today! 😮

Now I just want to learn a few more things.

1. Maybe I missed it, but what actually makes a real circle (apart from the fact that it is equally round no matter how you turn it)?
2. Does it have to consist of only three nodes or could it still have four or more nodes (again, as long as it is still completely round)?
3. Most important of all: How do I get, or rather, how do I achieve real circles at this point? Because ... OCD kicks in right now. 😅

Greetings
MrDoodlezz

[firstdefence]

Which apps can, do, draw true ellipses, circles and arcs?

[Sauerstoff]

Circles seem quite perfect with Inkscape (I have not tested arcs and ellipses).