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Pete123

How do I create an irregular trapezoid with exact dimensions ?

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I'm not sure if irregular trapezoid is the correct english term, but in any case, I am desperatly trying to create a shape that has 4 sides, of which none are the same length and no side is parallel.

I know the exact length of each side, but I can't seem to create the shape in Designer.

 

I'm currently fiddling with drawing rectangles as measurement tools, but this is impossible to get correct. (does a measure tool exist, I know it has been requested by many users, but I can't seem to find any means of measuring aside from drawing rectangles ?).

I can't create diagonal lines with exact lengths. I can create horizontal or vertical lines and use the transform tool for exact lengths, but since I don't know the required rotation, I'm at a loss.

It would be great if exact dimensions where displayed when draging nodes....

 

If anybody has any tips how I would create this in Designer ? I'm not using 1.7 currently, does 1.7 have anything that could help ?

 

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Can you be more specific?

Do you only have a list of the lengths? Something like A  B = 12, B C = 13,  etc? Seems like if a series of circles w. those radii were made, it shouldn't be too hard.

Or, w. some fuss, create a protractor w. the cog tool.


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Yes indeed, I have 4 lengths. Nothing more.

I had thought about circles, but I'd at least need one diagonal, which I don't have.

I think what I'm trying to do is impossible without more data.

 

In practice what is happening, I am given a technical drawing of a lightbox for which I need to design the fabric that goes in front. Upon measuring (with the fiddly rectangles and rotation acrobatics in designer, please serif give us an elegant way to measure stuff...) I have noticed that the technical drawing is not accurate. I'm told that the dimensions that are displayed on the drawing are exact though, so I'm trying to recreate the shape, but without at least one diagonal I think I can't...

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The name you are looking for is an irregular quadrilateral.

Two possible algorithms could be:

Draw a series of four line segments of indeterminate lengths with the angle between each less than 90degrees. . Rotate so that the first line is horizontal and adjust the length to the first target. This will appear in the Transform panel. Then rotate  so that the second segment is horizontal and repeat. 

Create four isolated lines, of your target lengths, and then move and rotate them individually into a quadrilateral shape. This has the advantage that the line should keep their fixed lengths. You could now create a new four-sided polygon and drag the four vertices to overlay the endpoints of yous first set.

I have not tried these ideas. They are just thoughts.

John


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1 hour ago, John Rostron said:

The name you are looking for is an irregular quadrilateral.

A trapezoid in North American English is what we would call a trapezium in British English; i.e. a quadrilateral with two sides parallel. Just to add to the confusion, the term ‘trapezium’ is used in North America to refer to an irregular quadrilateral!


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Confusing it is.

In my language we also speak of Trapezium. I mentioned trapezoid because that is the name that is used inside Designer, and because it sounds a bit cooler (I'm also a fan of sci-fi movies and such... :-)

 

Anyway, I did try the suggestions John has offered, but the problem still remains when trying fit all the sides and corners together. There is no problem making sides of the correct length, but rotating each side until all 4 corners are correct is impossible without a diagonal. Not to mention that is fiddly...

I do think it could be done in software though, to have a dialog box, or an expanded transform tool where you can type in lengths of all sides and Designer (or a plugin) computes the resulting shape. "Artificial Intelligence" sort of speak, as is the buzzword these days...

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Seems like the inaccurate drawing is technically not a technical drawing.O.o

I searched around, focusing on threads from CAD forums. Some respondents said that w/o at least 1 angle it was impossible. 1 respondent claimed to have a solution, but ended up admitting that it was just less inaccurate than other proposals.

I've tried "fiddly" in 1.6, am going to try 1.7. But if CAD users don't have a method for doing this, I have to wonder how a design illustration app would be useful.

Any rate, another question. Do you have at least a sequence for the 4 lines. That is, A = w, B = x, C = y, D = z?


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Hi gdenby, I appreciate the effort, and I agree that it is an odd question to ask. I've already settled on the notion that this is something that a design illustration app should not be required to do.

Posting this question here was more out of frustration that I wasn't even able to  easily measure and verify the existing drawing in the first place (drawing rectangles and rotating them to get a dimension = not very elegant). And my next mission was to try and recreate the shape... and the rest is what you see in this thread.

 

fwiw :

A = 1815,7mm

B = 2458,3mm

C = 1909,2mm

D = 2461,9mm

 

For my problem, I have solved it by making the design for the fabric a few mm smaller on each side, so that I am sure there is enough tension when stretching and inserting the fabric into the lightboxes.

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47 minutes ago, gdenby said:

I searched around, focusing on threads from CAD forums. Some respondents said that w/o at least 1 angle it was impossible.

Assuming the context is an irregular trapezoid (in the U.S. sense of no parallel sides), it is not impossible given nothing more than the lengths of the 4 sides, but the problem is there are many irregular trapezoids that could have sides with those lengths. You would need at least one other measurement for a unique solution, like an angle or the total enclosed area.

It is easy to see the truth of this from a simple experiment: cut 4 straws or uncooked spaghetti strands or whatever to 4 different lengths & arrange them on a flat surface in the shape of an irregular trapezoid. Now, squish the shape by pushing closer together two opposing corners, while keeping all four corners touching to create a different irregular trapezoid. If you allow an interior angle to exceed 90° you can even collapse it down to what begins to resemble a triangle with an extra long leg.

FWIW, when I was in grade school a million years ago, one of my teachers taught us about regular & irregular geometric shapes using soda straws strung together with string, like a necklace. If you have young children you could do the same with them to maybe give them a head start on STEM. :)


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Looking at the dimensions, I'm guessing the lightbox is a very slightly distorted square. The best I can make is a reasonable approximation, an average. But, yes, as far as I can tell there are any number of shapes that can be made having only the lengths and no angle or diagonal reference.

1 hour ago, R C-R said:

FWIW, when I was in grade school a million years ago, one of my teachers taught us about regular & irregular geometric shapes using soda straws strung together with string, like a necklace. If you have young children you could do the same with them to maybe give them a head start on STEM.

Going off topic, hereinafter acronymized as GOT, I'm reaching infinity years beyond the last time I needed to use anything beyond elementary geometry. But I do have 2 grandkids. Once they get beyond the anything small enough goes in the mouth stage, I'll be sending them "K'nex" and then "Zometools." I hope those will fascinate them.

Early starts in anything is good. Honestly, start playing Bach by age 6 latest, assuming there is a competent teacher.


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15 minutes ago, gdenby said:

Early starts in anything is good.

Early or late, learning about geometric shapes is very useful when working with apps like the Affinity ones. :)


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23 minutes ago, gdenby said:

Looking at the dimensions, I'm guessing the lightbox is a very slightly distorted square.

If you have access to a physical object just measure a diagonal and construct two triangles. Join them et voila.


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20 minutes ago, Old Bruce said:

If you have access to a physical object just measure a diagonal and construct two triangles. Join them et voila.

Well, that's the problem... the lightboxes are being built as we speak in Italy and will be shipped directly to the US, and I am in Belgium where I have a local printer that will print the fabric. So it's a global effort :)

Not to mention the deadlines. I'm already a week late.... :$

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5 minutes ago, Pete123 said:

the lightboxes are being built as we speak in Italy

Someone is going to have to get the measurement of a diagonal or at least one Angle in degrees.

Not to make fun of your predicament but this sounds like a scene from the movie "Spinal Tap" and the twenty inch tall copy of Stonehenge for a huge stadium show.


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That's a bit scary... it is actually a Stonehenge exhibition that I'm working on...

 

The "technical" drawings I received where off by 4mm to the dimensions they displayed, and I'm assured that the dimensions are correct, so I took the drawing that was sent to me and adjusted for the 4mm difference.

I'm pretty confident everything will turn out right, it's just not the way I like to work... I'd rather be exact, hence why I would have liked to recreate the shape in Designer...

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Just now, Pete123 said:

it's just not the way I like to work...

No one sane wants to work that way.

Best of luck.


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One way of fixing the diagonals (and angles) would be to declare that they constitute a cyclic quadrilateral, with all the vertices on a circle. That being so, then there are simple formulae for the length of diagonals. Look at the Wikpedia page on Cyclic Quadrilaterals.

You will need to scroll down to the heading Diagonals and Angle Formulas.

John

 


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5 minutes ago, John Rostron said:

One way of fixing the diagonals (and angles) would be to declare that they constitute a cyclic quadrilateral, with all the vertices on a circle. That being so, then there are simple formulae for the length of diagonals. Look at the Wikpedia page on Cyclic Quadrilaterals.

You will need to scroll down to the heading Diagonals and Angle Formulas.

John

 

I've just scrolled down that page and by the end, I was la la'ing the archers theme tune in my head. :D


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3 minutes ago, firstdefence said:

I've just scrolled down that page and by the end, I was la la'ing the archers theme tune in my head. :D

Whilst you are boggling, scroll down a bit further to Parameshvara's circumradius formula. If you create a circle with this radius you can more readily (!) fit your vertices to this circle.

John


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3 hours ago, John Rostron said:

Whilst you are boggling, scroll down a bit further

Scroll back up to the exceptions. We don't know if the quadrilateral is "cyclic"


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9 hours ago, Old Bruce said:

We don't know if the quadrilateral is "cyclic

No. There are too many degrees of freedom in the original problem. My suggestion of a cyclic quadrilateral is a proposal to constrain the possibilities.

John


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A small update to my original question.

I now received the diagonal dimensions... 

I'm now trying to recreate the shape, but I'm still stumbling in Designer. 

Is there a way to snap to any place on a circle ? I'll try to embed a video. I've first drawn the base line (horizontal), then I've drawn a vertical line, and I've positioned a cricle that represents my first diagonal. Moved the rotation point on the vertical line, and now I'm trying to rotate the vertical so it snaps to the diagonal... but nothing is snapping. I've tried a few different settings in the snap tool,  and would have thought that "snap to object geometry" would be perfect for this... but my circle is not snapping at all...

The diagonals are 3027,4 and 3142,7

Sorry to bark on with this, but I'm trying to get a better understanding of how Designer works...

 

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2 hours ago, Pete123 said:

A small update to my original question.

I now received the diagonal dimensions... 

I'm now trying to recreate the shape, but I'm still stumbling in Designer. 

Is there a way to snap to any place on a circle ? I'll try to embed a video. I've first drawn the base line (horizontal), then I've drawn a vertical line, and I've positioned a cricle that represents my first diagonal. Moved the rotation point on the vertical line, and now I'm trying to rotate the vertical so it snaps to the diagonal... but nothing is snapping. I've tried a few different settings in the snap tool,  and would have thought that "snap to object geometry" would be perfect for this... but my circle is not snapping at all...

The diagonals are 3027,4 and 3142,7

Sorry to bark on with this, but I'm trying to get a better understanding of how Designer works...

That sort of object manipulation is tedious in Designer 1.6. You can rotate the line via its bounding box, but bounding boxes do not snap to object geometry. Working with the Node Tool, the line's nodes will snap to object geometry, but there's no way to constrain the length of the line while moving a single node. One solution is to draw a second circle with radius equal to the length of the line, and centred on a node of the line, and then the other node of the line can be snapped to the intersection of the two circles to effectively rotate the line without changing its length

Designer 1.7 beta has Point Transform Tool which does enable anchoring the line at one end and rotating the other end until it snaps to the circle without affecting the length of the line.

 

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