Impossible Cubes

[Acorn]

The following design has no images:

Xara - Impossible Cubes.xar

Do note, this JPEG shows the construction, not the final HTML rendering:



I couldn't resist building it but my technique was very imprecise.



Acorn

[gwpriester]

The first example there is a problem with the third cube down on the left. The second looks great.

Not sure what you mean HTML rendering. Need more info.

[Acorn]

The first example there is a problem with the third cube down on the left. The second looks great.
Not sure what you mean HTML rendering. Need more info.

No Gary, the TG JPGing of the image destroys the transparency in the first image.
I let it be as it shows how I folded the bottom left, second in, cube to make it appear both over and under the touching cube.

"HTML rendering" is looking at the design file Preview or other web output.

The second image was such a screen grab.

Open the design file and check the funny cube actually has an extra lid.

The point of making it like this is to show how small the payload is and how much you can scale without any jaggies.
I want Xara to deliver more web content that is vector, be it through HTML, CSS or SVG.

My inspiration was https://a.singlediv.com.

Acorn

P.S.
The index.htm file is just 12.37kB so very fast to load.
Each face is code like:
<span class="xr_ar xr_t280" style="left:274px;top:361px;width:143px;height:143 px; background-color: #92EDE3; transform: matrix(-0.866,0.500,0.000,1.000,0,0);"></span>
Pure maths: the -0.866 is sin^-1(-60)^o​. Far clearer than a tacky JPEG.

[gwpriester]

Would this work as well? Especially for people who are short on time?

[Acorn]

Would this work as well? Especially for people who are short on time?

Thanks Gary.

The approach would require a Intersect All any time you moved the overlap.
The resultant shapes are rendered as images so will become blocky at scale.
There is no need for the Yellow kite as the Green shapes overlap already.

My approach does not end up with any images so is one HTTP fetch, smaller and sharper.

---

I do notice your edges are not aligned as the comers do not touch exactly.

To make the 'perfect' Xara cube:

1. With the Rectangle Tool, click-drag a square.
2. Rotate 45^o.
3. Resize the width to 1,000,000 mp (Xara accepts milliPoint values typed in directly to the W & H boxes).
4. With Aspect Ratio unlocked, set your Height to 577,350 mp (Xara uses milliPoints in its internal calculations).
5. You now have one Face with angle 30^o.
6. Clone and Rotate to 90^o.
7. Clone and Flip horizontally.
8. Colour and marry the three Faces as a common intersection.
9. Soft-Group and keep as your Master Cube.

I still want to create the Face without the Steps 3&4 calculations.
The use of the Isometric Grid is no real use.

Any takers?

Acorn

[gwpriester]

My cube examples were very quick and crude.

I'm an artist not a mathematician. And I have made hundreds of cubes for my stereograms.

My method is more primitive but it works for me.

I use the QuickShapes Tool to make a hexagon using the Radius Creation Option.

I zoom in and snap two guidelines to the center of the cube.

I use the Shape Tool to draw the top shape.

Rotate and duplicate the top shape around the bottom point 120 degrees. Then once more.

It works for me.

[Acorn]

My cube examples were very quick and crude.

I'm an artist not a mathematician. And I have made hundreds of cubes for my stereograms.
My method is more primitive but it works for me.
I use the QuickShapes Tool to make a hexagon using the Radius Creation Option.
I zoom in and snap two guidelines to the center of the cube.
I use the Shape Tool to draw the top shape.
Rotate and duplicate the top shape around the bottom point 120 degrees. Then once more.
It works for me.

Thanks Gary, you inspired me.

Create a hexagon.
Clone it and position the one's centre to the apex of the second.
Intersect and you are left with the exact shape.
As it is a Shape and I want a Rectangle looking the same I can create a square, rotate 45^o and centre on the shape and Shift-Drag corners to snap-fit.

No math / maths.



Acorn

[gwpriester]

Whatever works.

[handrawn]

are you eschering new ideas?

[Acorn]

are you eschering new ideas?

No, not me:



Acorn