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Rotating the 3D Slice, 2D Faces Projections, Marble scenes, and plenty of extra! « mtbdesignworks Weblog [Miegakure, 4D Toys, Marc ten Bosch]

Rotating the 3D Slice, 2D Faces Projections, Marble scenes, and plenty of extra! « mtbdesignworks Weblog [Miegakure, 4D Toys, Marc ten Bosch]

2023-06-25 10:15:38

Hello!

It is a Mega-Replace ®™ that focuses on options that folks have been requesting for a very long time.

I’ve a ton of stuff in Miegakure that may very well be shared with 4D Toys however what takes growth time shouldn’t be the cool 4D stuff however all of the UI/UX round it. Initially as a result of there may be the VR model, the mouse/keyboard model, and the touchscreen model, which all require barely totally different customized interfaces, but additionally as a result of I all the time wish to have the 2D/3D ranges to indicate the decrease dimensional model of the identical factor, as a way to clarify what is definitely occurring. In order that’s like six totally different variations!

However in any case, here’s a giant batch.

1. Rotating your 3D slice arbitrarily in 4D

Clearly an typically requested function! The enjoyable half was developing with a easy interface: If you happen to simply rotate the 3D slice across the digital camera you may make the extent fully invisible, as a result of it doesn’t belong to your slice anymore, or at greatest is off to the aspect in 3D.



My aim was to design the interface to let gamers give attention to the cool 4D stuff as an alternative of the digital camera/slice orientation/place. For instance there may be nonetheless no actual want to maneuver the digital camera across the degree, as the extent is all the time in entrance of you regardless of the way you rotate in 4D!

By the way, you can even maintain a form when you rotate your slice and it’ll rotate with you!

The interface combines each steady and discrete 90 diploma rotations: you should utilize the arrows to rotate the slice in 90 diploma increments, much like Miegakure’s fundamental mechanic. That is necessary as a result of axis-aligned rotations are the best to grasp!

The three coloured traces symbolize the three horizontal dimensions. You’ll be able to commerce which of those dimensions you’ll be able to see by utilizing the brand new rotation controller.

For instance: The extent above is sloped, and you may both see the slope however not the 4th dimension, or you’ll be able to see the 4th dimension however not the dimension that slopes down. So it seems to be like the extent is flat generally, nevertheless it’s simply that you just can not see the slope. (There’s a 2D/3D degree that present this).

(If you happen to can see the pink and inexperienced traces however the white line is perpendicular to the display screen, you might be aligned usually, i.e. you’ll be able to see the 2 common horizontal dimensions however not the 4th dimension. However should you can see the white line, you have got traded certainly one of your common dimensions for the 4th dimension)

The 2D/3D mode helps perceive what which means, however you can even simply mess around with it! 4D Toys and Miegakure are two totally different complementary approaches to explaining the fourth dimension. 4D Toys is about taking part in with 4D in a high-bandwidth, undirected means, and Miegakure is one big refined and detailed tutorial.
(I wrote about this in additional element in the 4D Toys release post)

 

2. Projection of the 2D Faces of the 4D objects

An typically requested function! That is just like the 1D Strains projection from Update 1.6. When enabled, the 2D faces of objects are projected onto the present slice.

That implies that regardless of the place the slice is, the faces of the objects will all the time be seen. It’s an “old-fashioned” and really mathy means of displaying 4D objects which you will have seen earlier than! The projections are helpful to roughly see the place there are 4D objects, however that’s about it as a result of it’s very simple for the projections to overlap an excessive amount of.

I’ve had a good cooler model of that in Miegakure because the starting… and which is able to present up in 4D Toys in some unspecified time in the future!


You too can allow the coloured model of the wireframe mode by long-pressing the wireframe button (I understand that is fairly hidden proper now … sorry).


 

3. Lots of buildings made to play with “marbles” and roll them round

I made these scenes the place you’ll be able to play with marbles that roll round on fascinating terrain shapes. They took little or no time to make due to the 4D procedural mesh technology methods I constructed. I feel probably the most enjoyable half is seeing the spheres shrink/disappear then reappear/develop whereas they roll down a path that curves within the fourth dimension. It’s additionally neat to see them transfer on the projection then re-appear into your slice.

I discovered it fascinating that it was sort of arduous to give you many extra fascinating paths than these… I feel it’s because 4D objects are simply shifting alongside 1D paths, even when these paths are embedded in 4D!

 

4. Fixed Torque scenes

I added scenes with Tesseracts which might be mounted at some extent however with a torque that retains them rotating.
This contains a few scenes with a double rotation: two perpendicular planes of rotation on the similar time.
In 4 or extra dimensions, an object can rotate in additional than a single aircraft on the similar time.
It’s enjoyable to cease one rotation whereas the opposite retains occurring.

 

5. The 1D model of the 2D “Davinci” 4D Objects

That is much like the shapes I made that have been impressed by these Davinci Drawings (see this blog post), however it’s the 1D model as an alternative of the 2D model.

In 3D every face is two-dimensional, and we are able to carve holes in every 2D face, which quantities to preserving the 1D traces of every face (identical to the drawing beneath).

Leonardo da Vinci's Polyhedra

See Also

However in 4D every face is three-dimensional, so we are able to do two issues! Take every 3D face (referred to as a cell) and both make it hole inside (which quantities to preserving its 2D faces, as earlier than) or make every cell into one thing just like the drawing beneath (which quantities to preserving its 1D traces).

I don’t wish to spoil it nevertheless it seems to be cool once you activate the 2D Face projection!

6. A static Klein bottle with a sphere which you could roll inside

This permits to get a really feel for what “inside” a 2D Klein bottle in 4D even means. Additionally it makes it simpler to have a look at the Klein Bottle whereas it’s standing upright. Up to now you had to make use of the anti-gravity function… It’s arduous to maintain the 4D model of the Klein Bottle upright as a result of the Klein Bottle is a 2D object, and a 2D object in a 4D world is skinny, like a 1D wire is skinny in a 3D World.

 

7. A 120 cell (faces) and a sphere collectively

I made this to check the collision some time again. It’s enjoyable to see the sphere push round or roll round contained in the 120 Cell.

 

8. Auto-Comply with the final touched form

Whereas energetic, your slice all the time strikes to the place of the final form you touched. It’s enjoyable to make use of on marble scenes to observe a marble round at a bizarre slice orientation.

** As with the earlier replace, there’s a web page to the suitable of the extent choose hub. After you play the related ranges the brand new buttons can be unlocked **

Buy 4D Toys

Miegakure growth is progressing properly

I’ve been giving month-to-month updates on Patreon.

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