Hot answers tagged angles
See the instruction for that set on pages 56-59, 65 and 68/69 for the 3 different roofs of it. they're using a different technique and different pieces for all of them, so this perfectly shows up some alternatives (technic-like parts for the big roof to the right, blocks with studs on the sides for the small 90°-roofs and 1x1 with clips for the roof to the ...
In the past, LEGO produced a perfect element for this: It's probably hard to find in big quantities now, so I give it more for reference than anything. I wish LEGO would still produce it though (not to mention its educative value).
To keep it simple I would use hinges placed on top of the wall, connect the roof plates and angle them to fit. <-- or --> Edit: You could even add a small plate hinge at the roof ridge, under the roof plates. This would keep them from separating.
Scale is the obvious answer. The Legoland model is huge, which means you're not seeing the brick-level quantisation as easily (quantisation is most obviously seen in mosaics but that works in 3D too). Getting the same effect at smaller scales usually means a lot of SNOT and using sloped bricks. These days there is a huge range of slopes available, from 4 ...
How firm does it need to be? Wouldn't something like this be enough? If not, you can try to lock the parts into place with "cheese" slopes, but it's not as neat:
45° angles are tricky because of the dimensions of 45-45-90 triangles: The fact that the hypotenuse needs to be a multiple of radical two makes it difficult to build out of LEGO plates which are generally limited to integers or halves. The best you can do in a reasonably small amount of space is a 5 x 5 x 7.07 triangle, but that doesn't come close enough ...
It appears that some LEGO pieces are designed with the proportions of 45-degree right triangles in mind. For example, the 3x3 plate with one corner removed has a diagonal edge that is very close to three studs long, as can be seen in this construction: Likewise, the 8x8 corner plate has a diagonal edge that is very close to 10 studs long:
Hinges can work, I have used this technique before, if you sandwich the hinges between two plates you get 45 degree 'bricks' that are quite solid. In most cases, tiles and plates in the right place will keep sufficient contact with the base plate to have a stable model.
Yeah you pretty much have the two choices you outlined... hinges or make it so big that the squareness of the bricks melts into nothingness at that resolution. OR... build your structure over tiles and use single studs, like at the ends of the ends of the hypotenuse of a 3-4-5 triangle... but that will be seriously flimsy the higher you build the walls, ...
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