I've been looking at Mike Gallagher's SNOT roads, in particular this one because it joins two roads at a ~45 degree angle:

http://gallaghersart.com/gallery/view/category/roads

However, as you can see in the image I made below, it is not *exactly* 45 degrees. Has anyone come up with a working method of joining SNOT roads at regular angles? Thanks.

 

Edited January 18, 20187 yr by Dilvish

You will always need to approximate it I guess. LEGO is very much 90-degrees oriented so making this is already amazing ;)

This must be the most expensive roads per square meter i've ever seen!

Never mind, guys. I was able to get an *exact* 45 degrees using the following step pattern.

:)

[edit]

I made some more progress:

They all align to either 32 or 64 stud widths.

[edit]

This is my next goal:

 

Edited November 3, 20168 yr by Dilvish

couldn't you flip the studs the other way on your 45° road (and switch to regular slopes instead of inverted) and fill in those gaps with #92946 "Slope 45 2 x 1 with 2/3 Cutout"? 

They do flip to either side of the yellow center line. Which is why I can't use the smaller slope.

Download:

http://www.mediafire.com/file/qgt1zrq8v514t93/ldr_diagonal_snot_roads_20161104.zip

Edited November 4, 20168 yr by Dilvish

Some updated designs done in GeoGebra. I have not tried to model them in MLCAD yet.

http://www.mediafire.com/file/0m7e4sd8s9oe865/ldr_diagonal_snot_roads_20171215.zip

Each grid cell is 2x2 baseplates wide.

Edited December 15, 20177 yr by Dilvish

Using texture mapping I was able to create a part to act as a guide while building.

 

Instead of using the above guide, I recreated the shape by hand in SVG, then converted to PNG and input the image into LDraw Digital Mosaic Generator (LDDMG).

 

Here's a screenshot from when I was still working out some of the kinks. The image to the left is 5120x5120 pixels and depicts an area that covers 4x4 baseplates. There are issues with anti-aliasing/sampling in the image to the right. The solution at the moment is to process each color separately. The next version of LDDMG will feature an optional nearest neighbor sampling method, which will eliminate the artifacts supposedly.

 

The result is what you see below. I still have a lot of tedious work to do, since a lot of the parts are in the correct location, but are turned around 180 degrees from what I need them to be. The output of LDDMG is a model consists completely of 1x1 plates. These need to be consolidated into larger plates and bricks as well. The road surface also needs to be lowered by a few units below the sidewalks.

 

Edited December 29, 20177 yr by Dilvish

Wow! That's a lot of work to get the geometry just right.

I have just updated LDDMC so that you can set the scaling quality (Edit->Settings). By using "Nearest neighbor, don't change colors (fast)", you should no longer get the issue with changing colors. Unfortunately there is no line recognition, so you still risk having holes in the lines.

Thanks, Lasse!

First intersection is done.

http://www.mediafire.com/file/7co4p04pt1ru42s/ldr_intersection_left_01_20171231.zip

 

 

very impressive!

I'd be curios to see the ldd file for take some trick for my tramway track!

good work!

 

I uploaded the LDraw model. I think you could import it into LDD by following these instructions:

http://wiki.ldraw.org/index.php?title=LDraw_to_LDD_conversion

Edited January 3, 20187 yr by Dilvish

Does anyone know of a ratio of studs (e.g. "four studs left and seven studs forward", or something) that would allow me to attach a 45 degree build to an "in system" build?

Is that what this Wikipedia article is sort of about?

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

"integer triangle" a.k.a. "Pythagorean triple"

I'm not sure there are any for 45 degree angles.

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Are there any special parts which would allow me to make integer connections?

[edit]

Stack Exchange says the answer to the first question is "No".

https://math.stackexchange.com/questions/2607147/is-there-an-pythagorean-triple-whose-angles-are-90-45-and-45-degrees

Edited January 16, 20187 yr by Dilvish

I think this topic is fascinating, but entirely out of my league. 

The only thing I can think of that may make this build, well, buildable, is by using a kind of tongue and groove to make the 45 degree section mesh up with the aligned freeway. I'll stay out of it, but if you have any questions on the math, I wouldn't mind taking another look. 

 

MAC

Apparently, there are TLG designed models that work within tolerances, where the connection might not be exact, but it's "close enough" for the parts to fit together.

See the yellow 1x6 bars on page 32 here:

http://lego.brickinstructions.com/lego_instructions/set/6199/Hydro_Crystallisation_Station_

I also started another thread here:

https://bricks.stackexchange.com/questions/9652/connecting-out-of-system-roads

Edited January 20, 20187 yr by Dilvish