Angle Plate Angles?

[mouseketeer]

I hope I'm not being incredibly silly asking this, but it's driving me crazy! Could someone tell me what angle I need these angled plates to be at in order to make a full curve - I've been doing it by trial and error but constantly have the last plate overhang in whatever direction, meaning I can't snap bricks around it. Thank you!

[Murdoch17]

This is one of LDD's greatest flaws: it is almost impossible to do this "properly" in the program, but it is easy in real life... i blame the hinge tool's bad design. Basically, as far as I know, (and I could be wrong) it ain't happening without slight overhang. sorry.

[Beck]

I would use the formula for the sum of the interior angles of a polygon. (n-2)180

Your polygon pictured above is a Hexadecagon (16 sided polygon)

(16-2)180 = 2520

dividing by 16 gives you the interior angle of each of the angles 2520/16 = 157.5

however the angle you input for the hingle plate is the exterior angle therefore you must subtract 157.5 from 180 to get 22.5.

 

About the overhang, just don't worry about it

 

[SylvainLS]

From the top left: ±21.094°, ±23.906°, ±23.906°, ±21.094°. (21.1° and 23.9° should work.)

Found with a little geometry: the green segment figures the middle segment of the curve, it’s 2 studs long, 1 on each side of the symmetry x=y axis (not shown), and as you want symmetry, it will be at −45° (or at right angle from the x=y axis). We don’t know where it will be exactly but its left end will be on the blue line (perpendicular with the green segment).

The red segment is the top left segment, its left end is 4 studs from the center of the curve we’re making. It’s 2 studs long (hence the bigger circle) and its right end will also be on the line drawn from the end of the green segment. As we want the curve to be convex, we take the right-most intersection point between the bigger circle and the line.

And we find that the inner angle is 68.906°, so the first hinge part angle will be (90°−68.906=) ±21.094° (sign depends on the subpart you turn). As we want the middle segment at 45°, the second hinge will be at (45°−21.094°=68.90°−45°=) ±23.906°. And symmetrics for the two other hinges.

Easy peasy 

Just now, Beck said:

I would use the formula for the sum of the interior angles of a polygon. (n-2)180

You can’t use that because it’s not a regular polygon: its summits have to be on studs. (Here, the “radius” for the connected sides is exactly 2.5 the length of a side. A regular hexadecagon has a radius of about 2.56 times its side.)

[mouseketeer]

Thank you everyone, and especially @SylvainLS! That's genuinely impressive - it might take me a bit of time to understand precisely how you figured that out, haha, but it does work! Thank you!

[gedren_y]

I have done several sizes of circular builds in LDD. The geometry of LEGO will not allow for a truly circular curve that lines up in the way you wish. You would need to calculate the curve as part of a near circular ellipse, or the apex curve of a parabola, and the points along the curve would be the centers of the hinges rather than the studs. I haven't the mathematics background to calculate this myself, but I understand enough geometry to see the problem.

There is an easier solve, and that is the curved section of wall not connect to both straight sections, but simply sits against one wall. This is easy to do with the hinge control tool, but perfect angular calculation goes out the proverbial window.