A Little Maths Problem

I have a question for all those more mathematically minded than me:

I'm running a small road through some land that I own in Wainscot (106,134,47) and I need to make a couple of turns. I'm not trying anything fantastic, it's actually a simple shift to the side by 10m. The road I've used so far is 10m wide and made of two 10x5x5 prims (come see it if you want to know what I mean).

I've put something in place already but what I've actually ended up doing is simply skewing the road by 45degrees, rather than actually turning. I reckon the skewed section to be approx 7m wide rather than the 10m it should be.

Can anyone tell me the best way to construct the pieces I need? If you want to meet inworld at the site I'd be happy to, send me an IM in world and I'll do my best to get back to you ASAP. I'm in the UK mind you so times I'd be available to meet you would be dependant on being 8hours behind SL time.

Any help would be VERY much appreciated!

I had a similar problem for a path and I just cut a cylinder to a less than 90 degree segment and hollowed it to fit path width and aligned it to path. Then shift copied and flipped and rotated the next prim to bring the curve out onto the new line I wanted.

Hope that makes sense. Sorry at work atm so I'm flipping my hands around in the air and twisting my head to imagine it and drawing strange looks from colleagues.

That is one possibility I guess but I can't see the texture fitting then. I'm using one of the library road textures which requires two prims for each stretch. One for the left of the road and one for the right. I do like the idea though, certainly would've been a great help were it not for the texture!

Am I right in thinking you essentially need 2 90-degree bends, using 2 prims each and using the standard Linden road textures?

No, I need a 45 degree bend that can be made from a few prims, I will then go straight from there so far and then turn back 45 degrees again so that we're running parallel to the original piece. The only reason for two prims on the existing road is because of the Linden textures, yes. Come by and see what I've done so far if you like

http://slurl.com/secondlife/Wainscot/106/134/47

What you want to do is this:



The two triangles are each cubes, simply cut in half.

Yep, I get it now - I can't swing by right now because I'm at work, but I will do later - if I understand you correctly, it shouldn't be hard to create. Complicated by the fact that Linden roads are 2 prims, each textured with half the road, like you say, but do-able nontheless.

Chosen, yes, that's what I want to do, only as I mentioned each prim is already split in 2, so it's not that simple. I guess it would be more like this:


or maybe like this (which would be better I think):

Oh, i was thinking about making it actually curve, not straight diagonals.

A curve would be impractical because of the textures, though more ideal in reality. If you look at how roads are created in games you find they're constructed from flat faces rather a curve because in these environments the computer creates a curve from a number of flat faces anyway. Less prims in using a cylinder but less control over what's happening!

well, you could make the road smaller. Just combine the two terxtures into one, then it would be much easier to work with. Then you could have each length of road just 10x10x5, and with the two triangle method, you could do it easier (In my mind it works perfect, maybe not in reality).

Another method would be to either make your own road textures meant FOR the bend, or invest in prefab road pieces, with curves, or even have someone else make them if you arent able to find or make yourself. Plenty of people more than capable in SL o.o

How can I combine the two textures when they're library textures? If I were able to export them then I would but I can't can I?

What do you mean "combine the two textures?" I'm assuming you have one texture that looks like the width of a road, with a dotted line running lengthwise down the middle, yes? You can stretch or shrink the texture to repeat itself X times on the surface of the prim; in the above case, you'd only want it to appear one time on the width of the prim, but any number of times (including less than one) on the length of the prim?

Can you not make a cube, rotate it 90-degrees on x-axis, then taper-x to 50 or so and shear-x to -25 or so? Then, take copy, and change the shear-x to +25.

Copy the texture from the library to your inventory. Then double click it to open it in the viewer, and then go File -> Save Textrure As...

Thanks for explaining that chosen few, I was about to respond to it then read yours ^^ Anywya, also, you could always just find a single image road, maybe even better quality than the supplied ones. Works just as well!

Yeah, probably, but personally I don't have a problem with the library one. Didn't realise I could save it though, thanks for that, I shall do that and reduce the prims! Still to work out that corner though!

OK, I exported the library texture and made it into a one piece texture so I can reduce the number of prims required. With that done I figured the triangle I needed would be a simple (in my head) case of an isosceles triangle with two long edges needing to be 10m but what would the other be?

Well the inner angle would be 45degrees, we know that already, so I set about trying to find out how to calculate the height of the triangle, since we all know that SL's building tools aren't advanced enough to be able to create triangles by angles. I couldn't find the information I needed so then it occurred to me that an isosceles triangle is actually two identical right-angled triangles back to back. With that in mind I went looking for right-angled triangle calculators on the web and found this one:

http://www.cleavebooks.co.uk/scol/calrtri.htm

Using that I set the hypotenuse as 10m and the angle 'A' as 22.5 degrees (half of 45 degrees since two triangles will merge to make one) and calculated the rest. I got a height of 9.240 and a width of 7.660. I set these figures and got the triangle I wanted.

Now, the placement... SL won't place it how I want to by using the 'Center Copy' option which I use to accurately place things when I'm working on the square, so I dropped a prim in the exact centre of the triangle while it was still at 0degrees rotation and moved it to the point. I then linked the two with the new prim as the parent. I can now work out exactly where I want it placing by simply moving 5m across the X and 5m across the Y from the last 10x10m road prim. Once there I rotated the whole thing by 22.5degrees and there it is, sat perfectly in place.

The only problem I've had now is getting the road between the two to fit perfectly. My maths worked it out to be a round 17m between the two so I dropped a couple of prims in rotated at 45degrees and figured they'd be perfect. One side is, couldn't ask for more, but the other side has a slight overlap which is bugging me. I'm a bit of a perfectionist and it's really annoying me! I'll figure out what's happened soon, I suspect it's something to do with SLs accuracy levels. I'm used to being able to work to much finer degrees of accuracy but I figure it's good enough!

Thanks for the help guys, do feel free to pop by and see what you think.

Landing, I gotta tell ya, you're making this way more complicated than it needs to be. All that math is totally unnecessary. SL makes it really easy just to snap things into place.

Assuming your configuration is like that of the diagram I posted, which it sounds like it is, do the following:

1. Place the first cube. Name it Cube 1. Size it to 10x10M on X and Y.

2. Make sure Use Grid is turned on in the editor, and set the ruler mode to local.

3. Shift-drag Cube 1 along the positive local X axis to leave a new copy behind (Remember, when you shift-drag, the one that stays behind is the copy; the one you moved is the original. Name the new one Cube 2.), and then snap Cube 1 to be flush with Cube 2 by moving the mouse onto the on-screen ruler while you're dragging. Repeat the process to create a third cube (Cube 3), so you have 3 in a row. The order from West to East should be Cube 2, Cube 3, Cube 1.

4. Select Cube 3 (the one in the middle) and cut in half to make it into a right triangle. Make the cut run from 0.5 to 1, so that the hypotenuse runs NE/SW and so that the two non-hypotenuse sides are the North side and the West side. Cut Cube 1 (the one on the East side) in half as well, but make this cut run the other way (0.25 to 0.75), so that two hypotenuses frame a wide open V-shaped space.

5. Now, select Cube 3 (the middle one) and press shift-G (with chat closed). This will put the ruler in reference mode, with Cube 3 as the origin. Rotate Cube 1 by 45 degrees, and snap it to 0 on both X and Y on the reference grid. The bottom most corners of both triangles should now be flush.

6. This part here is the only part you won't be able to snap, so work carefully. I'd recommend going into wireframe view (ctrl-shift-R) and zooming way in, so you can see precisely what's happening. Select Cube 3 (the middle one), and shrink it along the X axis until its NE corner is flush with NE edge of Cube 1 (the one you rotated). Once you've got that done, you'll be able to snap Cube 1 to the same size, since Cube 3 is still our reference object for the grid units. Assuming you do everything correctly, you should now have two perfectly aligned right triangles, flush at the hypotenuses. Exit wireframe view (ctrl-shift-R).

6. Put the ruler back into local mode. Shift-drag Cube 1 along the local positive X axis to leave a new copy behind (Cube 4), and snap Cube 1 to be flush with it. Now uncut Cube 1 so that it becomes a rectangle again instead of a triangle, and stretch back out so that it is 10M long again. You're done.

This whole process should take just a few minutes, no math needed whatsoever.

You're going to have to show me that because I have the following problems with it:

1) I'm not sure I understand what you're saying

and

2) It sounds like you're creating a triangle with a height of 10m and not a 10m hypotenuse. I don't see how you've created a triangle with a 45degree angle in it either

If you want to meet up in world sometime you can show me your theory but in the mean time I'd be inclined to stick with the way I know

Oh, I've done it like this by the way:

If you're doing it by your diagram, then my method wouldn't work. That's not what you described you your last post though. You said you wanted to use two right triangles to create a 45-degree turn. To me, that sounds exactly like the diagram I posted. Your diagram doesn't have a right triangle in it at all.

The reason you don't see how I created a triangle with a 45 degree angle is because I didn't. I created two right triangles, each with 22.5 degree angle, which when butted together, hypotenuse to hypotenuse, combine to form a 45 degree turn. This is precisely what was in my diagram.

As for not understanding what I'm saying, have you tried following the steps one by one? Granted, it's somewhat difficult to explain these procedures just with words, but I think you'll find that if you do exactly what the words say exactly when they say to do them, that you'll be able to follow along. If you tried just to read the whole thing at once, then it's understandable that you might be lost.

Sorry, but I'll have to decline meeting with you in-world. I don't mind putting a couple hours a day into the forums, as one post can help thousands of readers. If I were to meet with everyone individually, it would take years to accomplish the same thing, and I'd never get anything else done. As a rule, I never bring forum business in-world. Hope you understand.

I'm happy to keep discussing it here if you wish.

Sorry, what I meant when I said that I'd used two right angled triangles is that an isosceles triangle is two right angled triangles backed up to each other, so that was how I worked out the measurements I needed.

I had a go at your instructions but it did loose me somewhat, when I have a little more time I'll have another go. I can't be doing with having to work everything out with a calculator if I don't have to but I will need to find a more precise way of lining up than your 'by-eye' method, that would never do for me the way I build.

Thanks for your time anyway, I understand that you can't make it in world to explain further, I appreciate the time you've already put in.

Ok, I get what you meant now, Landing.

So you know, there was only one small part of one step in my whole post that required aligning anything by eye. Everything else utilized snapping to the grid, which is actually way more precise than the numbers in the editor can be.

More precise? My understanding is that the displayed numbers are rounded but that doesn't prevent entering higher precision numbers.

BTW, I can see why Landing found your instructions difficult to follow. You might want to revisit step 3 as it's a little confusing. Might be easier to just rename the dragged prim twice so the order ends up as 1, 2, 3

Landing, if you need to do this frequently it might be worth figuring out the math equivalent to calculate the X size in Chosen's step 6 as his way will definately be quicker once you get the hang of it. Most builders either use eye or a calculator in their building for things like this, it's personal preference which it is.

As I understand it you need to be working to a minimum 0.005 accuracy, and doing it by the math should be just as accurate as by the grid. I tend to work to a 0.125 accuracy which normally serves me well by the grid but then type the exact figures when I need more accuracy.

I followed your steps as best as I could and this is how it went for me (each block shaded to show differences; 1 is lightest, 3 darkest):







Clearly I did something wrong but I'm not familiar with this reference rule, I always work by world.