Three Rivers Region

[metarvo]

It looks like you're actually learning to BAT quite well, or at least modify an existing model, and you'll be moving on to texturing soon, it sounds like.  I think the windows are the best part.  

 

Wait, the pics are from RL, not SC4.  Anyway, I'm looking forward to whatever it is you have next, David.  

[Jmouse]

Good luck with your project David and hurry back to us soon. Your legion of fans is hungry for puzzle pieces!

Later...
Joan

[dragonshardz]

Congrats, metarvo, welcome to the Triple-0 Club!

[io_bg]

It looks we hit 8000 comments! Congratulations!

[Pat]

David your Photoshopping skills are real good there!!! Man you got talent!!! ooooh wait I am sooo confussed those are RL pics lol hehehehe.......



Special Announcement!!!  Special Announcement!!!  Special Announcement!!!

Oooo oooo for anyone wondering when the rest of the Podcast Interview with David is coming, trust me its coming here soon!!! I had gotten a new computer and ran into a few snags with going from XP to VISTA uggh......

Anyways Stay tuned to the Podcast thread where there will be the next episode coming soon with a GREAT surprise!!!!  Sorry little excited here as this next episode is going to be umm kinda HD or at least digital experience lol....

OK Back to regular scheduled programing here and David sorry for hijacking here,

Pat

[calibanX]

That looks like a fun project David. I wish I was handy with the tool box like you are. I'm actually all thumbs. 

Congrats on 8000.

Geoff

[girlfromverona]

Looks like you're just as handy in RL as you are with making stuff for SC4, David! 

[frdrcklim]

Wow. That's balance or RL and SC4. I dun think I can do something like that. Cheers to David .

[dedgren]

I'm going to go canoeing with my daughter for a couple of hours this afternoon.  I'll try to bring back a couple of pics.

This morning, I'm getting a start on the HDR transition curves.



I'm hoping that Steve (z) and I can move the first phases of that project along pretty quickly, as it is very straightforward work.

UPDATE:  Done with this one.



These are 4x oversize, which is why the newer WRC/FAR textures look so much better in the game than the old ones.  I'll be cleaning those up, too.

* * *

Congrats to our great friend metarvo for joining the Triple-0 Club.  We'll have to do something about that...

Later.


David

313643

[z]

My goodness!  David just got back, and already he's building these pieces faster than I can design them!  I guess it's time to design a few more. 

This post is a major followup to my first post, and summarizes most of my thinking in this area at this point.  It's divided into three parts.  First, I'll answer various questions that people have asked since my first post.  Second, I'll answer a whole class of questions by explaining just a little of the math behind FARs.  This will explain such things as why Half Diagonal Roads are 26.565° and not 22.5°, why it's not possible to make straight FARs of 30° and 60°, and in general, what the relationship of FARs and their angles is.  Third, I will unveil Infinitely Variable FARs, which will allow roads of any angles to be built with a relatively small number of puzzle pieces.  So you can build a FAR of 30° or 60° or whatever, but such FARs would have slight, occasional curves in them.

Questions

Even though the new roads are meant for urban areas, there are indeed some rural areas that might benefit from varying angles of roads.  Will there be an option to build a sidewalk-less HDR, HDA, or FAA? 

Definitely.  I just put in the sidewalks because it was an easy way to illustrate the roads and their orientation.  But these roads will be like all network pieces, in that different base textures (or none) will automatically appear, depending on surroundings.

With all the add-ons and puzzle pieces being made for roads and rail, urban and rural and euro, I can't be the only person playing this game who's game menus are getting very crowded, complex, and tedious to wade through to find that "just right" piece of whatever that I want to use.

No, you have lots and lots of company!  I think that what you see later in this message would be virtually impossible to manage without the DAMN menus, which were mentioned earlier.  For network pieces, they allow both a hierarchical structure, and tab rings as well.

I like the DAMN stuff, and the stuff that hides lots until they are plopped, then disappear again when bulldozed, but for some reason, even with those installed, I still get every single lot showing in my menu's.  The military, airport, HSR all show in my menu's, even if I do not plop those lots that are supposed to show them

This can all be easily customized.

FARs, Angles, and Trigonometry

Here I'll explain the math behind FARs, as promised above, including why completely straight FARs can be built only at certain angles.  I'll keep the math simple.  Those with a good knowledge of trigonometry can skip this section, as can those who just hate math.

First, consider the following diagram, which is an abstract version of an SC4 map:

Each square represents a square on the map.  A, B, and C represent roads.  A is a road ten squares long going east, while C is a standard diagonal road that goes ten squares east and ten squares north.  B is what I have called a Half Diagonal Road (HDR); it goes ten squares east and five squares north.  Since A and C join at a standard 45° angle, and B rises exactly half the distance of C in the same number of squares, you might at first think that the angle between A and B is half the angle between A and C, or 22.5°.  But if you look at the picture, it looks like it's more than half the angle.  In fact, it is; it's 26.565°, and that's the angle that HDR's run at.

Where did that number come from, and why is it not 22.5°?  If the starting point on the left were the center of a circle, and A, B, and C all extended to the circle's edge, then the point where B intersected the circle would be exactly between A and C when the angle between A and B was 22.5°.  The difference between that example and the picture above is that in a circle, all lines connecting the center to the circle are of equal length.  Here, A, B, and C are all different lengths.  Since A, B, and D form a right triangle (there's a 90° angle at the right end of A), and A, C, and D form another right triangle, we can use the Pythagorean formula x² + y² = z² to determine the lengths of B and C.  Since A and D are each ten squares long, and B intersects D at its midpoint, this formula tells us that C is 14.14 squares long, and B is 11.18 squares long.

So what happens if we take a line starting from the left point, make it as long as C, and angle it at 22.5°?  We get line E.  Line E also ends five squares north of A, but it does so three squares east of the end of A.  And it intersects D less than four squares north of A, less than 40% of the ten-square length of D.  So roads running at 22.5° are not particularly useful in this context.

How do we know that the angle of our HDR is 26.565°?  The answer is that we use the tangent and arctangent (also known as inverse tangent) functions.  For triangles shaped like ours, the tangent of an angle is the ratio of its D side to its A side.  So for a 45° angle, where D and A are equal, the tangent is 1.  The line B intersects D at its halfway point, so the tangent of its angle is .5.  We find out what angle corresponds to a tangent of .5 by using the arctangent, or inverse tangent function.  And the arctangent of .5 is 26.565°.

Now we're ready for the final step.  How do we know what angles we can use for FARs?  Let's start with David's original 2x3 FAR, which in one orientation, rises one square north for every three squares it travels east.  This means that its tangent is 1/3, or .33333333...  If you type the latter number into your calculator and hit the "arctangent" button (or "inverse" and "tangent" buttons), you get 18.435°, which is the angle of this FAR.  So the two FARs we've mentioned so far have had tangents of .5 and .33333333...  Both of these numbers can be represented as fractions with small denominators, which means that they can be constructed as small puzzle pieces.

What if we wanted to build a FAR with an angle of 22.5°?  What shape would its puzzle piece be?  The tangent of 22.5° is 0.41421362373095..., which is an irrational number.  This means it would be impossible to build a puzzle piece that could be tiled with that angle.  Similarly, for those interested in 30° and 60° FARs, the tangents of these angles are also irrational, at 0.57735... and 1.73205..., respectively.  So it's impossible to build FARs for those angles as well.

What can we do then?  Quite a bit, actually.  And that's the subject for the next section.

Infinitely Variable FARs

So you want to destroy the grid, you say?  Really destroy it, so there's no trace left?  Here's how you do it.

Since the game began, up until last year, the straight roads of the game could be represented by the following diagram:

These include roads that run in one of the two grid directions, as well as the 45° diagonal roads.  All possible road angles are separated by 45°.  When David introduced the straight FAR piece, along with its standard variations, that diagram became this:

Quite a difference!  And the road spacings are pretty symmetrical.  I think that a diagram like this, especially when compared to the one above, showed how significant a change David's one straight FAR piece produced.  Differences in possible road angles now range from 18° to 27°.  Now here's what happens when you add in the HDR I proposed in my last major post:

There are certainly more possibilities, but also a wider range (in percentage terms) of separation between possible road angles, which now range from 8° to 19°.  Yet the higher end of that range is almost as low as the lower end of the previous range (18°).

Where do we go from here?  Is it possible to fill in the bigger gaps and get a fairly uniform distribution of angles, at the same time adding a relatively small number of simple puzzle pieces?  Fortunately, the answer is "yes," and the resulting difference of angles between any two roads will lie in the rather narrow range of 8° to 11°.  We will end up with a picture looking something like this:

(I say "something like this" because it will actually be more uniform; my drawing skills just aren't that great.)  This is just for completely straight FARs; intermediate angles (the "infinitely variable" part) can be simulated, as I describe below.

What does it take to get this really complete type of coverage?  Just two more types of FARs.  And interestingly enough, they're both related to David's original FAR.  To determine what these are, once again, it's easier to work with tangents than angles.  We only have to consider tangents up to 1 (angles up to 45°); the other angles are taken care of by rotations and mirrors of these pieces.

Fortunately, this can be done by using the principle of using tangents that can be expressed as fractions with low denominators.  So instead of thinking about angles of 30°, 60°, and 90°, in this case we think of tangents of 1/3, 2/3, and 1.  David's original FAR piece has a tangent of 1/3; the standard diagonal has a tangent of 1.  Currently, their is no piece with a tangent of 2/3.  That would correspond to an angle of 33.69°.  This fits very nicely in the gap between the HDR at 26.565° and the full diagonal at 45°.  Here's what such a piece would look like, in both road and avenue form:

     

The road piece is 3x3, while the avenue is 3x4.  Once again, the avenue still tiles quite nicely at the standard avenue width.  (BTW, these pictures are completely to scale.)

Now all that's left is the large space between the two axes and the various forms of the original 2x3 FAR piece.  This space can be cut almost exactly in half with a 2x6 road piece; the avenue piece is 3x6.  This size is a little ungainly, but for this angle, there's really not much choice.  The tangent of the angle is 1/6, or half that of the original FAR piece; the angle itself is 9.46°.  Here are the pieces:

So that's it for the straight FAR pieces!  What else is necessary?  First of all, I promised Infinitely Variable FARs, and we don't yet have enough to do that.  But all we need to do this are a pair of transition pieces for each FAR, one going up to the next higher angle, and one going down to the next lower angle.  By mixing these transition pieces with the various FARs, we can then get any angle of road, although part of the road will be curved.  For example, suppose we really wanted a 30° road.  The two closest straight FARs are 26.565° and 33.69° - almost equidistant from 30°.  So we could run a stretch of the first FAR, plop a transition piece to the second FAR angle, run a similar stretch of that road, and then plop a transition piece back to the first FAR angle.  We know we'll have built this correctly if at the end of our road, the ratio of the road's height above its starting point to the length it's run (in other words, its tangent) is approximately .577, which is the tangent of 30°.

What else do we have to do?  Intersections!  These are obviously a necessity for city usage.  At this point, I don't think it's necessary to create all types of intersections between all types of FARs.  And there should generally be enough flexibility in placing the transition pieces so that intersection versions of them need not be made.  But just dealing with the straight FARs, there's plenty of work to do.  I think that for each type of FAR, the types of intersections that David has made for his original FAR should cover the road intersections nicely.  But in addition to these, intersections with grid-aligned streets and avenues are also necessary, as well as underpasses for straight and diagonal elevated highways.  Finally, intersections with grid-aligned versions of as many of the existing networks as possible would be an important part of this project.

That's it for now.  This obviously is not a complete spec, but it's enough to get started, if people so decide.  At that point, the exact details can be worked out.  However, I think that what I've spelled out here is enough to create a set of FARs that will permit the building of roads at any angle.

[mike3775]

And here I thought I was done with math years ago 


You guys are simply amazing the way your taking an obsolete game, and making it brand new again, all without the help of Maxis and getting into the .exe

[metarvo]

Wow, z!  You've made all of the FAR calculations look so easy, and the new FAR pictures may well be one of the highlights of my week.  From what you said about the sidewalks, it sounds like the new puzzle pieces will be wealth-dependent.  If so, that would be great.



Of course, I am also impressed with the transition curves.  Good work, David!  This is just one more excellent 3RR Moment, and it is yet another highlight of my week.

[sithlrd98]

OK...The math is way over my head , but I like your charts (need some color )lol

Of course , with the subject of side walking these , if people want it , I will do it.(although I am still trying to get them to follow the curve correctly).

Jayson

[abcvs]

Well hello there... I have just had a very pleasant catch-up from page 390 or so...   you folks have been busy in the last 10 pages...  past the 300K views, and having a crack at David's old nemesis...  "NO TRANSIT UNDER BRIDGES" ...  heh...  I think 'can't be done' is something that is not in the lexionary thinking around here...

Oh... and I did see this little snippet..

I'm fixing that pesky STR S-curve path...

Did ya, did ya, did ya?  Did ya remember us poor lefties?

Now... I know this may seem a little unusual... (and I hope no one minds) but this guy has only posted at Simpeg a couple of times...

You guys just HAVE to take a look at what he has done with Peg's PPond Flora with a little sprinkling of RRP for colour...

http://paeng.e-workers.de/gallery/city_journals/mountainview/index.php

Man I will probably bust his bandwith posting the link in here but it is seriously well worth a look - simply stunning stuff.

[MandelSoft]

Just read your post while I'm sitting here in my mathematics class, and I did understand what you're trying to show, honest! Great work you come up with!

[dedgren]

Back from canoeing.

My daughter Liz and I drove out to Long Lake



a beautiful mile long lake south of the Glenn Highway about 40 miles/65 kilometers from where I live.



The lake is long and narrow, and lies at about 3,700 feet/950 meters above sea level.  As noted, I took Liz



who paddled bow.  She's my "Peace Corps" daughter, and has gone to work for SGS North America [linkie] as an environmental testing tech pending heading for medical school a year from now.

Long Lake is at the base of a high ridge, and many interesting rocks dot the water's edge on the north shore.



Big interesting rocks.



I can only imagine the splash this one made falling in the water from several hundred feet up the ridge.



To the south, the mile and a half/2,500 meter high peaks of the Chugach Mountains are always visible.



Headed east along the north shore, the Glenn Highway crosses several avalanche chutes as it climbs to the top of the ridge above the lake.



Up close, those are car-sized rocks just waiting to fall.



The road affords beautiful views of the lake as it ascends.



It's not so bad from down below, either.



So, four hours well-spent.  On returning, I picked back up with the HDR textures.

Here's the HDR to FAR transition.



I think Steve's (z) correct- these will really expand your road-building options.  They're fun to put together, too.

Later.


David

313983

[Pat]

Steve some great math there and even though that is way abouve my head looking good there for sure!!!!!

David your going HDR??? wow!!!


WOW awesome pics there David from canoeing today!!!! Ooooh hey good news so far the final productions are going good!!!

[z]

David, all I can say is WOW!    I was a little concerned about how these transitions would actually look, but what you've shown is better than anything I imagined.    If the Infinitely Variable FARs get done, they will definitely live up to their name.

[sithlrd98]

Beautiful pics David! That is one thing that living up there definitely has....nature! The HDR piece is coming along quite nicely as well!

Jayson

[wes.janson]

Wonderful pictures David. It looks like you had a great time. Reminds me of my summers in the B.C. interior.