Geodesic-like tiles to model terrain-scapes
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Jonathan Shaw
May 15, 2013, 2:31:26 PM5/15/13
to geodes...@googlegroups.com
I've been battering my brains against a problem for 5 years, but I'm close to conceding I'm just not smart enough to solve it.
I want to make terrain tiles (e.g. for tabletop miniature wargaming etc.) that allow an indefinite range of natural-looking hills. A small number of basic tiles would be put together in any number of ways. I can see how I could make this a fantastic product, but the geometry of it is killing me. So far the only solutions I have involve far too many basic tiles - something like 6 or 8 for every hill gradient allowed.
The problem is kind of similar to those involved in geodesic domes etc. But there's a twist: not only do we have to have dome-like things (i.e. hills) but these have to fit nicely into a 2d plane - surrounding flat ground. Firstly our domes need to "bell out" at the bottom so as to converge back to the flat plane; but worse the vertices of a dome at its bottom edge need to line up with the vertices of the flat tiles.
The good news is that flat tiles can bend in 1 axis (being made of rubber) and possibly are also reversible (can be used both upside or downside).
Any one got any clues for me? I've spent a lot of time thinking hexes, but maybe I need to break out of the box and go to something weird like diamonds. Classic hex/pent geodesic dome geometry I can't see how to line up with the hex grid on the flat 2d plane. The dome (fundamentally or at its crudest) has 5 "sides" but is being lined up for a 6 sided hole on the plane.
I can see how to share real money with someone who can solve this. But I'd also love to hear any hints anyone can throw out so I can keep scratching away ... it's become an obsesssion.
Jonathan
TaffGoch
May 15, 2013, 2:42:35 PM5/15/13
to Geodesic Help Group
Jonathan,
Temcor, Inc. builds 6-sided, radially-symmetrical geodesic roofs, so there may be hope, yet.
-Taff
Jonathan Shaw
May 15, 2013, 4:27:28 PM5/15/13
to geodes...@googlegroups.com
Thanks for the quikc reply!
That hex roof dome is made of 6 identical triangles as far as I can see, so it nicely illustrates a more general point that we can get what we want using big complex-curved triangles, that flare out at the bottom to join the ground. But what I can't see is how to break those triangles into smaller reusable parts so that we can have different size hills from the same tiles.
Jonathan
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Adrian Rossiter
May 29, 2013, 9:26:22 AM5/29/13
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Hi Johnathan
On Wed, 15 May 2013, Jonathan Shaw wrote:
> I want to make terrain tiles (e.g. for tabletop miniature wargaming etc.)
> that allow an indefinite range of natural-looking hills. A small number of
> basic tiles would be put together in any number of ways. I can see how I
> could make this a fantastic product, but the geometry of it is killing me.
> So far the only solutions I have involve far too many basic tiles -
> something like 6 or 8 for every hill gradient allowed.
For a flat surface you have 6 around a vertex, you have three
kinds of peak with 3, 4 or 5 around a vertex. For saddles you
have 7 or more around a vertx. If the equilateral triangle
surface is too course perhaps you could use some additional
triangle tiles that make shallow pyramids, to various heights,
over an equilateral triangle base.
Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian
On Wed, 15 May 2013, Jonathan Shaw wrote:
> I want to make terrain tiles (e.g. for tabletop miniature wargaming etc.)
> that allow an indefinite range of natural-looking hills. A small number of
> basic tiles would be put together in any number of ways. I can see how I
> could make this a fantastic product, but the geometry of it is killing me.
> So far the only solutions I have involve far too many basic tiles -
> something like 6 or 8 for every hill gradient allowed.
> The good news is that flat tiles can bend in 1 axis (being made of rubber)
> and possibly are also reversible (can be used both upside or downside).
>
> Any one got any clues for me? I've spent a lot of time thinking hexes, but
> maybe I need to break out of the box and go to something weird like
> diamonds. Classic hex/pent geodesic dome geometry I can't see how to line
> up with the hex grid on the flat 2d plane. The dome (fundamentally or at
Maybe you could do something based on equilateral triangles.
> and possibly are also reversible (can be used both upside or downside).
>
> Any one got any clues for me? I've spent a lot of time thinking hexes, but
> maybe I need to break out of the box and go to something weird like
> diamonds. Classic hex/pent geodesic dome geometry I can't see how to line
> up with the hex grid on the flat 2d plane. The dome (fundamentally or at
For a flat surface you have 6 around a vertex, you have three
kinds of peak with 3, 4 or 5 around a vertex. For saddles you
have 7 or more around a vertx. If the equilateral triangle
surface is too course perhaps you could use some additional
triangle tiles that make shallow pyramids, to various heights,
over an equilateral triangle base.
Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian
Adrian Rossiter
May 29, 2013, 10:30:28 PM5/29/13
to geodes...@googlegroups.com
Hi Jonathan
On Wed, 29 May 2013, Adrian Rossiter wrote:
> On Wed, 15 May 2013, Jonathan Shaw wrote:
>> I want to make terrain tiles (e.g. for tabletop miniature wargaming etc.)
>> that allow an indefinite range of natural-looking hills. A small number of
...
and triangles would. This allows the angle around the vertices
to be chosen in 30 degree increments, allowing the general
surface to be smoother.
I think I have seen this in a link recently, maybe posted to
this list, but I can't find it. It was an art exhibit with
the surface made of tiles and hanging like a bumpy curtain
(which probably also moved). I can't remember the exact tiles
used but it was the same principle.
On Wed, 29 May 2013, Adrian Rossiter wrote:
> On Wed, 15 May 2013, Jonathan Shaw wrote:
>> I want to make terrain tiles (e.g. for tabletop miniature wargaming etc.)
>> that allow an indefinite range of natural-looking hills. A small number of
> Maybe you could do something based on equilateral triangles. For a flat
> surface you have 6 around a vertex, you have three
> kinds of peak with 3, 4 or 5 around a vertex. For saddles you
> have 7 or more around a vertx. If the equilateral triangle
> surface is too course perhaps you could use some additional
> triangle tiles that make shallow pyramids, to various heights,
> over an equilateral triangle base.
I don't think the pyramids would help, but using both squares
> surface you have 6 around a vertex, you have three
> kinds of peak with 3, 4 or 5 around a vertex. For saddles you
> have 7 or more around a vertx. If the equilateral triangle
> surface is too course perhaps you could use some additional
> triangle tiles that make shallow pyramids, to various heights,
> over an equilateral triangle base.
and triangles would. This allows the angle around the vertices
to be chosen in 30 degree increments, allowing the general
surface to be smoother.
I think I have seen this in a link recently, maybe posted to
this list, but I can't find it. It was an art exhibit with
the surface made of tiles and hanging like a bumpy curtain
(which probably also moved). I can't remember the exact tiles
used but it was the same principle.
Adrian Rossiter
May 29, 2013, 10:50:16 PM5/29/13
to geodes...@googlegroups.com
http://www.mymodernmet.com/profiles/blogs/ronan-erwan-bouroullec-bivouac-clouds
It looks like squares and equilateral triangles only, with the
squares divided into four triangles.
Gerry in Quebec
May 30, 2013, 6:27:25 AM5/30/13
to Geodesic Help Group
Jonathan,
You may get some ideas for your tiled terrain from the work of the
late Alain Lobel, a French architect. He investigated the geometric
diversity available from assembling many equilateral triangles into 3D
shapes. The edge connections result in both ridges and valleys (i.e.,
concave-convex surfaces). The advantage here for you is that you would
need to manufacture only one tile shape. The disadvantage is that,
because there are both ridges and valleys, you wouldl have "local"
uneveness in your terrain. The tiles must be small enough relative to
the area covered that your terrain appears "globally" smooth.
http://www.equilatere.net/
The Lobel website is in English as well as French.
- Gerry Toomey
You may get some ideas for your tiled terrain from the work of the
late Alain Lobel, a French architect. He investigated the geometric
diversity available from assembling many equilateral triangles into 3D
shapes. The edge connections result in both ridges and valleys (i.e.,
concave-convex surfaces). The advantage here for you is that you would
need to manufacture only one tile shape. The disadvantage is that,
because there are both ridges and valleys, you wouldl have "local"
uneveness in your terrain. The tiles must be small enough relative to
the area covered that your terrain appears "globally" smooth.
http://www.equilatere.net/
The Lobel website is in English as well as French.
- Gerry Toomey
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