On 7/24/2022 11:56 PM, Skybuck Flying wrote:
> Is this algorithm going to work ?:
>
> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
>
> I need it implemented, preferably in Delphi, but C/C++ will do as well.
>

Map a 2d hexgrid to a sphere?

On Thursday, 28 July 2022 at 02:40:01 UTC+3, Chris M. Thomasson wrote:
> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
> > Is this algorithm going to work ?:
> >
> > "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
> >
> > I need it implemented, preferably in Delphi, but C/C++ will do as well.
> >
> Map a 2d hexgrid to a sphere?

To map hexgrid to torus is not a problem but to sphere it is impossible. Have to have 12 pentagons in mix kind of like classical football does. <https://en.wikipedia.org/wiki/Ball_(association_football)> there can be lot more hexagons but then these do not remain regular.

On 7/27/2022 11:35 PM, Öö Tiib wrote:
> On Thursday, 28 July 2022 at 02:40:01 UTC+3, Chris M. Thomasson wrote:
>> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
>>> Is this algorithm going to work ?:
>>>
>>> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
>>>
>>> I need it implemented, preferably in Delphi, but C/C++ will do as well.
>>>
>> Map a 2d hexgrid to a sphere?
>
> To map hexgrid to torus is not a problem but to sphere it is impossible.

Agreed. Some pentagons need to be used wrt sphere.

> Have to have 12 pentagons in mix kind of like classical football does. <https://en.wikipedia.org/wiki/Ball_(association_football)> there can be lot more hexagons but then these do not remain regular.

:^)

On 7/27/2022 11:35 PM, Öö Tiib wrote:
> On Thursday, 28 July 2022 at 02:40:01 UTC+3, Chris M. Thomasson wrote:
>> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
>>> Is this algorithm going to work ?:
>>>
>>> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
>>>
>>> I need it implemented, preferably in Delphi, but C/C++ will do as well.
>>>
>> Map a 2d hexgrid to a sphere?
>
> To map hexgrid to torus is not a problem but to sphere it is impossible. Have to have 12 pentagons in mix kind of like classical football does. <https://en.wikipedia.org/wiki/Ball_(association_football)> there can be lot more hexagons but then these do not remain regular.

Yeah. I was just wondering where Skybuck Flying was going with this.

On Thursday, 28 July 2022 at 23:41:22 UTC+3, Chris M. Thomasson wrote:
> On 7/27/2022 11:35 PM, Öö Tiib wrote:
> > On Thursday, 28 July 2022 at 02:40:01 UTC+3, Chris M. Thomasson wrote:
> >> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
> >>> Is this algorithm going to work ?:
> >>>
> >>> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
> >>>
> >>> I need it implemented, preferably in Delphi, but C/C++ will do as well.
> >>>
> >> Map a 2d hexgrid to a sphere?
> >
> > To map hexgrid to torus is not a problem but to sphere it is impossible.. Have to have 12 pentagons in mix kind of like classical football does. <https://en.wikipedia.org/wiki/Ball_(association_football)> there can be lot more hexagons but then these do not remain regular.
> Yeah. I was just wondering where Skybuck Flying was going with this.

He did not say, but probably needs some models for visualising his UFO or
satellite research or something. To keep all data about whole planet in
memory can be pointless. The parts are more closer to each other in size
compared to for example grid made using geographic coordinate system.

Mapping and flattening parts of such (even irregular, with few pentagons)
hexagon grid to screen gives fine maps. Grid based on geographic coordinate
system also results with irregular pieces so there are no benefit. Easier is to
have more close sub-portions of whole and to convert the coordinates if
needed (as that is just a formula), or even to draw geographic coordinate grid
(as those are just lines).

On Wed, 27 Jul 2022 16:39:43 -0700, Chris M. Thomasson wrote:

> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
>> Is this algorithm going to work ?:
>>
>> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
>>
>> I need it implemented, preferably in Delphi, but C/C++ will do as well.
>>
>
> Map a 2d hexgrid to a sphere?

If so, and with a little compromise to use triangles rather than hexagonals,
then there's plenty of prior art in the "geodesic dome" category.

A "4V Icosa Alternate" geodesic dome, for instance, divides each face of
an icosahedron into component triangles, then subdivides those triangles
such that each triangular section of an icosahedron face contains 16 smaller
triangles. The resulting polyfaceted solid approximates a sphere closer than
an icosahedron does, and still retains the vertices (somewhat warped) of the
original base icosahedron.

All the metrics of such a solid are well known, well documented, and readily
computed. And, it is "triangles all the way down" (sic).

--
Lew Pitcher
"In Skills, We Trust"

On 7/29/2022 10:05 AM, Lew Pitcher wrote:
> On Wed, 27 Jul 2022 16:39:43 -0700, Chris M. Thomasson wrote:
>
>> On 7/24/2022 11:56 PM, Skybuck Flying wrote:
>>> Is this algorithm going to work ?:
>>>
>>> "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication"
>>>
>>> I need it implemented, preferably in Delphi, but C/C++ will do as well.
>>>
>>
>> Map a 2d hexgrid to a sphere?
>
> If so, and with a little compromise to use triangles rather than hexagonals,
> then there's plenty of prior art in the "geodesic dome" category.
>
> A "4V Icosa Alternate" geodesic dome, for instance, divides each face of
> an icosahedron into component triangles, then subdivides those triangles
> such that each triangular section of an icosahedron face contains 16 smaller
> triangles. The resulting polyfaceted solid approximates a sphere closer than
> an icosahedron does, and still retains the vertices (somewhat warped) of the
> original base icosahedron.
>
> All the metrics of such a solid are well known, well documented, and readily
> computed. And, it is "triangles all the way down" (sic).

You know, I never really messed around with geodesic's too much. I am
pretty good with conformal maps where straight lines get bent, and
circles, remain circles. Here is an example of a simple half plane to
disc map:

https://youtu.be/Y6wOS7c7_Xg

https://youtu.be/bpBvK-VhSjA
(try playing it slow motion...)

thanks for the excellent reply. I need to refresh my brain.
Unfortunately, I am currently porting some of my old code to my new'ish
plotter. I will get back to you.

https://commons.wikimedia.org/wiki/File:G%C3%A9ode_V_3_1_duale.gif