DGGS/Proj/DT: Difference between revisions

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[[File:Disdyakis_30.png|thumb]]

Projection onto a 120-sided polyhedron, from the English [[wikipedia:Disdyakis triacontahedron|'''D'''isdyakis '''T'''riacontahedron]] (a Catalan solid with 120 identical triangular faces), proposed in 2020 by https://www.mdpi.com/2220-9964/9/5/315

Projection onto a 120-sided polyhedron, from the English [[wikipedia:Disdyakis triacontahedron|'''D'''isdyakis '''T'''riacontahedron]] (is a Catalan solid with 120 identical triangular faces), proposed in 2020 by https://www.mdpi.com/2220-9964/9/5/315

Below is the 120-faced polyhedron:

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== Modeling the rhombic triacontahedron ==

The assembly of 4 by 4 faces results in a [[wikipedia:Rhombic triacontahedron|Rhombic ~~Triacontahedron~~]] with 120/4=30 quadrilateral faces, used as L0 of a [[Generalized Geohash/pt|GGeohash]].

The assembly of 4 by 4 faces results in a [[wikipedia:Rhombic triacontahedron|Rhombic triacontahedron]] with 120/4=30 quadrilateral faces, used as L0 of a [[Generalized Geohash/pt|GGeohash]].

[[File:RhombicTriacontahedron-30facesFrom120.png|340px]] [[File:Rhombictriacontahedron_net.svg|340px]]

On the faces of the [[wikipedia:Rhombic triacontahedron]], the smaller angle of the rhombus is 63.43°, closer to 90° than the rhombus of the [[DGGS/Proj/ISEA]] projection, therefore superior (with capacity) also in the shape ~~of the cell~~.

On the faces of the [[wikipedia:Rhombic triacontahedron]], the smaller angle of the rhombus is 63.43°, closer to 90° than the rhombus of the [[DGGS/Proj/ISEA]] projection, therefore superior (with capacity) also in the cell shape.

Recent works by Liang et al. 2022 re-equated the [[DGGS/Proj/Planos concorrentes|construction]] of the quadrilaterals of the projection, https://doi.org/10.1080/17538947.2022.2130459

[[File:Tjde a 2130459 f0007 ob.png|center|thumb|680px|Same ''Rhombic triacontahedron'' in alternative construction. ]]

[[File:Tjde a 2130459 f0007 ob.png|center|thumb|680px|Same ''Rhombic triacontahedron'' in alternative construction.]]

[[File:Fig3-dingEtAll2024.png|center|semmoldura|680x680px]]

== Local country adjustment ==

[[File:ProjDT-BR-dobras1.png|thumb|380px|Example of possible altitude adjustment over Brazil. ]]

[[File:ProjDT-BR-dobras1.png|thumb|380px|Example of possible altitude adjustment over Brazil.]]

Still under study if truly viable... Complementary strategies, using [[DGGS/Proj/Planos_concorrentes#Proposta_da_re-proje%C3%A7%C3%A3o_linear_em_planos_concorrentes|Proposal of linear re-projection (hinges)]], for adjustment to the country's ~~relief~~, or at least its median altitude. The strategy may ~~make use of~~:

Still under study if truly viable... Complementary strategies, using [[DGGS/Proj/Planos_concorrentes#Proposta_da_re-proje%C3%A7%C3%A3o_linear_em_planos_concorrentes|Proposal of linear re-projection (hinges)]], for adjustment to the country's terrain, or at least its median altitude. The strategy may utilize:

* Change of ellipsoid radius, so that the geoid better tangents the median altitude. Not well regarded ~~as it causes~~ undesirable side effects in positioning.

* Change of ellipsoid radius, so that the geoid better tangents the median altitude. Not well-regarded due to causing undesirable side effects in positioning.

* Change in the choice of the "secant plane to the ellipsoid". This allows some compatibility between the two, DGGS and [[DNGS]], as they use the same polygons in the projection (solid angles are preserved).

In the use of DT for each DNGS (each country), the choice of quadrilaterals ~~ceases to have~~ a greater commitment to the ''rhombic triacontahedron'', it is free. It returns ~~to being the commitment~~ to m<sup>2</sup> as a reference.

In the use of DT for each DNGS (each country), the choice of quadrilaterals no longer has a greater commitment to the ''rhombic triacontahedron'', it is free. The commitment returns to m<sup>2</sup> as a reference.

The "compatibility" between DNGS and DGGS (based on DT projection) would be ~~only~~ in the use of the reference projection and simplicity in the conversion algorithms between grids.

The "compatibility" between DNGS and DGGS (based on DT projection) would only be in the use of the reference projection and simplicity in the conversion algorithms between grids.

== ISEA Conversion ==

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* [[DGGS/Proj/ISEA]]

* ~~Use~~ in https://www.mdpi.com/2220-9964/11/6/322 for distance transform Canada

* Usage in https://www.mdpi.com/2220-9964/11/6/322 for distance transform Canada

[[Category:Public]]

@@ Line 1: / Line 1: @@
-{{idiomas}}
+{{Idiomas}}
 [[File:Disdyakis_30.png|thumb]]
-Projection onto a 120-sided polyhedron, from the English [[wikipedia:Disdyakis triacontahedron|'''D'''isdyakis '''T'''riacontahedron]] (a Catalan solid with 120 identical triangular faces), proposed in 2020 by https://www.mdpi.com/2220-9964/9/5/315
+Projection onto a 120-sided polyhedron, from the English [[wikipedia:Disdyakis triacontahedron|'''D'''isdyakis '''T'''riacontahedron]] (is a Catalan solid with 120 identical triangular faces), proposed in 2020 by https://www.mdpi.com/2220-9964/9/5/315
 Below is the 120-faced polyhedron:
@@ Line 17: / Line 18: @@
 == Modeling the rhombic triacontahedron ==
-The assembly of 4 by 4 faces results in a [[wikipedia:Rhombic triacontahedron|Rhombic Triacontahedron]] with 120/4=30 quadrilateral faces, used as L0 of a [[Generalized Geohash/pt|GGeohash]].
+The assembly of 4 by 4 faces results in a [[wikipedia:Rhombic triacontahedron|Rhombic triacontahedron]] with 120/4=30 quadrilateral faces, used as L0 of a [[Generalized Geohash/pt|GGeohash]].
 [[File:RhombicTriacontahedron-30facesFrom120.png|340px]] [[File:Rhombictriacontahedron_net.svg|340px]]
-On the faces of the [[wikipedia:Rhombic triacontahedron]], the smaller angle of the rhombus is 63.43°, closer to 90° than the rhombus of the [[DGGS/Proj/ISEA]] projection, therefore superior (with capacity) also in the shape of the cell.
+On the faces of the [[wikipedia:Rhombic triacontahedron]], the smaller angle of the rhombus is 63.43°, closer to 90° than the rhombus of the [[DGGS/Proj/ISEA]] projection, therefore superior (with capacity) also in the cell shape.
 Recent works by Liang et al. 2022 re-equated the [[DGGS/Proj/Planos concorrentes|construction]] of the quadrilaterals of the projection, https://doi.org/10.1080/17538947.2022.2130459
-[[File:Tjde a 2130459 f0007 ob.png|center|thumb|680px|Same ''Rhombic triacontahedron'' in alternative construction. ]]
+[[File:Tjde a 2130459 f0007 ob.png|center|thumb|680px|Same ''Rhombic triacontahedron'' in alternative construction.]]
 [[File:Fig3-dingEtAll2024.png|center|semmoldura|680x680px]]
 == Local country adjustment ==
-[[File:ProjDT-BR-dobras1.png|thumb|380px|Example of possible altitude adjustment over Brazil. ]]
+[[File:ProjDT-BR-dobras1.png|thumb|380px|Example of possible altitude adjustment over Brazil.]]
-Still under study if truly viable... Complementary strategies, using [[DGGS/Proj/Planos_concorrentes#Proposta_da_re-proje%C3%A7%C3%A3o_linear_em_planos_concorrentes|Proposal of linear re-projection (hinges)]], for adjustment to the country's relief, or at least its median altitude. The strategy may make use of:
+Still under study if truly viable... Complementary strategies, using [[DGGS/Proj/Planos_concorrentes#Proposta_da_re-proje%C3%A7%C3%A3o_linear_em_planos_concorrentes|Proposal of linear re-projection (hinges)]], for adjustment to the country's terrain, or at least its median altitude. The strategy may utilize:
-* Change of ellipsoid radius, so that the geoid better tangents the median altitude. Not well regarded as it causes undesirable side effects in positioning.
+* Change of ellipsoid radius, so that the geoid better tangents the median altitude. Not well-regarded due to causing undesirable side effects in positioning.
 * Change in the choice of the "secant plane to the ellipsoid". This allows some compatibility between the two, DGGS and [[DNGS]], as they use the same polygons in the projection (solid angles are preserved).
-In the use of DT for each DNGS (each country), the choice of quadrilaterals ceases to have a greater commitment to the ''rhombic triacontahedron'', it is free. It returns to being the commitment to m<sup>2</sup> as a reference.
+In the use of DT for each DNGS (each country), the choice of quadrilaterals no longer has a greater commitment to the ''rhombic triacontahedron'', it is free. The commitment returns to m<sup>2</sup> as a reference.
-The "compatibility" between DNGS and DGGS (based on DT projection) would be only in the use of the reference projection and simplicity in the conversion algorithms between grids.
+The "compatibility" between DNGS and DGGS (based on DT projection) would only be in the use of the reference projection and simplicity in the conversion algorithms between grids.
 == ISEA Conversion ==
@@ Line 54: / Line 55: @@
 * [[DGGS/Proj/ISEA]]
-* Use in https://www.mdpi.com/2220-9964/11/6/322 for distance transform Canada
+* Usage in https://www.mdpi.com/2220-9964/11/6/322 for distance transform Canada
 [[Category:Public]]