Re: Flattening the sphere

On Oct 2, 5:05 am, zircher <tzirc...@xxxxxxxxx> wrote:
Gerry Quinn wrote:

Well, if you put this that way then I guess most of us uses slices:
horizontal connections between map squares are implied by euclidean
geometry, but vertical connections between some squares are handled
as if they were nodes -- they can link to other squares on the same
or different level, and they can require some additional conditions
to be traveled.

(pure vapourware from a long-time lurker)
For an overworld map, I've been toying with the idea of tesselating a
sphere and storing terrain information in the sphere facets. The
player's
map is a portion of the sphere projected onto a rectangular display
(each tile in the display is projected onto the sphere, the tile
takes
the value of the facet the projection ray hit). The display would be
centered on the player's position since I think the center tiles are
the most
accurate.

At full zoom-out, When the player is on the equator, he will see and
band
of ice at the top and bottom of the display (when zoomed out to see
the
entire planet). If the player travels north to the pole, he would see
a circle
of ice centered in the display, three rings of temperate, equatorial
and
temperate land/sea, and the edge of the map would be the ice of the
south
pole.

Since the display is meerly a projection of spherical data, and is re-
projected after each move, when the player moves diagonally his
position
could change by 'one unit' in the selected direction, rather than 1
unit for
a non-diagonal direction, and 1.41 units for a diagonal direction.

It might be necessary to perform super-sampling when performing the
projection to reduce 'jitter' when the player moves.

One problem with this idea is the data volume - an Earth sized planet
tesselated down to 1km^2 facets would take approximately 127 million
facets. Using 16km^2 facets (4km edges, somthing akin to the distance
that can be walked per hour) requires about 8 million facets.
The vector data can be reduced using 8-fold or perhaps 16-fold
symmetry.
(With 8 fold symmetry, a single facet have 8 slots for terrain info -
one for
+x+y+z, one for +x+y-z, etc.)

.

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