Polygon CCW winding check request

[Francois-Xavier PINEAU]

Le 14/06/2018 à 18:22, Arnold Rots a écrit :
> The downside is that this only applies to spherical celestial 
> coordinate systems.
You are right, my mistake. I should have talked about the z-axis 
unit-point (i.e. the point of coordinate (0, 0, 1)).

Said differently to be more generic:

the z-axis unit point is in the inside area of the polygon if it is on 
the left (or a better term to say (v1 x v2) . z > 0) of the first edge 
whose support plane is not coplanar with the z-axis.

(it is only an example of possible convention)

The x-axis correspond to (lon, lat) = (0, 0)
The y-axis correspond to (lon, lat) = (pi/2, 0)
The z-axis correspond to (lon, lat) = (0, pi/2)
We suppose that we always use the right-hand rule.

> And I maintain that it is a very bad idea to allow self-intersecting 
> polygons.
Sorry, but I am not sure to understand why.

If we let a user the possibility to draw a polygon by hand on the 
sphere, why forbidding self-crossing polygons?

E.g. in the TOPCAT 2D-plot, you are allowed to draw self-crossing regions.
Both as a TOPCAT user and as an implementor, I think this is the easier 
way to go in an application.

 > the halfspaces used by the SDSS people provide a perfect and 
unambiguous way to specify any shape, with the exception of ellipses.
And the exception of HEALPix cells, and ...



François-Xavier


>
>   - Arnold
>
> -------------------------------------------------------------------------------------------------------------
> Arnold H. Rots Chandra X-ray Science Center
> Smithsonian Astrophysical Observatory tel:  +1 617 496 7701
> 60 Garden Street, MS 67   fax:  +1 617 495 7356
> Cambridge, MA 02138 arots at cfa.harvard.edu <mailto:arots at cfa.harvard.edu>
> USA http://hea-www.harvard.edu/~arots/ 
> <http://hea-www.harvard.edu/%7Earots/>
> --------------------------------------------------------------------------------------------------------------
>
>
> On Thu, Jun 14, 2018 at 9:13 AM, Francois-Xavier PINEAU 
> <francois-xavier.pineau at astro.unistra.fr 
> <mailto:francois-xavier.pineau at astro.unistra.fr>> wrote:
>
>
>     Le 13/06/2018 à 23:58, Markus Nullmeier a écrit :
>
>         Hello list,
>
>         On 13/06/18 10:05, Francois-Xavier PINEAU wrote:
>
>             Example: if we take the case of a simple 4 vertices's
>             polygon having a
>             butterfly shape (i.e. having two crossing great-circle
>             arcs), then the
>             inside of one "wing" is in the counter-clockwise sense
>             while the inside
>             of the other "wing" is in the clockwise sense.
>
>         Well, a definition that allows polygon edges to intersect would be
>         unsound, probably in several ways. One of them is the mentioned
>         inability to describe the complement of a polygon as a single
>         polygon.
>
>     Ok, a polygon (defined by a list of successive vertices) defines
>     two complementary areas on the unit sphere.
>     To know which one is considered as being inside the polygon, why
>     not taking a reference point like the North pole (N):
>
>     If N is on the left side of the first great-arc of the polygon
>     (mathematically, if ((vertex1 cross_product vertex2)
>     scalar_product north pole) > 0), then N is in the area considered
>     as being inside the polygon, else it is in the outside area.
>
>
>     I see one possible complication:
>      if N is a vertex or on an edge of the polygon, then:
>      - the first edge must not contain N
>      - if N is considered as inside: the inside is defined by the
>     area(s) on the left part of the edge(s) containing N
>      - if N is considered as outside: the inside is the complement of
>     the area considering N inside
>
>     This simple definition is able to deal with both simple and
>     self-intersecting polygons.
>
>     In attachment, 3 large polygons (2 self intersecting, and one
>     having a surface area > 2*pi): I adapted the following 10 lines of
>     code (in 2d) to the spherical case
>     (https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html
>     <https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html>).
>
>     Kind regards,
>
>
>     François-Xavier
>
>
>
>
>
>

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