Polygon CCW winding check request

[Francois-Xavier Pineau]

After some reflexion, discussion with colleagues, and considering that we
probably want a unique way to describe a same polygon in different celestial
reference frame (i.e. we do not want to have to change the order of the 
vertices
when changing the frame), here a new proposition which I believe to be
***compatible with the current definition for convex polygons*** and 
which is compatible
with self-intersecting polygons.

We choose as "reference" point the centroid of the first 3 vertices
which are not on a same great-circle (mathematically,
the "reference" point p = v1+v2+v3 / ||v1+v2+v3||).
p is inside the polygon if it is located on the left of the first segment
(i.e. if (v1 x v2).p > 0), else it is outside.



Le 14/06/2018 à 18:22, Arnold Rots a écrit :
> The downside is that this only applies to spherical celestial 
> coordinate systems.
> And I maintain that it is a very bad idea to allow self-intersecting 
> polygons.
>
>   - 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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