Polygon CCW winding check request

Arnold Rots arots at cfa.harvard.edu
Thu Jun 14 18:22:51 CEST 2018

```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

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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
USA
http://hea-www.harvard.edu/~arots/
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On Thu, Jun 14, 2018 at 9:13 AM, Francois-Xavier PINEAU <
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//Res
> earch/Short_Notes/pnpoly.html).
>
> Kind regards,
>
>
> François-Xavier
>
>
>
>
>
>
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