Re: Geometric data type for an arc.

why don't you use a composite data type for define a arc type? you
could add the result field in the type definition like

CREATE TYPE arc AS (
center point,
A point,
B point,
lenght double
);

http://www.postgresql.org/docs/9.1/interactive/rowtypes.html

2012/5/10 John W. Kitz <John(dot)Kitz(at)xs4all(dot)nl>:
> Binand,
>
> First of all thanks for taking the time to reply.
>
> You are right of course that "two coordinates of a center point, two
> coordinates of two end points of an arc and the radius of the circle of
> which the arc is a part" as mentioned in my initial post defines two arcs
> (which I have seen referred to as the minor and major arc in some
> documentation) instead of one that collectively define the circumference of
> a circle. I realized that a couple of minutes after I sent the post.
>
> So storing an arc in a DB would require a data type consisting of the center
> point (C) coordinates XC,YC, both coordinates of the endpoints of the arc
> (A1 and A2) XA1,YA1 and XA2,YA2, the radius (R) of the circle and some value
> that indicates which of the two arcs the data defines, which may be e.g.
> numeric (e.g. the angle in degrees between the two radii connecting the
> center point to the endpoints of the arc), boolean (e.g. 1 for the major arc
> and 0 for the minor one), character (e.g. "b" for the major or big arc and
> "s" for the minor or small one) or text (e.g. "major" for the big arc and
> "minor" for the small one).
>
> Where Boolean seems to most obvious choice in order to use the least amount
> of space.
>
> The benefit that I imagine storing the arc in a DB once over calculating the
> arc from a stored circle and several other stored values as appropriate
> every time the arc is needed is reduced application processing and hence
> time.
>
> The down side I assume being that it would require the addition of a
> geometric data type for an arc. Correct?
>
> Thanks, Jk.
>
> -----Original Message-----
> From: binand(at)gmail(dot)com [mailto:binand(at)gmail(dot)com] On Behalf Of Binand
> Sethumadhavan
> Sent: donderdag 10 mei 2012 13:37
> To: John(dot)Kitz(at)xs4all(dot)nl
> Cc: pgsql-novice(at)postgresql(dot)org
> Subject: Re: [NOVICE] Geometric data type for an arc.
>
> On 10 May 2012 16:24, John W. Kitz <John(dot)Kitz(at)xs4all(dot)nl> wrote:
>> What would be the easiest way to store in PostgreSQL an arc or partial
>> circle, defined by the two coordinates of a center point, the two
>> coordinates of the two end points of the arc and the radius of the
>> circle of which the arc is a part?
>
> This doesn't uniquely define the arc, you know. This defines two arcs (plus
> the radius is redundant, since it is also the distance between the centre
> and one of the points and can be computed from the given coordinates).
>
> I'd imagine the canonical way of storing an arc of a circle in a DB would be
> to store the circle to which the arc belongs to (see link you
> posted) along with the angles the two radii to the end points of the arc
> have with the positive X axis, and an indicator as to which of the two arcs
> you intended. The angles can be calculated as invsin(y/r) for each of the
> points where r is the radius.
>
> Take a look at this picture (MS Paint, sorry!):
>
> https://picasaweb.google.com/112929706764240025005/STUFF#5740866485548434802
>
> You know the coordinates of C (c1, c2) and A & B ((a1, a2) and (b1,
> b2) respectively), as well as r, the radius of the circle.
>
> The first thing to do is to perform these sanity checks:
>
> r^2 = (a1-c1)^2 + (a2-c2)^2
> r^2 = (b1-c1)^2 + (b2-c2)^2
>
> Assuming they are fine, the idea is to store the circle itself (completely
> identified by coordinates of the centre and the radius), and the angles ACD
> and BCD. These angles can be calculated by:
>
> ACD = invsin((a2-c2)/r)
> BCD = invsin((b2-c2)/r)
>
> The last piece of information needed is to know which of the two arcs
> - the small one or the big one - you are interested in. You can do this by
> convention, by saying that you will traverse the circle in the
> counter-clockwise direction and the angle stored in the first column in the
> database is that of the first endpoint encountered while traversing.
>
> The reverse calculation is equally simple:
>
> For A:
>
> x = c1 + r . cos ACD
> y = c2 + r . sin ACD
>
> For B:
>
> x = c1 + r . cos BCD
> y = c2 + r . sin BCD
>
> Binand
>
>
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--
Simone