[Haskell-cafe] Abstraction in data types

[Darrin Chandler]

On Wed, Mar 17, 2010 at 09:56:14PM -0700, Alexander Solla wrote:
> I wrote this to Darrin, but didn't CC cafe:
> 
> On Mar 17, 2010, at 9:20 PM, Darrin Chandler wrote:
> 
> >type Cartesian_coord = Float
> >
> >type Latitude  = Float
> >type Longitude = Float
> >
> >data Point	= Cartesian (Cartesian_coord, Cartesian_coord)
> >		| Spherical (Latitude, Longitude)
> >
> >type Center = Point
> >type Radius = Float
> >
> >data Shape	= Circle Center Radius
> >		| Polygon [Point]
> >
> >This obviously stinks since a Polygon could contain mixed
> >Cartesian and
> >Spherical points. Polygon needs to be one or the other, but not mixed.
> 
> My suggestion would be to use an alternate representation of
> "spherical" points in terms of polar coordinates, and then to
> normalize and mix at will:
> 
> type Theta = Float
> type Radius = Float
> 
> data Point = Cartesian (Cartesian_coord, Cartesian_coord)
>            | Polar   (Theta, Radius)
> 
> normalize_point :: Point -> Point
> normalize_point Cartesian x y = Cartesian x y
> normalize_point Polar t r = Cartesian x y where x = r * cos t; y = r
> * sin t;
> 
> It really depends on what you want to do with your points.  If you
> want to do linear algebra, you might want your points to depend on a
> basis, for example.  But your "spherical" points don't really form a
> basis in three-space, or even over all of two-space.

I see what you mean, but I don't think that's what I need. I want to
have keep Lat/Lon, as I may have large groups of shapes in Lat/Lon and
want to do things with them as is. And the same for cartesian coords.
Sometimes I will translate betweem lat/lon and cartesian, but many times
I will be doing calculations in "native" coordinates. But it's a nice
technique you show, and it will come in handy elsewhere.

-- 
Darrin Chandler            |  Phoenix BSD User Group  |  MetaBUG
dwchandler at stilyagin.com   |  http://phxbug.org/      |  http://metabug.org/
http://www.stilyagin.com/  |  Daemons in the Desert   |  Global BUG Federation
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