# Boost :

Subject: Re: [boost] [Review] GGL review starts today, November 5th
From: Rutger ter Borg (rutger_at_[hidden])
Date: 2009-11-12 02:08:41

Barend Gehrels wrote:

> We've implemented the hull as an "agnostic" strategy because it is not
> dependant on coordinate system itself. It is however dependant on two
> underlying strategies, "side" and "compare". So in cartesian coordinate
> systems the "side" is implemented differently from how it would be
> implemented in a spherical coordinate system. Same for compare
> (spherical compare assumes that the coordinates do not span more than
> halve of the sphere).
>
> So yes, for points we need to know in which coordinate system they are
> placed, in order to get the calculation strategy. Note that the
> point-type does not have to have one, but the Point Concept. So using a
> traits class you can bind a coordinate system to a point type.
>
> So if you define a "dictionary coordinate space" where the "side" is
> probably still as defined as it is now for cartesian in the library (it
> can just register the same calculation class), you can call the convex
> hull for it.
>
>
>
> Regards, Barend
>
>

Hello Barend,

thanks for the answer. I guess I am being pedantic :-). The name Geometry
means something like the wikipedia definition for me:

Geometry is a part of mathematics concerned with questions of size, shape,
relative position of figures and with properties of space.

A coordinate system is a property of a subset of types of spaces. A
coordinate system is just a way to express where points are situated in a
certain space. Distances are properties of a space -- not of a coordinate
system.

One of the consequences is that the distance between points in a Euclidean
space expressed in Cartesian or polar (or ...) coordinate systems are, by
definition, the same.

This is probably one of the pieces that is causing my confusion.

Cheers,

Rutger