On 9/20/06, james.jones@firstinvestors.com <james.jones@firstinvestors.com> wrote:

From: "Olivier Grant" <olivier.grant@gmail.com> On 9/20/06, Walter Landry <wlandry@ucsd.edu> wrote:

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This seems wrong. If I want to add a vector2d to a vector3d, then I should have to do it manually. Otherwise, it should be a type error.

it depends how you see the problem I suppose. A 2D vector is just a 3D vector with z == 0. A 3D vector is a 4D vector with w == 1. And so on by extension. Since these vector classes are not supposed to be used in a polymorphic way, each argument of a function call is well-known by the user - or at least should be :) - so I would not raise an exception in the case of the use of two vectors with different dimensions.

But a 2D vector is NOT just a 3D vector with z = 0!! It might sit in a subspace of a 3D vector space, but not necessarily in the z=0 plane. It could just as easily be a 2D vector in the x - 2y + 3z = 0 plane.

I completly agree. I was implying that they both use the same global coordinate system. To me, what you are saying in your example - with the 2D vector plane being x - 2y + 3z - means that they don't use the same coordinate system. The work could be extended so vectors can be converted from one subspace to another. Adding a 2D vector and a 3D vector would convert the 2D vector to the corresponding 3D vector based on the plane in the 3D space it resides in - not sure that was clear but I'm sure you get the point :). Certainly do it this way if you want to - maybe it makes perfect sense for

your particular application. But I'd never want to see something like this standardized in BOOST. It just ain't right. :)

I wasn't even proposing this as a BOOST lib, even though I would be interested in taking part in the development of one. Is there any work being done on this or is there already a library considered to implement all geometrical vector algebra that meets BOOST standards ? Also, if a 2D vector is a 3D vector with z=0, and a 3D vector is a 4D vector

with w=1, "and so on by extension", then how would a 4D vector compare with a 5D vector? I don't get the extension. When you first posted your example, I assumed you'd made a typo when you set w=1, but now I think you did that on purpose. Why wouldn't w=0?

I was thinking of 3D control points, but that was a bad example. I just wanted to point out that the implementation allowed users to define specific default values for each coordinate. -

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Thanks for your comments and questions, Olivier.