Somewhere in the E.U., le 08/11/2004 Bonjour What Reece described is the difference between a vector space and an affine space. A vector space has one "special" element, the zero vector, whereas an affine space has none (every point is equivalent to every other). You *have* to choose one point in an affine space and label it as the "origin". There is (intrinsically) no way to choose such a point canonically. The confusion (that there is some magical way to choose the origin) comes from the fact that a vector space can *also* be endowed with an affine space structure (usually, but not necessarily, by choosing the zero vector as the origin). Likewise, one can derive a vector space from an affine one, but both are conceptually, and practically, two very different beasts. "Point+Point" is meaningless, "Point+Vector" is meaningful. Hubert Holin In article <1852440446.20041105235430@digiways.com>, Val Samko <boost@digiways.com> wrote:
RD> MFC gets the intended use of CPoint/CSize wrong.
RD> In a mathematical sense, a point is a 0-size location in an nD RD> coordinate system. In this case, it is a 2D coordinate system, so is RD> (x,y). This is used for positioning, e.g. moving the graphics cursor, so RD> I call it gui::position. It does not make sense to perform point [+-*/]= RD> point since points are locations in a space (how do I add the location RD> of my house to the location of Jupiter)?
I do not follow your logic. In mathematics, in Cartesian nD coordinate system, a point is represented by a set of distances between that point and the centre of coordinates, along each axe. Just like a vector. And vectorA + vectorB is a very common operation.
RD> The size type stores width and height information, so it can be treated RD> as a 2D vector. In this case, standard arithmetic operations make sense. RD> Also, it is possible for sizes to interact with points, e.g. point += size.
Once again, in geometry, vector and point are practically the same thing.
RD> If you do point - point, then the resulting type is a size type that RD> represents the distance between the two points.
Just like size - size.
RD> So in a mathematical sense, the difference between size and position is RD> entirely relevant, it's just that some libraries (not mentioning names) RD> do not adhere to the above mathematical rules.
There are no mathematical rules, which say that a point in nD Cartesian coordinate system is not just a set of corresponding distances along each axe.
Valentin
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