Hervé Brönnimann schrieb:
Ben: I would add to your reading list the article
A Coordinate Free Geometry ADT (1997) by Stephen Mann, Nathan Litke, Tony DeRose http://citeseer.ist.psu.edu/191514.html
Yes, that's exactly what we've been discussing. I still think, however, that the topic is out of the scope of the library. (The discussion is still quite informative though.) The library provides a tool suitable to represent objects of Euclidean geometry. Objects of Euclidean geometry are points in space. Choosing an orthonormal basis (i.e. an origin and a set of orthogonal base vectors), points can be represented by their Cartesian coordinates, i.e. as tuples of numbers. Defining vector operations makes Cartesian coordinates a vector space. Further, defining a norm introduces the idea of a length and makes it also a normed vector space, which is, due to the similarities to Euclidean geometry, often called an Euclidean vector space. Objects of an Euclidean geometry and members of a vector space are still very different. The former are real world objects, the later abstract representations. The former exit per se, the later are defined only by choosing a basis. The objective of the library is to provide a type save implementation of the vector space of Cartesian coordinates. As such, it implements an abstract concept. The instantiation of that concept to a particular representation, i.e. choosing a basis, is application specific. The user is free to define several representations, but it will be the users responsibility to distinguish between them. It might be reasonable to support this by type checking very similar to dimensional analysis, but this doesn't need to be the case. In my recent application (and probably many similar graphical applications) this is done by a hierarchy of widgets. Each widget defines its own vector space as a reference to the drawing operations it offers. The main functionality of a parent widget is to arrange its child widgets and transform their coordinates into this representation. Since widgets are typically created at run time, this can't be subject of static type checking. Other applications will have different requirements, so the ADT presented in the paper or a similar implementation in templates might be the appropriate solution. In any case, however, it will be independent of the vector implementation and should consequently not be part of the vector library. Andreas