On the other hand, a point is not a very interesting object. For example, can points be added or multiplied with a scalar? Strictly speaking, that makes sense only for distances, i.e. vectors.
You're right, there is a difference between points and vectors. A point, for example, has a dimension of zero, while a vector has always a dimension of one, regardless what the dimension of the vector space is. (So when talking about a three-dimensional vector, we're actually talking about a one-dimensional object in a three-dimensional space.) But this distinction is hardly ever made in mathematics, unless in introductions and maybe in very special discussions. Typically a point and it's position vector are treated synonymously, so I wonder if we really need to make the distinction here? We could cleanly separate both
This issue also arises in the context of unit conversions. A salient example is the case of converting between temperatures in Fahrenheit and those in Kelvin : How do we convert 32 degrees Fahrenheit to Kelvin? If we are talking about absolute temperatures (points), then the correct expression is Absolute temperature (K) = (Absolute temperature (F) - 32)*5/9 +273.15 However, if we're talking about temperature differences (vectors), then the correct expression is Temperature difference (K) = Temperature difference (F)*5/9 The same issue arises in times (time point vs. time difference). It is unfortunately very difficult to come up with a completely generic solution to this problem - you can define an algebra that behaves sensibly on points and vectors, which for many applications will be fine. This sort of value type will also work with our units library. However, in order to correctly implement conversions, the unit and the value type become entangled. It is possible to do this by specializing the quantity conversion helper, but requires separate specializations for each unit having affine conversion factors (demo coming). Matthias