February 24th, 2016, 1:52 pm
Hmmm..I'd say that any time one ignores relationships between objects, one has issues, too.Each individual ellipse is also a _distinct_ well-defined mathematical concept. Yet we intentionally ignore that distinctness in order to manage the many as a one. It's then a matter of taste and the particulars of the application that lets one say circles might also belong in the set of ellipses because mathematically, the set of all circles is a subset of the set of all ellipses.And within the set of all possible ellipses, there exist subsets of ellipses with special properties. Circles might be one subset. Isometric projections of circles might be another subset. Ellipses defining gears of pitch, P, might be a third. Mathematically, all those shapes are ellipses in that they are defined by a second order equation. Yet in some ways they are not ellipses.At issue is the set of "admissible transformations" for each of these subsets. A generalized ellipse can be rotated, scaled, and squashed (change in aspect ratio) arbitrarily. Circles can be scaled but not squashed and rotation does not make any sense. Elliptical gears can be squashed or rotated but arbitrary scaling is impossible (only very specific values constrained by the gear pitch are valid). Isometric projections of circles can be scaled but cannot be not squashed arbitrarily nor freely rotated.Yet even if one considers circles, isometric projections of circles, and elliptical gears to be distinct from general ellipses, they can all use the same graphics software routines for drawing them on the screen even if they can't all share the same input widgets for creating and changing them.