|WikiProject Mathematics||(Rated C-class, Mid-importance)|
About One Point Is Affine And The Other At Infinity: I think this is misleading. After all, by a projective transformation one can put both points in general position - which is the first case considered. In fact it is 'illegal' to speak about (0:0:0:0).
Charles Matthews 07:49, 14 Jul 2004 (UTC)
I believe the whole linear combinations paragraph is useless and inelegant. We already have the definition of scalar multiplication and addition - and exactly to avoid these problem, we do rescaling by multiplying for the last coordinate (w) of the other point - which avoids the = 0 special case. Additionally, the current text is probably incorrect when - and this brings an interesting point up: which is the result of ?
I do not see your point about applying the projective transformation - yes, we can apply the transformation, add the two points and transform them back, but there is no point in using that.
Paolo Giarrusso 18:01, 8 December 2005 (UTC)
The definition of addition for a pair of projected points doesn't look correct in the case that both of those points are in the plane at infinity.
left and right homogeneous coordinates
Homogeneous coordinates of quaternion vector spaces can be either left or right. That is one can specify that left multiplication by quaternions produces equivalent coordinates, or right multiplication does. Is left and right homogeneous coordinates, standard terminology to refer to both these situations? --MarSch 10:35, 19 October 2006 (UTC)
Notation and terminology
First, the term homogeneous coordinates has a generic meaning in addition to the one given here, namely any system of coordinates where multiplying by a constant does not affect the position of the point represented. So in this sense, barycentric coordinates and trilinear coordinates are homogeneous but aren't the same as the coordinates defined here. Perhaps projective coordinates would be a better term here.
Second, I couldn't find anything about square brackets vs. round brackets in the reference given. In any case, this seems to only apply to the context a specific work and is not a generally accepted notation.
Third, the use of colons for homogeneous coordinates is justifiable since they really represent ratios. But this article uses them with ordinary Cartesian coordinates which seems highly non-standard.