Ken Sloan and I were having a private joke here, because this issue of
point versus vector has come up time and again, with some folks saying
it's convenient to not distinguish them, and others of us saying that
that leads to confusion and mistakes. Your example is a vote for the
latter position, which happens to be my own.
Whatever the source of your graphics education, it looks like you've
got a muddled collection of concepts. None of what you "understand" is
accurate! Let's try to correct that, briefly.
POINT. Whether on a line, in a plane, in 3D space, or whatever, we
think of a point as something without length, width, height, or any
other dimension; just a placeholder at a particular position.
VECTOR. We think of these as displacements from one point to another,
translating the entire space of points. Vectors do have magnitude
(length) and direction, unlike points themselves. There is also a
distinguished "null" or zero-magnitude vector. We can add vectors, and
stretch and shrink (scale) them. Adding vectors means we combine their
displacements. We can also "add" a vector to a point, meaning we are
displacing the point. And it is convenient to say we "subtract" two
points to get the vector that displaces one to the other. But a vector
has no position in the same sense a point does.
LINE. Take a point and a vector, and displace that point by all
possible scaled versions of that vector to get an infinite collection
of points. Those points form a line. A line does have a position, but
unlike the generating vector it does not have a direction. Remember we
keep only the points, not the generators. (And any number of different
points and vectors can generate the same line.) However, ...
DIRECTED LINE. This is a more sophisticated concept, because along
with the points of a line we have an ordering. Given two distinct
points on the line we can say "this one comes before that one".
LINE SEGMENT. Snip off a piece of a line; or limit the scaling of the
generating vector for the same effect. A line segment has a position
and a length, but again no direction. However, ...
DIRECTED LINE SEGMENT. This collection of points is ordered, so we can
say it goes from this end to that end, not the other way around. Thus
a directed line segment has position, length, and direction. We can
generate it using the point at one end and the vector from that to the
OPPORTUNITY FOR CONFUSION: If a point is *assumed* (such as the origin
of a coordinate system for a plane) a vector implies any of the other
constructs! Displace the origin to get a point, displace scaled to get
a line, preserve direction to get directed line, and so on.
But a tank of gas is not a town, even though it may power a vehicle to
get you from one town to another.
>> >Gee...points are (a,b,c), vectors are (a,b,c) - can't you just treat
>> >them all the same?
>> Yes, you can. However not all treatments lead to successful cures. ;-D
>Thanks People for all your help, The above comments underline the confusion
>about vectors I have, when is a vector a vector and not a line segment, as a
>line segment also has a magnitude & direction, it's my understanding that a
>2D Vector has 4 components
>D = Vector direction in 2D Space
>M = Vector Magnitude
>X = X Coord of the endpoint
>Y = Y Coord of the endpoint
>Why would an entity with just the last two components be called a Vector?