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

other end.

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?