Very general question about the implementation of vectors, vertices, edges, rays, lines & line segments

This is just a LARGE generalized question regarding rays (and/or line segments or edges etc) and their place in a software rendered 3d engine that is/not performing raytracing operations. I'm learning the basics and I'm the first to admit that I don't know much about this stuff so please be kind. :)

I wondered why a parameterized line is not used instead of a ray(or are they??). I have looked around at a few cpp files around the internet and seen a couple of resources define a Ray.cpp object, one with a vertex and a vector, another used a point and a vector. I'm pretty sure that you can define an infinate line with only a normal or a vector and then d开发者_JS百科efine intersecting points along that line to create a line segment as a subset of that infinate line. Are there any current engines implementing lines in this way, or is there a better way to go about this?

To add further complication (or simplicity?) Wikipedia says that in vector space, the end points of a line segment are often vectors, notably u -> u + v, which makes alot of sence if defining a line by vectors in space rather than intersecting an already defined, infinate line, but I cannot find any implementation of this either which makes me wonder about the validity of my thoughts when applying this in a 3d engine and even further complication is created when looking at the Flash 3D engine, Papervision, I looked at the Ray class and it takes 6 individual number values as it's parameters and then returns them as 2 different Number3D, (the Papervision equivalent of a Vector), data types?!?

I'd be very interested to see an implementation of something which actually uses the CORRECT way of implementing these low level parts as per their true definitions.

I'm pretty sure that you can define an infinate line with only a normal or a vector

No, you can't. A vector would define a direction of the line, but all the parallel lines share the same direction, so to pick one, you need to pin it down using a specific point that the line passes through.

Lines are typically defined in Origin + Direction*K form, where K would take any real value, because that form is easy for other math. You could as well use two points on the line.