Thread: Test yourself

Originally posted by Shadow12345
a point and a terminal vector (the ones in math and physics) are completely different, but a point and a vector (the vector that is the abstract idea of a quantity with a bunch of components) are the same because a point, no matter what basis you are in, is still a quantity which is made up of components. right? That's the only way to explain why vectors are used to represent points so much. oh well I'm not arguing over this too much but i think im right. I haven't seen anyone develop a point class: they just use vector.

Actually, no. A point isn't just "a quantity made up of components." It's a "a quantity made up of components which represents a location." A vector represents direction with magnitude.

Just because a point has similar components to a vector doesn't change that simple fact. They are in no way the same no matter the context. If it makes it easier to think about, look at other ways of representing vectors. In 2D space you can represent a vector by an angle (IE in radians, degrees, etc.) and a magnitude. In that circumstance it's very easy to understand that a vector is not a point. The more common form of vector (with components similar to points) is the same thing as our other vector representation. It's just that it's more practical for us to represent the direction and magnitude through force along each axis rather than an angle measure with magnitude in most cases because it ends up allowing us to use less trigonemetric functions when dealing with them. Simply because the most common form of vector has similar components to a point does not, in any way, make it a point.

A comparison I can make that may also help you out is comparing velocity to acceleration to jerk. Each one can be represented by a single scalar. Does that make them the same? Not at all. A point and a vector both usually have the same number of components. Does that make them the same? Not at all.

The reason most people don't make the distinction is because they don't understand them fully (which is an unnervingamount of mathematically educated people) or because they are lazy and they just want to get a program up and running really quickly.

Originally posted by Shadow12345
EDIT: a plane specifically means 2 dimensions, but what is the word that specifically means 3 dimensions? cube? lol

Trust me, you knew this.
Ever hear of "space?"

It actually depends.

USUALLY adding points is considered an undefined operation, but when the points are scaled and added in such a way that the coefficients when added together equal one, then it's an affine combination (a way of representing a single point based on the "weights" of other points).

EDIT: Please don't tell me I'm doing your homework

Poly you didn't change what I said at all, you simpy won't give up the math/physics vector, where in reality there is a much more general purpose definition for vector. In short a vector is just a quantity with components. In x86 assembly it's "A set of integer or floating point values, called elements, packed into a single operand". In STL it's a templated data structure that holds elements of an arbitrary type. If you go on dictionary.com and look for the definition of vector you'll first see the vector you keep describing (the magnitude and direction vector from math/physics) but directly under that you will see 'one dimensional array' as the second meaning for vector. Gametutorials uses a vector to represent a point, nehe uses a vector to represent a point, opengl game programming uses a vector to represent a point, opengl superbible uses a vector to represent a point, the opengl api itself has, and I quote vectored versions of their functions!! Even the ones used for setting points! (glVertex3fv takes a vector to set a point). Your last post isn't even a valid one poly, because you were trying to prove to me that a point isn't a magnitude and direction whcih I agree with, but you don't even ackknowledge the other meaning of vector which every source in the universe accepts as correct (even the opengl api) except for you.

EDIT:
I already understand everything you said in your last post, I wasn't ever trying to say a vector used to represent a point is the same as a vector used to represent a surface normal or distribution of forces. I was trying to say that you can use a vector to represent a point in the same way the vectored version of opengl api functions accept arrays (an array being a quantity made up of components) the same way stl vector class is a quantity made up of components, the same way SIMD operands are described as vectors in x86 assembly (well I am technically getting this from an x86-64 assembly book) because they are packed with bytes the same way any thing that is made up of a bunch of different components can legally be called a vector.