# Vector2 and Point2

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Which are the differences between a point and a vector,since the point of view of programming ? The only thing that I know is that (point - point = vector), so, I would make a class Vector2 and a class Point2 ? or only Vector2 (the same for Vector3) ? thnx

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I tend to define two separate classes Point and Vector. The allowed operations are:
Vector + Vector = Vector
Vector - Vector = Vector
Vector * Number = Vector
Number * Vector = Vector
Point + Vector = Point
Point - Vector = Point
Point - Point = Vector
a_1*Point + a_2*Point + ... + a_n*Point = Point if a_1+a_2+...+a_n=1 (baricenter)

A lot of people would just have a single class for both, although that is not as type-safe as having separate classes. For instance, adding two points is not defined, and the compiler will complain if you have separate classes and try to do it.

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if the point doesnt add any behavior over the vector, its not needed to give it its seperate class. imho.

if it holds other information, you could derive a point class from vector, or just create a point class with a member 'vector position'

it does make sense to create a point class with some extended behavior, like storing position in local and worldcoordinates or other properties.

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Conceptually, I like to think of a point being non-representative, with vectors representing the actual point. (just because most of the math involves vectors, and doesn't make sense for points). For a point class, I put a place vector in to describe the point, that way my algorithms make sense. Something like:

class xPoint3D{private:   xVector3D placeVector;public:   xVector3D operator- ( xPoint3D );  // retrieve vector from subtraction   xPoint3D operator+ ( xVector3D );  // translate point by vector   xPoint3D operator* ( xScalar );    // scale point (from origin)   xPoint3D operator* ( xMatrix3x3 ); // transform point through matrix   // etc.};

and in my vector class ...
class xVector3D{private:   double compX, compY, compZ; // x,y and z components representing vectorpublic:   // vector related functions};

Hope this helps and good luck!

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You might do a search for 'homogenous coordinates' and read some of the threads on that topic. With homogenous coordinates you can represent points with w = 1 and vectors with w = 0. Then, all the math comes out correctly (for example the properties in alvaro's post are enforced, among other things).

However, I haven't seen much use of homogenous coordinates in production code (except for projection, shadow volumes, or other techniques that use 4x4 matrices). You end up with a lot of pointless operations (multiplication by 0 and 1, etc.), so in practice, people seem to just stick with a 3d vector class and use it for both points and vectors.

With this approach, it's up to the programmer to avoid operations that don't make sense, such as translating a normal.

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