Euclidean Vector

An euclidean vector is represented by its Cartesian coordinates: (p₀, p₁,..., p_{d - 1}) (in a d-dimensional vectorial space). It can be defined by the difference between two points (Locations), A and B: if A has coordinates (a₀, a₁,..., a_{d - 1}) and B (b₀, b₁,..., b_{d - 1}), then vector $\bf AB$ = B - A has coordinates (b₀ - a₀, b₁ - a₁,..., b_{d - 1} - a_{d - 1}).

The requirements of Euclidean Vector are very similar to those of Location, and could actually have been represented by a Location. However, an euclidean vector is very different from a point, or location, (from a mathematical point of view) and it would have been confusing to represent these two entities by the same concept.

Refinement of

Default Constructible, Assignable, Equality Comparable

Associated Types

• Coordinate type

  A::coordinate_type

  The type of the coordinates p_i, . Operations +, -, * must be defined on this type. The coordinate type should also be convertible to type double

Notations

A		A type that is a model of Euclidean Vector
a, b		Objects of type A
C		coordinate type: A::coordinate_type
i		object of type unsigned int

Valid Expressions

• Dimension

  A::dimension

  Return type:		int
  Semantics:		returns the dimension of vectors of type A

• Copy Constructor

  A(a)

  Return type:		A
  Postcondition:		A(a) is a copy of a

• Copy Constructor

  A b(a)

  Postcondition:

  b is a copy of a

• Assignment

  b = a

  Return type:		A
  Postcondition:		b is a copy of a

• Coordinate Access Function

  a[i]

  Return type:		C
  Precondition:
  Semantics:		returns the ith coordinate of the vector

• Equality Comparison

  a == b

  Return type:		bool
  Semantics:		checks if two vectors are identical

Models

• euclidean_vector_2d
• euclidean_vector_3d