Multidimensional vectors and computing pi (revisited)
We will start by defining a vector in three dimensions; this is a vector in the mechanical sense and not the Julia vector sense, that is, a one-dimensional array.
We will define a V3D module using the following code:
#=
This module uses Float64 components but could use a
parameterised type {T} as will be seen later
=#
module V3D
# import operators from Base and Linear Algebra
import Base: +, *, /, ==, <, >, zero, one, iszero
import LinearAlgebra: norm, dot
# and export the type Vec3 and norm, dist functions (for Vec3)
export Vec3, norm, dist
# define a simple structure to hold the coordinates of the vector
struct Vec3
x::Float64
y::Float64
z::Float64
end
# and the 'usual' runs for manipulating vectors
(+)(a::Vec3, b::Vec3) = Vec3(a.x+b.x, a.y+b.y, a.z+b.z)
(*)(p::Vec3, s::Real) = Vec3(p.x*s, p.y*s, p.z*s)
(*)(s::Real, p::Vec3) = p*s
(/)(p::Vec3, s...