andyferris / affinespaces.jl

The perfect Julia package for those who love being pedantic about points

AffineSpaces

The perfect Julia package for those who love being pedantic about points

`abstract AffineSpace{T}``

An AffineSpace object represents points in an affine space, which is similar to a Cartesian space but where no special meaning can be assigned to the origin. Subtypes of AffineSpace should have a field named pos with vector-like abilities describing the coordinates.

The consequences are that points do not have vector-like abilities such as multiplication by a scalar (scaling the distance relative to the origin), unary inversion (reflection about the origin) or addition of the coordinates of two points (coordinates being relative to the origin).

Outside these restriction, one can take affine combinations of points, finding for instance the midpoint of two points. Affine combinations are built with the colon operation p₁:p₂ and indexed with a scalar (p₁:p₂)[i], where i = 0.0 indicates the point p₁, and i = 1.0 indicates the point p₂, and other values of i trace out the line connecting the two points. Generally, the affine combination of n points can be generated with (p₁:...:pₙ)[i₁,...,iₙ] so long as the iⱼs sum to 1 (or the last iₙ is not given, and is automatically calculated).

Furthermore, standard vectors can be added and subtracted from affine points as a displacement of the point. The displacement vector between two points is given by their subtraction.

The goal of these types are to provide some programmer safety to avoid conceptual mistakes regarding manipulation of points, by removing the meaning of the possibly-arbitrary origin.

AffinePoint{N,T} <: FixedAffineSpace{T}

A concrete type describing a point in an affine space, where the Cartesian coordinates of the point are stored in a FixedSizeArrays.Vec{N,T}. See AffineSpace for a description of the interface for affine points.