Add more documentation

[hyrodium]

TODO:

• BSplineManifold vs CustomBSplineManifold
• KnotVector vs UniformKnotVector
• bsplinebasis vs bsplinebasisall
• BSplineSpace vs UniformBSplineSpace
• issubset vs issqsubset
• bsplinebasis vs bsplinebasis₊₀ vs bsplinebasis₋₀
• unsafe_* methods
• bsplinebasis′
• BSplineDerivativeSpace
• Interactive examples with Makie.jl

[UnnamedMoose]

Hi, I have just come across your package and it seems exactly like what I need. Ultimately, I want to be able to compute the signed distance function from a spline. To do that, I need to evaluate the curve at specific s-parameter values. I am trying to understand how to do that from the code, but being new to Julia, I am progressing very slowly. Could you please point me to the right place?

[hyrodium]

Thank you for your interest in this package!

Ultimately, I want to be able to compute the signed distance function from a spline. To do that, I need to evaluate the curve at specific s-parameter values.

I'm not much familiar with s-parameter etc. Could you provide some math expressions or references for this?

[UnnamedMoose]

I just mean the non-dimensional length of the curve ranging from 0 to 1. For instance, in the NURBS.jl package you can do this:

evalpoints = collect(0:0.0005:1.0)
CBspline = curvePoints(NBspline, evalpoints)

However, that library seems to no longer be maintained and therefore I was hoping to use yours instead.

[hyrodium]

Ah, I see. Here's a simple example:

julia> using StaticArrays, BasicBSpline

julia> k = KnotVector([0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0])  # knot vector in parameter space
KnotVector([0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0])

julia> P = BSplineSpace{2}(k)
BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0]))

julia> C = BSplineManifold([SVector(1,2), SVector(2,3), SVector(-2,2), SVector(-4,1)], P)
BSplineManifold{1, (2,), SVector{2, Int64}, Tuple{BSplineSpace{2, Float64, KnotVector{Float64}}}}((BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0])),), SVector{2, Int64}[[1, 2], [2, 3], [-2, 2], [-4, 1]])

julia> C.(0:0.1:1)
11-element Vector{SVector{2, Float64}}:
 [1.0, 2.0]
 [1.2800000000000002, 2.3400000000000007]
 [1.3199999999999998, 2.5600000000000005]
 [1.12, 2.6599999999999997]
 [0.6799999999999997, 2.6399999999999997]
 [0.0, 2.5]
 [-0.7999999999999996, 2.2800000000000002]
 [-1.5999999999999996, 2.0200000000000005]
 [-2.4000000000000004, 1.72]
 [-3.2, 1.38]
 [-4.0, 1.0]

An instance of BSplineManifold is callable, so you can just add arguments to that. Note that there is also unbounde_mapping function. This function extrapolate the manifold.

julia> unbounded_mapping.(C, 0:0.1:1)
11-element Vector{SVector{2, Float64}}:
 [1.0, 2.0]
 [1.2800000000000002, 2.3400000000000007]
 [1.3199999999999998, 2.5600000000000005]
 [1.12, 2.6599999999999997]
 [0.6799999999999997, 2.6399999999999997]
 [0.0, 2.5]
 [-0.7999999999999996, 2.2800000000000002]
 [-1.5999999999999996, 2.0200000000000005]
 [-2.4000000000000004, 1.72]
 [-3.2, 1.38]
 [-4.0, 1.0]

julia> unbounded_mapping.(C, -1)
2-element SVector{2, Float64} with indices SOneTo(2):
 -15.0
  -8.0

julia> C(-1)
ERROR: DomainError with -1:
The input -1 is out of range.
Stacktrace:
 [1] macro expansion
   @ ~/.julia/dev/BasicBSpline/src/_BSplineManifold.jl:146 [inlined]
 [2] (::BSplineManifold{1, (2,), SVector{2, Int64}, Tuple{BSplineSpace{2, Float64, KnotVector{Float64}}}})(t::Int64)
   @ BasicBSpline ~/.julia/dev/BasicBSpline/src/_BSplineManifold.jl:146
 [3] top-level scope
   @ REPL[26]:1

Please check the documentation for more information.

[UnnamedMoose]

Fantastic, this is exactly what I was looking for. Thanks!