Benchmark

Concrete type determination; generality vs speed performance

B-spline space

There are two subtypes of AbstractBSplineSpace.

julia> subtypes(AbstractBSplineSpace)
2-element Array{Any,1}:
 BSplineSpace
 FastBSplineSpace

• BSplineSpace
  • General degree of polynomial is supported.
• FastBSplineSpace
  • 5 or less degree of polynomial is supported.
  • But much faster than BSplineSpace

B-spline manifold

There are five subtypes of AbstractBSplineManifold.

julia> subtypes(AbstractBSplineManifold)
5-element Array{Any,1}:
 BSplineCurve
 BSplineManifold
 BSplineSolid
 BSplineSurface
 FastBSplineManifold

• BSplineManifold
  • General degree of polynomial is supported.
  • General dimension of polynomial is supported.
• FastBSplineManifold
  • 5 or less degree of polynomial is supported.
  • General dimensional manifold is supported.
  • Much faster than BSplineManifold
• BSplineCurve
  • 5 or less degree of polynomial is supported.
  • Only one dimensional manifold (curve) is supported.
  • Much faster than FastBSplineManifold
• BSplineSurface
  • 5 or less degree of polynomial is supported.
  • Only two dimensional manifold (surface) is supported.
  • Much faster than FastBSplineManifold
• BSplineCurve
  • 5 or less degree of polynomial is supported.
  • Only three dimensional manifold (solid) is supported.
  • Much faster than FastBSplineManifold

Detailed Benchmarks

B-spline basis function

In this section, we compare the implementation of Cox-de Boor algorithm.

Naive implementation

using BenchmarkTools

function B(i,p,k,t)
    if p==0
        return float(k[i]≤t<k[i+1])
    else
        return B(i,p-1,k,t)*(t-k[i])/(k[i+p]-k[i]) + B(i+1,p-1,k,t)*(k[i+p+1]-t)/(k[i+p+1]-k[i+1])
    end
end

knotvector = sort(rand(10)) # Vector{Float64} with 10 elements
p = 3
i = 1
t = 0.2

@benchmark B(i,p,knotvector,t)

Result: 118.757 ns

Use type BSplineSpace

using BenchmarkTools
using BasicBSpline
knotvector = sort(rand(10)) # Vector{Float64} with 10 elements
p = 3
i = 1
t = 0.2
k = Knots(knotvector)
P = BSplineSpace(p,k)
@benchmark bsplinebasis(i,P,t)

Result: 223.359 ns

Slower than naive implementation.

Use type FastBSplineSpace

using BenchmarkTools
using BasicBSpline
knotvector = sort(rand(10)) # Vector{Float64} with 10 elements
p = 3
i = 1
t = 0.2
k = Knots(knotvector)
P = FastBSplineSpace(p,k)
@benchmark bsplinebasis(i,P,t)

Result: 46.722 ns

The fastest.

B-spline manifold

Use type BSplineManifold

Use type FastBSplineManifold

Use type BSplineSurface