From 6774c9ad0558bc632b771c90d29d80f460a66494 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 30 Sep 2023 15:52:15 +0000 Subject: [PATCH] build based on 15dc66b --- previews/PR334/.documenter-siteinfo.json | 2 +- previews/PR334/1dim-manifold.html | 4 +- previews/PR334/2dim-manifold-currying.html | 4 +- previews/PR334/2dim-manifold.html | 4 +- .../PR334/basicbsplineexporter/index.html | 2 +- previews/PR334/bsplinebasisall-1.html | 4 +- previews/PR334/bsplinebasisall-2.html | 4 +- previews/PR334/bsplinebasisall-3.html | 4 +- .../PR334/bsplinebasisderivativeplot.html | 4 +- previews/PR334/bsplinebasisplot.html | 4 +- previews/PR334/bsplinebasisplot2.html | 4 +- previews/PR334/cardioid.html | 6 +-- previews/PR334/contributing/index.html | 2 +- previews/PR334/geometricmodeling-arc.html | 4 +- previews/PR334/geometricmodeling-circle.html | 4 +- ...eometricmodeling-hyperbolicparaboloid.html | 4 +- .../PR334/geometricmodeling-paraboloid.html | 4 +- previews/PR334/geometricmodeling-torus.html | 4 +- previews/PR334/geometricmodeling/index.html | 2 +- previews/PR334/helix.html | 6 +-- previews/PR334/histogram-uniform.html | 4 +- previews/PR334/index.html | 2 +- previews/PR334/internal/index.html | 4 +- previews/PR334/interpolation_cubic.html | 4 +- previews/PR334/interpolation_linear.html | 4 +- previews/PR334/interpolation_periodic.html | 4 +- .../PR334/interpolation_periodic_sin.html | 4 +- previews/PR334/interpolations/index.html | 2 +- previews/PR334/math-bsplinebasis/index.html | 42 +++++++++---------- .../PR334/math-bsplinemanifold/index.html | 6 +-- previews/PR334/math-bsplinespace/index.html | 12 +++--- previews/PR334/math-derivative/index.html | 10 ++--- previews/PR334/math-fitting/index.html | 2 +- previews/PR334/math-inclusive/index.html | 10 ++--- previews/PR334/math-knotvector/index.html | 22 +++++----- .../math-rationalbsplinemanifold/index.html | 2 +- previews/PR334/math-refinement/index.html | 4 +- previews/PR334/math/index.html | 2 +- previews/PR334/plotlyjs/index.html | 2 +- previews/PR334/plots-arc.html | 4 +- previews/PR334/plots-bsplinebasis-raw.html | 4 +- previews/PR334/plots-bsplinebasis.html | 4 +- .../PR334/plots-bsplinebasisderivative.html | 4 +- previews/PR334/plots-cardioid.html | 4 +- previews/PR334/plots-helix.html | 4 +- previews/PR334/plots-surface.html | 4 +- previews/PR334/plots/index.html | 2 +- previews/PR334/subbsplineplot.html | 4 +- previews/PR334/subbsplineplot2.html | 4 +- previews/PR334/sumofbsplineplot.html | 4 +- previews/PR334/sumofbsplineplot2.html | 4 +- previews/PR334/sumofbsplineplot3.html | 4 +- 52 files changed, 134 insertions(+), 134 deletions(-) diff --git a/previews/PR334/.documenter-siteinfo.json b/previews/PR334/.documenter-siteinfo.json index 32ab9324c..3acc2aec6 100644 --- a/previews/PR334/.documenter-siteinfo.json +++ b/previews/PR334/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-30T14:59:47","documenter_version":"1.1.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-09-30T15:51:13","documenter_version":"1.1.0"}} \ No newline at end of file diff --git a/previews/PR334/1dim-manifold.html b/previews/PR334/1dim-manifold.html index 9cec63286..adc90fb9a 100644 --- a/previews/PR334/1dim-manifold.html +++ b/previews/PR334/1dim-manifold.html @@ -1,7 +1,7 @@ -
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GitHub

Contributing

The main contributer Hyrodium is not native English speaker. So, English corrections would be really helpful. Of course, other code improvement are welcomed!

Feel free to open issues and pull requests!

+Contributing · BasicBSpline.jl
GitHub

Contributing

The main contributer Hyrodium is not native English speaker. So, English corrections would be really helpful. Of course, other code improvement are welcomed!

Feel free to open issues and pull requests!

diff --git a/previews/PR334/geometricmodeling-arc.html b/previews/PR334/geometricmodeling-arc.html index 3e23ddd42..811fa54d4 100644 --- a/previews/PR334/geometricmodeling-arc.html +++ b/previews/PR334/geometricmodeling-arc.html @@ -1,7 +1,7 @@ -
+
+
+
+
+
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{"editable":false,"responsive":true,"staticPlot":false,"scrollZoom":true}, diff --git a/previews/PR334/histogram-uniform.html b/previews/PR334/histogram-uniform.html index f2e036166..3d4c68723 100644 --- a/previews/PR334/histogram-uniform.html +++ b/previews/PR334/histogram-uniform.html @@ -1,7 +1,7 @@ -
+
GitHub

Private API

Note that the following methods are considered private methods, and changes in their behavior are not considered breaking changes.

BasicBSpline.r_nomial — Function

Calculate $r$-nomial coefficient

r_nomial(n, k, r)

\[(1+x+\cdots+x^r)^n = \sum_{k} a_{n,k,r} x^k\]

source
BasicBSpline._lower_R — Function

Internal methods for obtaining a B-spline space with one degree lower.

\[\begin{aligned} +Private API · BasicBSpline.jl

GitHub

Private API

Note that the following methods are considered private methods, and changes in their behavior are not considered breaking changes.

BasicBSpline.r_nomial — Function

Calculate $r$-nomial coefficient

r_nomial(n, k, r)

\[(1+x+\cdots+x^r)^n = \sum_{k} a_{n,k,r} x^k\]

source
BasicBSpline._lower_R — Function

Internal methods for obtaining a B-spline space with one degree lower.

\[\begin{aligned} \mathcal{P}[p,k] &\mapsto \mathcal{P}[p-1,k] \\ D^r\mathcal{P}[p,k] &\mapsto D^{r-1}\mathcal{P}[p-1,k] -\end{aligned}\]

source
+\end{aligned}\]

source
diff --git a/previews/PR334/interpolation_cubic.html b/previews/PR334/interpolation_cubic.html index d4ce1512e..f3552def1 100644 --- a/previews/PR334/interpolation_cubic.html +++ b/previews/PR334/interpolation_cubic.html @@ -1,7 +1,7 @@ -
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Refinement

Documentation

Example

Define original manifold

p = 2 # degree of polynomial
+Refinement · BasicBSpline.jl
GitHub
Refinement
Documentation
Example
Define original manifold
p = 2 # degree of polynomial
 k = KnotVector(1:8) # knot vector
 P = BSplineSpace{p}(k) # B-spline space
 rand_a = [SVector(rand(), rand()) for i in 1:dim(P), j in 1:dim(P)]
 a = [SVector(2*i-6.5, 2*j-6.5) for i in 1:dim(P), j in 1:dim(P)] + rand_a # random
-M = BSplineManifold(a,(P,P)) # Define B-spline manifold
h-refinement
Insert additional knots to knot vector.
julia> k₊ = (KnotVector([3.3,4.2]),KnotVector([3.8,3.2,5.3])) # additional knot vectors(KnotVector([3.3, 4.2]), KnotVector([3.2, 3.8, 5.3]))
julia> M_h = refinement(M, k₊) # refinement of B-spline manifoldBSplineManifold{2, (2, 2), StaticArraysCore.SVector{2, Float64}, Tuple{BSplineSpace{2, Float64, KnotVector{Float64}}, BSplineSpace{2, Float64, KnotVector{Float64}}}}((BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 3.3, 4.0, 4.2, 5.0, 6.0, 7.0, 8.0])), BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 3.2, 3.8, 4.0, 5.0, 5.3, 6.0, 7.0, 8.0]))), StaticArraysCore.SVector{2, Float64}[[-3.7392559679567654, -3.783078079871714] [-3.597411705002145, -2.6270907448400385] … [-4.27252342702906, 2.44794251443626] [-4.010429310201709, 3.869439330221196]; [-2.328731904641716, -4.1480930630807595] [-2.275419510381314, -2.8615581264721692] … [-2.736955136391798, 2.5020454657912223] [-2.786990222003846, 3.8096177268489324]; … ; [2.359972932445208, -3.6129585850258517] [2.373167856283101, -2.9446206124413257] … [2.210716406024899, 2.602631448306355] [2.3997592455372003, 3.5324898804805147]; [4.093841853317975, -3.9061261483801712] [3.8504632555175444, -2.9860983311743827] … [4.331025079311032, 2.333423772424664] [4.480663191353303, 4.436571553462537]])
julia> save_png("2dim_h-refinement.png", M_h) # save image
Note that this shape and the last shape are equivalent.
p-refinement
Increase the polynomial degree of B-spline manifold.
julia> p₊ = (Val(1), Val(2)) # additional degrees(Val{1}(), Val{2}())
julia> M_p = refinement(M, p₊) # refinement of B-spline manifoldBSplineManifold{2, (3, 4), StaticArraysCore.SVector{2, Float64}, Tuple{BSplineSpace{3, Int64, KnotVector{Int64}}, BSplineSpace{4, Int64, KnotVector{Int64}}}}((BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8])), BSplineSpace{4, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8]))), StaticArraysCore.SVector{2, Float64}[[-3.327939887958376, -3.381062882382532] [-3.2286534014564956, -2.3898453165277354] … [-3.857369028126979, 2.625613347418197] [-3.750274329305369, 3.444604754180493]; [-1.9190826728891883, -3.6996476508119316] [-1.8954644502285198, -2.596850938310199] … [-2.320089840437407, 2.6673570013295036] [-2.4013083859231266, 3.417615645058782]; … ; [2.63663136518713, -3.36586722890932] [2.6119919237133846, -2.773961995558151] … [2.5855688772510934, 2.690164285500753] [2.692907338976954, 3.352168201374152]; [3.7212735564249955, -3.491398425417405] [3.554093269596626, -2.759665500609979] … [3.9960174259147876, 2.6027151956081522] [4.087903053338675, 3.7248325816241836]])
julia> save_png("2dim_p-refinement.png", M_p) # save image
Note that this shape and the last shape are equivalent.

+M = BSplineManifold(a,(P,P)) # Define B-spline manifold

h-refinement

Insert additional knots to knot vector.

julia> k₊ = (KnotVector([3.3,4.2]),KnotVector([3.8,3.2,5.3])) # additional knot vectors(KnotVector([3.3, 4.2]), KnotVector([3.2, 3.8, 5.3]))
julia> M_h = refinement(M, k₊) # refinement of B-spline manifoldBSplineManifold{2, (2, 2), StaticArraysCore.SVector{2, Float64}, Tuple{BSplineSpace{2, Float64, KnotVector{Float64}}, BSplineSpace{2, Float64, KnotVector{Float64}}}}((BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 3.3, 4.0, 4.2, 5.0, 6.0, 7.0, 8.0])), BSplineSpace{2, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 3.2, 3.8, 4.0, 5.0, 5.3, 6.0, 7.0, 8.0]))), StaticArraysCore.SVector{2, Float64}[[-3.7392559679567654, -3.783078079871714] [-3.597411705002145, -2.6270907448400385] … [-4.27252342702906, 2.44794251443626] [-4.010429310201709, 3.869439330221196]; [-2.328731904641716, -4.1480930630807595] [-2.275419510381314, -2.8615581264721692] … [-2.736955136391798, 2.5020454657912223] [-2.786990222003846, 3.8096177268489324]; … ; [2.359972932445208, -3.6129585850258517] [2.373167856283101, -2.9446206124413257] … [2.210716406024899, 2.602631448306355] [2.3997592455372003, 3.5324898804805147]; [4.093841853317975, -3.9061261483801712] [3.8504632555175444, -2.9860983311743827] … [4.331025079311032, 2.333423772424664] [4.480663191353303, 4.436571553462537]])
julia> save_png("2dim_h-refinement.png", M_h) # save image

Note that this shape and the last shape are equivalent.

p-refinement

Increase the polynomial degree of B-spline manifold.

julia> p₊ = (Val(1), Val(2)) # additional degrees(Val{1}(), Val{2}())
julia> M_p = refinement(M, p₊) # refinement of B-spline manifoldBSplineManifold{2, (3, 4), StaticArraysCore.SVector{2, Float64}, Tuple{BSplineSpace{3, Int64, KnotVector{Int64}}, BSplineSpace{4, Int64, KnotVector{Int64}}}}((BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8])), BSplineSpace{4, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8]))), StaticArraysCore.SVector{2, Float64}[[-3.327939887958376, -3.381062882382532] [-3.2286534014564956, -2.3898453165277354] … [-3.857369028126979, 2.625613347418197] [-3.750274329305369, 3.444604754180493]; [-1.9190826728891883, -3.6996476508119316] [-1.8954644502285198, -2.596850938310199] … [-2.320089840437407, 2.6673570013295036] [-2.4013083859231266, 3.417615645058782]; … ; [2.63663136518713, -3.36586722890932] [2.6119919237133846, -2.773961995558151] … [2.5855688772510934, 2.690164285500753] [2.692907338976954, 3.352168201374152]; [3.7212735564249955, -3.491398425417405] [3.554093269596626, -2.759665500609979] … [3.9960174259147876, 2.6027151956081522] [4.087903053338675, 3.7248325816241836]])
julia> save_png("2dim_p-refinement.png", M_p) # save image

Note that this shape and the last shape are equivalent.

diff --git a/previews/PR334/math/index.html b/previews/PR334/math/index.html index d7a4f80ec..8e552127c 100644 --- a/previews/PR334/math/index.html +++ b/previews/PR334/math/index.html @@ -1,3 +1,3 @@ Introduction · BasicBSpline.jl
GitHub

Mathematical properties of B-spline

Introduction

B-spline is a mathematical object, and it has a lot of application. (e.g. Geometric representation: NURBS, Interpolation, Numerical analysis: IGA)

In this page, we'll explain the mathematical definitions and properties of B-spline with Julia code. Before running the code in the following section, you need to import packages:

using BasicBSpline
-using Plots; plotly()
Plots.PlotlyBackend()

Notice

Some of notations in this page are our original, but these are well-considered results.

References

Most of this documentation around B-spline is self-contained. If you want to learn more, the following resources are recommended.

日本語の文献では以下がおすすめです。

+using Plots; plotly()
Plots.PlotlyBackend()

Notice

Some of notations in this page are our original, but these are well-considered results.

References

Most of this documentation around B-spline is self-contained. If you want to learn more, the following resources are recommended.

日本語の文献では以下がおすすめです。

diff --git a/previews/PR334/plotlyjs/index.html b/previews/PR334/plotlyjs/index.html index 1b0052bd7..2abf4b12c 100644 --- a/previews/PR334/plotlyjs/index.html +++ b/previews/PR334/plotlyjs/index.html @@ -37,4 +37,4 @@ zs_f = getindex.(M.(ts),3) fig = Plot(scatter3d(x=xs_a, y=ys_a, z=zs_a, name="control points", line_color="blue", marker_size=8)) addtraces!(fig, scatter3d(x=xs_f, y=ys_f, z=zs_f, name="B-spline curve", mode="lines", line_color="red")) -relayout!(fig, width=500, height=500) +relayout!(fig, width=500, height=500) diff --git a/previews/PR334/plots-arc.html b/previews/PR334/plots-arc.html index 57c72d6dc..5bb4001d1 100644 --- a/previews/PR334/plots-arc.html +++ b/previews/PR334/plots-arc.html @@ -1,7 +1,7 @@ -
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