diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 7bf202ccd..e56a69470 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-11-10T15:39:08","documenter_version":"1.1.2"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-11-11T03:29:46","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/dev/1dim-manifold.html b/dev/1dim-manifold.html index f22193b30..2c65e100e 100644 --- a/dev/1dim-manifold.html +++ b/dev/1dim-manifold.html @@ -1,7 +1,7 @@ -
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{"editable":false,"responsive":true,"staticPlot":false,"scrollZoom":true}, ) diff --git a/dev/contributing/index.html b/dev/contributing/index.html index d8c18deea..4982d4e7d 100644 --- a/dev/contributing/index.html +++ b/dev/contributing/index.html @@ -1,2 +1,2 @@ -Contributing · BasicBSpline.jl

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

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/dev/geometricmodeling-arc.html b/dev/geometricmodeling-arc.html index 3557da28e..44929c7d1 100644 --- a/dev/geometricmodeling-arc.html +++ b/dev/geometricmodeling-arc.html @@ -1,7 +1,7 @@ -
+
+
+
+
+
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{"editable":false,"responsive":true,"staticPlot":false,"scrollZoom":true}, ) diff --git a/dev/histogram-uniform.html b/dev/histogram-uniform.html index ac0385f2d..32a9cc629 100644 --- a/dev/histogram-uniform.html +++ b/dev/histogram-uniform.html @@ -1,7 +1,7 @@ -
+

Private API

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

BasicBSpline.r_nomialFunction

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_RFunction

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

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

Private API

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

BasicBSpline.r_nomialFunction

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_RFunction

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

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

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+\end{aligned}\]

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Refinement

Documentation

Example

Define original manifold

p = 2 # degree of polynomial
+Refinement · BasicBSpline.jl

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/dev/math/index.html b/dev/math/index.html index 57be0ccef..cbbe137c8 100644 --- a/dev/math/index.html +++ b/dev/math/index.html @@ -1,3 +1,3 @@ Introduction · BasicBSpline.jl

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/dev/plotlyjs/index.html b/dev/plotlyjs/index.html index b9256500b..47c1a4853 100644 --- a/dev/plotlyjs/index.html +++ b/dev/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/dev/plots-arc.html b/dev/plots-arc.html index 4c6686098..b394bd1b3 100644 --- a/dev/plots-arc.html +++ b/dev/plots-arc.html @@ -1,7 +1,7 @@ -
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