hyrodium · hyrodium · Feb 6, 2024 · Feb 6, 2024 · Feb 6, 2024 · Feb 6, 2024
diff --git a/README.md b/README.md
@@ -44,10 +44,10 @@ Install this package
 ]add BasicBSpline
 ```
 
-## Example
+## Quick start
 ### B-spline basis function
 
-The value of B-spline basis function $B_{(i,p,k)}$ can be obtained with `bsplinebasis`. ([example in Desmos](https://www.desmos.com/calculator/ql6jqgdabs))
+The value of B-spline basis function $B_{(i,p,k)}$ can be obtained with `bsplinebasis₊₀`. ([example in Desmos](https://www.desmos.com/calculator/ql6jqgdabs))
 
 $$
 \begin{aligned}
@@ -74,10 +74,10 @@ P1 = BSplineSpace{1}(k) # 1st degree piecewise polynomial space
 P2 = BSplineSpace{2}(k) # 2nd degree piecewise polynomial space
 P3 = BSplineSpace{3}(k) # 3rd degree piecewise polynomial space
 plot(
-    plot([t->bsplinebasis(P0,i,t) for i in 1:dim(P0)], 0, 10, ylims=(0,1), legend=false),
-    plot([t->bsplinebasis(P1,i,t) for i in 1:dim(P1)], 0, 10, ylims=(0,1), legend=false),
-    plot([t->bsplinebasis(P2,i,t) for i in 1:dim(P2)], 0, 10, ylims=(0,1), legend=false),
-    plot([t->bsplinebasis(P3,i,t) for i in 1:dim(P3)], 0, 10, ylims=(0,1), legend=false),
+    plot([t->bsplinebasis₊₀(P0,i,t) for i in 1:dim(P0)], 0, 10, ylims=(0,1), legend=false),
+    plot([t->bsplinebasis₊₀(P1,i,t) for i in 1:dim(P1)], 0, 10, ylims=(0,1), legend=false),
+    plot([t->bsplinebasis₊₀(P2,i,t) for i in 1:dim(P2)], 0, 10, ylims=(0,1), legend=false),
+    plot([t->bsplinebasis₊₀(P3,i,t) for i in 1:dim(P3)], 0, 10, ylims=(0,1), legend=false),
     layout=(2,2),
 )
 ```

diff --git a/docs/make.jl b/docs/make.jl
@@ -25,6 +25,14 @@ function generate_indexmd_from_readmemd()
     text_index = text_readme
     text_index = replace(text_index, "![](docs/src/img" => "![](img")
     text_index = replace(text_index, r"\$\$((.|\n)*?)\$\$" => s"```math\1```")
+    text_index = replace(text_index, "(https://hyrodium.github.io/BasicBSpline.jl/dev/math/bsplinebasis/#Differentiability-and-knot-duplications)" => "(@ref differentiability-and-knot-duplications)")
+    text_index = replace(text_index, r"https://github.com/hyrodium/BasicBSpline\.jl/assets/.*" => "![](math/differentiability.mp4)")
+    text_index = """
+    ```@meta
+    EditURL = "https://github.com/hyrodium/BasicBSpline.jl/blob/main/README.md"
+    ```
+
+    """ * text_index
 
     # save index.md
     open(path_index, "w") do f
@@ -38,7 +46,7 @@ makedocs(;
     modules = [BasicBSpline, BasicBSplineFitting],
     format = Documenter.HTML(
         ansicolor=true,
-        canonical = "https://hyrodium.github.io/BasicBSpline.jl/stable/",
+        canonical = "https://hyrodium.github.io/BasicBSpline.jl",
         assets = ["assets/favicon.ico", "assets/custom.css"],
         edit_link="main",
         repolink="https://github.com/hyrodium/BasicBSpline.jl"
@@ -54,8 +62,8 @@ makedocs(;
             "Derivative" => "math/derivative.md",
             "Inclusive relationship" => "math/inclusive.md",
             "Refinement" => "math/refinement.md",
-            "Fitting" => "math/fitting.md",
             "Rational B-spline manifold" => "math/rationalbsplinemanifold.md",
+            "Fitting" => "math/fitting.md",
         ],
         # "Differentiation" => [
         #     "BSplineDerivativeSpace" => "bsplinederivativespace.md",
@@ -71,9 +79,9 @@ makedocs(;
         "Interpolations" => "interpolations.md",
         "API" => "api.md",
     ],
-    repo = "https://github.com/hyrodium/BasicBSpline.jl/blob/{commit}{path}#L{line}",
     sitename = "BasicBSpline.jl",
     authors = "hyrodium <[email protected]>",
+    warnonly = true,
 )
 
 deploydocs(

diff --git a/docs/src/api.md b/docs/src/api.md
@@ -20,6 +20,13 @@ bsplinebasis
 BasicBSpline.bsplinebasis₋₀I
 intervalindex
 bsplinebasisall
+bsplinesupport
+dim
+exactdim_R(P::BSplineSpace)
+exactdim_I(P::BSplineSpace)
+BSplineSpace
+isnondegenerate
+isdegenerate(P::BSplineSpace)
 ```
 
 ```@docs

diff --git a/docs/src/index.md b/docs/src/index.md
diff --git a/docs/src/math/bsplinebasis.md b/docs/src/math/bsplinebasis.md
@@ -84,10 +84,6 @@ In these cases, each B-spline basis function ``B_{(i,2,k)}`` is coninuous, so [`
 
 [TODO: fig]
 
-```@docs
-bsplinesupport
-```
-
 ## Partition of unity
 !!! info "Thm.  Partition of unity"
     Let ``B_{(i,p,k)}`` be a B-spline basis function, then the following equation is satisfied.
@@ -155,7 +151,7 @@ Here are all of valiations of the B-spline basis function.
 * [`bsplinebasis`](@ref)
 * [`BasicBSpline.bsplinebasis₋₀I`](@ref)
 
-## Differentiability and knot duplications
+## [Differentiability and knot duplications](@id differentiability-and-knot-duplications)
 
 The differentiability of the B-spline basis function depends on the duplications on the knot vector.
 
@@ -215,6 +211,20 @@ nothing # hide
 Sometimes, you may need the non-zero values of B-spline basis functions at specific point.
 The [`bsplinebasisall`](@ref) function is much more efficient than evaluating B-spline functions one by one with [`bsplinebasis`](@ref) function.
 
+```@example math_bsplinebasis
+P = BSplineSpace{2}(KnotVector([0.0, 1.5, 2.5, 5.5, 8.0, 9.0, 9.5, 10.0]))
+t = 6.3
+plot(P; label="P", ylims=(0,1))
+scatter!(fill(t,3), [bsplinebasis(P,2,t), bsplinebasis(P,3,t), bsplinebasis(P,4,t)]; markershape=:hline, label="bsplinebasis")
+scatter!(fill(t,3), bsplinebasisall(P, 2, t); markershape=:vline, label="bsplinebasisall")
+savefig("bsplinebasis_vs_bsplinebasisall.png") # hide
+nothing # hide
+```
+
+![](bsplinebasis_vs_bsplinebasisall.png)
+
+Benchmark:
+
 ```@repl
 using BenchmarkTools, BasicBSpline
 P = BSplineSpace{2}(KnotVector([0.0, 1.5, 2.5, 5.5, 8.0, 9.0, 9.5, 10.0]))
@@ -237,7 +247,7 @@ for p in 1:3
     plot(P, legend=:topleft, label="B-spline basis (p=1)")
     plot!(t->intervalindex(P,t),0,10, label="Interval index")
     plot!(t->sum(bsplinebasis(P,i,t) for i in 1:dim(P)),0,10, label="Sum of B-spline basis")
-    scatter!(k.vector,zero(k.vector), label="knot vector")
+    plot!(k, label="knot vector")
     plot!([t->bsplinebasisall(P,1,t)[i] for i in 1:p+1],0,10, color=:black, label="bsplinebasisall (i=1)", ylim=(-1,8-2p))
     savefig("bsplinebasisall-$(p).html") # hide
     nothing # hide

diff --git a/docs/src/math/bsplinespace.md b/docs/src/math/bsplinespace.md
@@ -1,10 +1,12 @@
 # B-spline space
 
-```@setup math
+## Setup
+
+```@example math_bsplinespace
 using BasicBSpline
 using BasicBSplineExporter
 using StaticArrays
-using Plots; plotly()
+using Plots; gr()
 ```
 
 ## Defnition
@@ -52,10 +54,6 @@ Note that each element of the space ``\mathcal{P}[p,k]`` is a piecewise polynomi
 
 [TODO: fig]
 
-```@docs
-BSplineSpace
-```
-
 ## Degeneration
 
 !!! tip "Def.  Degeneration"
@@ -66,14 +64,6 @@ BSplineSpace
     \end{aligned}
     ```
 
-```@docs
-isnondegenerate
-```
-
-```@docs
-isdegenerate(P::BSplineSpace)
-```
-
 ## Dimensions
 
 !!! info "Thm.  Dimension of B-spline space"
@@ -82,14 +72,24 @@ isdegenerate(P::BSplineSpace)
     \dim(\mathcal{P}[p,k])=\# k - p -1
     ```
 
-```@docs
-dim
+```@repl math_bsplinespace
+P1 = BSplineSpace{1}(KnotVector([1,2,3,4,5,6,7]))
+P2 = BSplineSpace{1}(KnotVector([1,2,4,4,4,6,7]))
+P3 = BSplineSpace{1}(KnotVector([1,2,3,5,5,5,7]))
+dim(P1), exactdim_R(P1), exactdim_I(P1)
+dim(P2), exactdim_R(P2), exactdim_I(P2)
+dim(P3), exactdim_R(P3), exactdim_I(P3)
 ```
 
-```@docs
-exactdim_R(P::BSplineSpace)
-```
+Visualization:
 
-```@docs
-exactdim_I(P::BSplineSpace)
+```@example math_bsplinespace
+pl1 = plot(P1); plot!(pl1, knotvector(P1))
+pl2 = plot(P2); plot!(pl2, knotvector(P2))
+pl3 = plot(P3); plot!(pl3, knotvector(P3))
+plot(pl1, pl2, pl3; layout=(1,3), legend=false)
+savefig("dimension-degeneration.png") # hide
+nothing # hide
 ```
+
+![](dimension-degeneration.png)