From ca125dd46fedc9210f6001dd74aeddf6807af9f1 Mon Sep 17 00:00:00 2001 From: hyrodium Date: Wed, 14 Feb 2024 18:29:25 +0900 Subject: [PATCH] update around refinement --- README.md | 10 +++++----- docs/src/math/refinement.md | 8 ++++---- 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/README.md b/README.md index 4da957ae..2a00f413 100644 --- a/README.md +++ b/README.md @@ -152,7 +152,9 @@ plot(M; controlpoints=(markersize=2,)) ![](docs/src/img/rational_bspline_surface_plotly.png) ### Refinement -#### h-refinement +#### h-refinement (knot insertion) +Insert additional knots to knot vectors without changing the shape. + ```julia k₊ = (KnotVector([3.1, 3.2, 3.3]), KnotVector([0.5, 0.8, 0.9])) # additional knot vectors M_h = refinement(M, k₊) # refinement of B-spline manifold @@ -160,9 +162,9 @@ plot(M_h; controlpoints=(markersize=2,)) ``` ![](docs/src/img/rational_bspline_surface_href_plotly.png) -Note that this shape and the last shape are equivalent. +#### p-refinement (degree elevation) +Increase the polynomial degrees of B-spline manifold without changing the shape. -#### p-refinement ```julia p₊ = (Val(1), Val(2)) # additional degrees M_p = refinement(M, p₊) # refinement of B-spline manifold @@ -170,8 +172,6 @@ plot(M_p; controlpoints=(markersize=2,)) ``` ![](docs/src/img/rational_bspline_surface_pref_plotly.png) -Note that this shape and the last shape are equivalent. - ### Fitting B-spline manifold The next example shows the fitting for [the following graph on Desmos graphing calculator](https://www.desmos.com/calculator/2hm3b1fbdf)! diff --git a/docs/src/math/refinement.md b/docs/src/math/refinement.md index ef555e01..2300d59a 100644 --- a/docs/src/math/refinement.md +++ b/docs/src/math/refinement.md @@ -27,8 +27,8 @@ nothing # hide ![](refinement_2dim_original.png) -### h-refinement -Insert additional knots to knot vector without changing the shape. +### h-refinement (knot insertion) +Insert additional knots to knot vectors without changing the shape. ```@repl math_refinement k₊ = (KnotVector([3.3,4.2]), KnotVector([3.8,3.2,5.3])) # additional knot vectors @@ -40,8 +40,8 @@ nothing # hide ![](refinement_2dim_h.png) -### p-refinement -Increase the polynomial degree of B-spline manifold without changing the shape. +### p-refinement (degree elevation) +Increase the polynomial degrees of B-spline manifold without changing the shape. ```@repl math_refinement p₊ = (Val(1), Val(2)) # additional degrees