geometry - 带有两个嘴的凹面六角形的标准网格？

Question

我正在计划通过带有两个嘴的凹双对称六边形对流动进行可视化处理。

边d1的长度等于边d2的另一长度的示例:

最初我讨论的是关于不规则六边形的here的命名。

有一个标准的“网格”工具，您可以在其中绘制自己的网格，但是我想拥有一些标准的库，以便以后可以与其他人更好地配合流动模拟。
我在MathCentral File Exchange here中找不到用于六角形的任何Mesh库。

是否有用于不规则六边形的标准网格库？
我也对任何其他语言都开放，因为我可以阅读代码并将其转换为Matlab库。

Answer 1

例如，您可以看一下Alexandra Baumgart和Hazuki Okuda使用Mathematica所做的示例。这可以通过 Manipulate 有效地创建基本UI来实现。

代码:

Manipulate[
Grid[{{Show[
ParametricPlot3D[{1.25Cos[t], 1.25 Sin[t],s+2-2w},{s,0,.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None, Lighting->"Neutral"], 
ParametricPlot3D[{r Cos[t], r Sin[t],2.25-2w},{r,0,1.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{r Cos[t], r Sin[t],2-2w},{r,0,1.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{1.25Cos[t], 1.25 Sin[t],s-2.25+2w},{s,0,.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{r Cos[t], r Sin[t],-2.25+2w},{r,0,1.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None],
ParametricPlot3D[{r Cos[t], r Sin[t],-2+2w},{r,0,1.25},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Gray],Mesh->None, Lighting->"Neutral"],  
ParametricPlot3D[{(1-s/2) Cos[t],(1-s/2) Sin[t],Max[0,-s+2 ]},{s,Min[2-(2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)-w,1.99],2},{t,0, 2 Pi},PlotStyle->Directive[Opacity[1],Hue[a]],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{r Cos[t], r Sin[t],Max[0,(2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)-w]},{r,0, .000000000001+w+((2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)-w)/2},{t,0,2Pi},PlotStyle->Directive[Opacity[1], Hue[a]],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{r Cos[t], r Sin[t], Min[0,-(2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)]},{r, 0, .00000000001+w+((2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)-w)/2},{t,0,2Pi},PlotStyle->Directive[Opacity[1],Hue[a]],Mesh->None, Lighting->"Neutral"],
ParametricPlot3D[{(1-s/2) Cos[t],(1-s/2) Sin[t],Min[0,s -2 ]},{s,w,2},{t,0, 2 Pi},PlotStyle->Directive[Opacity[.2],Gray],Mesh->None, Lighting->"Neutral"],ParametricPlot3D[{(1-s/2) Cos[t],(1-s/2) Sin[t],Max[0,-s + 2 - w]},{s,w,2},{t,0, 2 Pi},PlotStyle->Directive[Opacity[.2],Gray],Mesh->None, Lighting->"Neutral"], 
ParametricPlot3D[{(1-s/2) Cos[t],(1-s/2) Sin[t],Min[0,s-2+ w]},{s,w,Min[2-(2^(2/3) (2 \[Pi]-Min[2Pi,3 V((w^2)/(.04))])^(1/3))/\[Pi]^(1/3)-w,2]},{t,0, 2 Pi},Mesh->None, PlotStyle->Directive[Opacity[1],Hue[a]], Lighting->"Neutral"],  ParametricPlot3D[{(w/2) Cos[t],(w/2) Sin[t], b},{t,0,2Pi}, {b, -2 + w, 0}, PlotStyle->Directive[Opacity[1], Hue[a]],Mesh->None, Lighting->"Neutral"],PlotRange->All,ImageSize->{300,300}, SphericalRegion-> True]},{Row[{Text["time to empty = "], Text[2Pi (.04)/(3w^2)],Text[" seconds"]}]}}],{start,ControlType->None},{end,ControlType->None},
{{V,.01,"time (seconds)"},0.01,34,.01,ControlType->Animator,AnimationRate->1,AnimationRunning->False,ImageSize->Small}, 
{{w,.05,"neck width (millimeters)"}, .05, .3,.01,Appearance->"Labeled"}, 
{{a,0,"color of sand"}, 0, 1,Appearance->"Labeled"}]

资料来源: http://demonstrations.wolfram.com/FlowTimeInAnHourglass/