In[16]:=
Clear[width,spine,ripple,normalize,tangent,normal,
binormal]
Needs["Calculus`VectorAnalysis`"];
width[z_] = 0.1 z (1-z);
spine[z_] = {0, z^2, z};
normalize[v_] = v/Sqrt[v.v];
tangent[z_] = normalize[spine'[z]];
binormal[z_] =
normalize[CrossProduct[tangent[z], {0,1,0}]];
normal[z_] = CrossProduct[tangent[z], binormal[z]];
leaf =
ParametricPlot3D[
spine[z] + y width[z] normal[z],
{y,-1,1}, {z,0,1},
PlotPoints -> {2,30}, ViewPoint -> {2,1,0}];
This leaf must be rotated about the z axis to create a spider-plant type plant.
In[17]:=
spider =
Table[Rotate[leaf,theta,{0,0,1}], {theta,0,7Pi/4,Pi/4}];
In[18]:=
Show[spider];
Up to Aquarium