Plain Mathematica Examples

by Ian Markwood, illiMath REU Summer 2010

CubeMathematica currently supports all 3D surface display functions.  Evaluate the following to see how they work or investigate their examples  (30aug10)

?Plot3D
(*  click here for example *)

?ListContourPlot3D
(*  click here for example *)

?ParametricPlot3D
(*  click here for example *)

?RegionPlot3D
(*  click here for example *)

?SphericalPlot3D
(*  click here for example *)

These examples are "detached" from CubeMathematica to run in a 
plain 'matica front end.

■     ArcSine function displayed with Plot3D

Manipulate[Plot3D[a*Sin[x*y],{x,-2,2},{y,-2,2},Mesh->None,PlotStyle->Directive[Yellow,Specularity[White,20],Opacity[0.8]],ExclusionsStyle->{None,Red}],{a,1,5}]

■     "Exploded sphere" displayed with ListContourPlot3D

ListContourPlot3D[Table[x^2+y^2+z^2,{x,-2,2,0.2},{y,-2,2,0.2},{z,-2,2,0.2}],Contours->6,Mesh->None]

■     Cable Knot displayed with ParametricPlot3D

turn=9; ext=2; knot=4; dist=1; dia=0.2; par=ParametricPlot3D[{(ext+Cos[turn x]) Cos[knot x],(ext+Cos[turn x]) Sin[knot x],dist Sin[turn x]},{x,0,2 Pi},PlotStyle->Tube[dia],PlotRange->All,Axes->False,Boxed->False,ViewPoint->{0,0,6},ColorFunction->"DeepSeaColors",ImageSize->{400,300}]

■     Triaxial Tritorus displayed with ParametricPlot3D
[surface by Katie Poon]

ParametricPlot3D[{Sin[u](1+Cos[v]),Sin[u+2Pi/3](1+Cos[v+2Pi/3]),Sin[u+4Pi/3](1+Cos[v+4Pi/3])},
{u,-Pi,Pi},{v,-Pi,Pi},Mesh->False,ColorFunction->Function[{x,y,z,u,v},Hue[z]]]

■     Regions where xyz<1 displayed with RegionPlot3D

RegionPlot3D[(x y z<1)&&(x+y+z<1),{x,-5,5},{y,-5,5},{z,-5,5},PlotStyle->Directive[Yellow,Opacity[0.5]],Mesh->None]

■     Awesome Sphere displayed with SphericalPlot3D
[Note the MaxRecursion level  for adaptive mesh refinement is 1 for a jagged surface.  Increasing it to 2 or 3 takes longer to render but looks nicer.]

RenderSZG[SphericalPlot3D[Sin[5x + 7 y],x,y,ColorFunction->(ColorData["Rainbow"][#6]&),Mesh->None,PlotPoints->35,Boxed->False,Axes->False,MaxRecursion->3]]