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Graphics and Visualization Wolfram Language

3D parametric plot With 3 parameters

Joe Prendergast

Joe Prendergast, American Universiity

Posted 1 year ago

Hello, I'm trying to make a 3D Parametric Plot as follows: ParametricPlot3D[{X, Y, Z}, {a, 0, 1}, {b, 0, 1}, {c, 0, 1}] X, Y, and Z are each functions of the parameters a, b and c. However, ParametricPlot3D only works for two parameters or less and I have 3. Any thoughts on how to do this?

POSTED BY: Joe Prendergast

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 year ago

You may also consider `TransformedRegion`: Region@TransformedRegion[Cuboid[{0, 0, 0}], {Indexed[#, 1] Indexed[#, 2], Indexed[#, 1] + .5 Indexed[#, 2], Indexed[#, 3]} &]

POSTED BY: Gianluca Gorni

Sander Huisman

Sander Huisman, University of Twente

Posted 1 year ago

What about: ClearAll[myparametricplot3D] ConnectToMakeCube[{{{a1_,a2_},{a3_,a4_}},{{a5_,a6_},{a7_,a8_}}}]:=Line[{ {a1,a2}, {a3,a4}, {a1,a3}, {a2,a4}, {a5,a6}, {a7,a8}, {a5,a7}, {a6,a8}, {a1,a5}, {a2,a6}, {a3,a7}, {a4,a8} }] myparametricplot3D[fs:{fx_,fy_,fz_},xs:{x_,xmin_,xmax_,\[CapitalDelta]x_},ys:{y_,ymin_,ymax_,\[CapitalDelta]y_},zs:{z_,zmin_,zmax_,\[CapitalDelta]z_}]:=Module[{data}, data=Table[fs,xs,ys,zs]; BlockMap[ConnectToMakeCube,data,{2,2,2},1] ] Graphics3D[myparametricplot3D[{x+0.3y-0.1z^3,y-0.1x,0.2x-0.3y^2-z},{x,-1,1,0.25},{y,-1,1,0.25},{z,-1,1,0.25}],Axes->True,AxesLabel->{"x","y","z"}] giving:

What about:

ClearAll[myparametricplot3D]
ConnectToMakeCube[{{{a1_,a2_},{a3_,a4_}},{{a5_,a6_},{a7_,a8_}}}]:=Line[{
{a1,a2},
{a3,a4},
{a1,a3},
{a2,a4},

{a5,a6},
{a7,a8},
{a5,a7},
{a6,a8},

{a1,a5},
{a2,a6},
{a3,a7},
{a4,a8}
}]
myparametricplot3D[fs:{fx_,fy_,fz_},xs:{x_,xmin_,xmax_,\[CapitalDelta]x_},ys:{y_,ymin_,ymax_,\[CapitalDelta]y_},zs:{z_,zmin_,zmax_,\[CapitalDelta]z_}]:=Module[{data},
data=Table[fs,xs,ys,zs];
BlockMap[ConnectToMakeCube,data,{2,2,2},1]
]
Graphics3D[myparametricplot3D[{x+0.3y-0.1z^3,y-0.1x,0.2x-0.3y^2-z},{x,-1,1,0.25},{y,-1,1,0.25},{z,-1,1,0.25}],Axes->True,AxesLabel->{"x","y","z"}]

giving:

enter image description here