Re: Help with Graphics

• To: mathgroup at smc.vnet.net
• Subject: [mg6853] Re: [mg6817] Help with Graphics
• From: Xah Lee <xah at best.com>
• Date: Thu, 24 Apr 1997 02:44:32 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```At 2:02 AM -0400 4/21/97, Dr. Sergio Terrazas wrote:
>...
>I want to generate a 3-Dimensional
>grid of n x n x n (empty) boxes at first, and then, if the center point
>of a box is inside the region of integration,then show those boxes filled
>(using Cuboid[])
>...

One somewhat more symmetric way to generate a 3d grid is by drawing half a
box at each grid point, then map the space with these frames.

Example:

Clear[gridFrame, myGraPrim];

gridFrame::usage="gridFrame[3DPoint,sideLength] returns a list of Line
graphic primitives that represents a box of sidelength and one corner at
3DPoint. Example: gridFrame[{a,b,c},s]"

gridFrame[p_,s_]:=
Module[{},{Line/@(Transpose[{#,#+DiagonalMatrix[{s,s,s}]}&@Table[p,{3}]])}]

myGraPrim=Table[gridFrame[{i,j,k},1],{i,4},{j,3},{k,2}];

Show[Graphics3D[{Hue[0],myGraPrim}],AspectRatio->Automatic,Boxed->False,
Axes->True,ViewPoint->{1.354, -2.758, 1.418}];

Other ways of generating a grid may be drawing continuous lines from end to
end. This is somewhat unsymmetric and unflexible. Or, you can generate a
complete box at each point, but then neighboring grids overlap.

Xah
xah at best.com
http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html
Mountain View, CA, USA

```

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