Re: Region for ListPlot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg88728] Re: Region for ListPlot3D
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Wed, 14 May 2008 06:05:59 -0400 (EDT)
• Organization: University of Bergen
• References: <g0bt4i\$o42\$1@smc.vnet.net>

```Hugh Goyder wrote:
> Below I give a set of 3D points and attempt to plot them as a surface
> using ListPlot3D. I also plot the points directly using Graphics3D.
> The data fill a region that is approximately a trapezium except that
> one side is concave. ListPlot3D extrapolates the concave side out to
> the convex hull of the x -y coordinates thus giving a false impression
> of the surface. How can I make the plotting region conform to the data
> and exclude the extrapolation?
>

I just noticed that you have a regular matrix of 3D points.  What you
really need is not ListPlot3D, but a "ListParametricPlot3D", that AFAIK
does not exist.

So here's a very simple implementation:

listParametricPlot3D[points_, opt___?OptionQ] := Module[{xx, yy},
{yy, xx} = Take[Dimensions[points], 2];
Graphics3D[GraphicsComplex[Join @@ points,
Polygon[
Join @@
Table[{1 + i + xx j, 2 + i + xx j, 2 + i + xx (j + 1),
1 + i + xx (j + 1)}, {j, 0, yy - 2}, {i, 0, xx - 2}]
]], opt]
]

Fancy stuff like VertexNormals or interpolation is not handled.

listParametricPlot3D[pp] will create the plot you're looking for.

Here's another example:

listParametricPlot3D[
Table[{Cos[u] Cos[v], Cos[u] Sin[v], Sin[u]},
{u, -Pi/2, Pi/2, Pi/14}, {v, 0, 2 Pi, 2 Pi/28}],
Boxed -> False, SphericalRegion -> True
]

>
> pp = {{{0, 0, 0}, {5, 0, 0},
>          {10, 0, 0}, {14, 0, 0},
>          {19, 0, 0}, {24, 0, 0},
>          {29, 0, 0}, {33, 0, 0},
>          {38, 0, 0}, {43, 0, 0},
>          {48, 0, 0}},
>        {{0, 53, 3}, {5, 53, 3},
>          {10, 53, 3}, {14, 53,
>            3}, {19, 53, 3},
>          {24, 53, 3}, {29, 53,
>            3}, {33, 53, 3},
>          {38, 53, 3}, {43, 53,
>            3}, {48, 53, 3}},
>        {{0, 107, 18}, {5, 107,
>            19}, {10, 107, 19},
>          {14, 107, 19},
>          {19, 107, 19},
>          {24, 107, 18},
>          {29, 107, 18},
>          {33, 107, 18},
>          {38, 107, 18},
>          {43, 107, 18},
>          {48, 107, 18}},
>        {{0, 160, 81}, {5, 160,
>            81}, {10, 160, 81},
>          {15, 160, 80},
>          {20, 160, 80},
>          {25, 160, 80},
>          {30, 160, 80},
>          {35, 160, 79},
>          {40, 160, 79},
>          {45, 160, 79},
>          {50, 160, 79}},
>        {{0, 213, 142},
>          {6, 213, 142},
>          {12, 213, 141},
>          {18, 213, 141},
>          {25, 213, 140},
>          {31, 213, 140},
>          {37, 213, 140},
>          {43, 213, 139},
>          {49, 213, 139},
>          {56, 213, 138},
>          {62, 213, 138}},
>        {{0, 267, 93}, {9, 267,
>            93}, {18, 267, 93},
>          {27, 267, 93},
>          {36, 267, 93},
>          {45, 267, 93},
>          {54, 267, 92},
>          {63, 267, 92},
>          {72, 267, 91},
>          {82, 267, 91},
>          {91, 267, 90}},
>        {{0, 320, 60}, {13, 320,
>            60}, {26, 320, 60},
>          {40, 320, 60},
>          {53, 320, 59},
>          {66, 320, 59},
>          {79, 320, 58},
>          {92, 320, 58},
>          {105, 320, 58},
>          {118, 320, 58},
>          {132, 320, 57}},
>        {{0, 373, 40}, {18, 373,
>            40}, {36, 373, 40},
>          {54, 373, 40},
>          {72, 373, 40},
>          {90, 373, 40},
>          {108, 373, 40},
>          {126, 373, 40},
>          {144, 373, 40},
>          {162, 373, 40},
>          {180, 373, 40}},
>        {{0, 427, 29}, {23, 427,
>            29}, {47, 427, 29},
>          {70, 427, 29},
>          {93, 427, 29},
>          {116, 427, 29},
>          {140, 427, 29},
>          {163, 427, 28},
>          {186, 427, 28},
>          {210, 427, 28},
>          {233, 427, 28}},
>        {{0, 480, 22}, {29, 480,
>            22}, {58, 480, 22},
>          {87, 480, 22},
>          {116, 480, 22},
>          {145, 480, 22},
>          {174, 480, 22},
>          {203, 480, 22},
>          {232, 480, 22},
>          {260, 480, 22},
>          {289, 480, 22}},
>        {{0, 533, 17}, {35, 533,
>            17}, {70, 533, 17},
>          {104, 533, 17},
>          {139, 533, 17},
>          {174, 533, 17},
>          {209, 533, 17},
>          {244, 533, 17},
>          {278, 533, 17},
>          {313, 533, 17},
>          {348, 533, 17}}};

```

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