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Re: Points getting moved by BezierFunction? Moving an array of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg118326] Re: Points getting moved by BezierFunction? Moving an array of
  • From: Heike Gramberg <heike.gramberg at gmail.com>
  • Date: Fri, 22 Apr 2011 05:40:38 -0400 (EDT)

You forgot a comma in your pts array between the rows for z=-3 and z=-2. This should work better:

pts = {{{1.796875, 1.34375, -9}, {2.15625, 1.34375, -9}, {2.296875,
    1.359375, -9}, {2.375, 1.46875, -9}, {2.46875,
    1.671875, -9}, {2.53125, 1.78125, -9}, {2.578125,
    1.9375, -9}, {2.6875, 1.96875, -9}, {2.71875,
    1.78125, -9}, {2.734375, 1.609375, -9}, {2.921875,
    0.421875, -9}, {3.03125, 0.125, -9}, {3.078125,
    0.03125, -9}, {3.296875, 0.078125, -9}, {3.484375,
    0.0625, -9}, {11.5625, 0, -9}}, {{1.625, 1.171875, -8}, {2.234375,
     1.171875, -8}, {2.359375, 1.1875, -8}, {2.5,
    1.296875, -8}, {2.765625, 1.421875, -8}, {2.828125,
    2.015625, -8}, {2.9375, 2.328125, -8}, {3.1875,
    2.34375, -8}, {3.234375, 2, -8}, {3.328125,
    1.59375, -8}, {3.453125, 1.234375, -8}, {3.609375,
    0.75, -8}, {3.421875, 0.515625, -8}, {3.953125,
    0.09375, -8}, {4.234375, 0.203125, -8}, {11.4375,
    0.203125, -8}}, {{1.390625, 1.03125, -7}, {2.234375,
    1.015625, -7}, {2.46875, 1.0625, -7}, {2.59375,
    1.15625, -7}, {2.890625, 1.5625, -7}, {3.15625,
    2.1875, -7}, {3.359375, 2.796875, -7}, {3.625,
    2.78125, -7}, {3.734375, 2.171875, -7}, {3.90625,
    1.46875, -7}, {4.15625, 0.59375, -7}, {4.359375,
    0.03125, -7}, {4.453125, 0.15625, -7}, {4.5625,
    0.328125, -7}, {5.09375, 0.421875, -7}, {11.171875,
    0.390625, -7}}, {{1.203125, 0.875, -6}, {2.328125,
    0.84375, -6}, {2.578125, 0.875, -6}, {2.6875,
    0.953125, -6}, {3.140625, 1.515625, -6}, {3.4375,
    2.15625, -6}, {3.84375, 3.0625, -6}, {4.25, 3.0625, -6}, {4.40625,
     2.34375, -6}, {4.65625, 1.625, -6}, {5.0625,
    0.515625, -6}, {5.46875, 0.359375, -6}, {5.578125,
    0.53125, -6}, {5.84375, 0.5625, -6}, {6.625,
    0.59375, -6}, {10.96875, 0.5625, -6}}, {{1,
    0.6875, -5}, {2.546875, 0.671875, -5}, {2.734375,
    0.71875, -5}, {2.953125, 0.84375, -5}, {3.609375,
    1.609375, -5}, {4.0625, 2.578125, -5}, {4.359375,
    3.359375, -5}, {4.890625, 3.375, -5}, {5.15625,
    2.515625, -5}, {5.5, 1.734375, -5}, {6.0625,
    0.484375, -5}, {6.625, 0.390625, -5}, {6.75,
    0.59375, -5}, {6.9375, 0.703125, -5}, {8.03125,
    0.75, -5}, {10.84375, 0.734375, -5}}, {{0.75,
    0.53125, -4}, {3.265625, 0.515625, -4}, {3.390625,
    0.546875, -4}, {3.59375, 0.640625, -4}, {3.78125,
    0.828125, -4}, {4.25, 1.625, -4}, {5.015625,
    3.0625, -4}, {5.40625, 4.15625, -4}, {6.25,
    4.140625, -4}, {6.640625, 3.0625, -4}, {7.578125,
    1.21875, -4}, {8.234375, 0.40625, -4}, {9.171875,
    0.625, -4}, {9.390625, 0.765625, -4}, {9.703125,
    0.890625, -4}, {10.546875, 0.875, -4}}, {{0.484375,
    0.390625, -3}, {2.984375, 0.34375, -3}, {3.734375,
    0.34375, -3}, {3.890625, 0.359375, -3}, {4.046875,
    0.375, -3}, {4.265625, 0.453125, -3}, {5.609375,
    1.875, -3}, {6.5625, 2.6875, -3}, {6.78125,
    2.828125, -3}, {6.984375, 2.890625, -3}, {7.203125,
    2.96875, -3}, {8.34375, 3.09375, -3}, {7.46875,
    3.046875, -3}, {8.90625, 3.140625, -3}, {9.296875,
    3.125, -3}, {10.03125, 3.109375, -3}}, {{0.28125,
    0.234375, -2}, {1.75, 0.25, -2}, {2.796875,
    0.203125, -2}, {3.84375, 0.265625, -2}, {4.625,
    0.28125, -2}, {4.875, 0.28125, -2}, {5.046875,
    0.328125, -2}, {5.234375, 0.484375, -2}, {6.171875,
    1.109375, -2}, {6.796875, 1.578125, -2}, {7.234375,
    1.8125, -2}, {7.625, 1.984375, -2}, {7.921875,
    2.015625, -2}, {8.1875, 2.046875, -2}, {9.28125,
    2.015625, -2}, {9.84375, 2.015625, -2}}, {{0.625, 0.1, -1}, {1.25,
     0.1, -1}, {1.875, 0.1, -1}, {2.5, 0.1, -1}, {3.125,
    0.1, -1}, {3.75, 0.1, -1}, {4.375, 0.1, -1}, {5, 0.1, -1}, {5.625,
     0.1, -1}, {6.25, 0.1, -1}, {6.875, 0.1, -1}, {6.25,
    0.1, -1}, {8.125, 0.1, -1}, {8.75, 0.1, -1}, {9.375,
    0.1, -1}, {10.265625, 0.109375, -1}} }; ParametricPlot3D[
 BezierFunction[pts][u, v], {u, 0, 1}, {v, 0, 1},
 MeshFunctions -> {#1 &, #3 &}]


Heike

On 21 Apr 2011, at 08:09, Christopher O. Young wrote:

> Even though all the control points have their maximum x coordinate around
> 10, the BezierFunction is plotting a long, narrow surface that gets
> stretched out to x = 40 or so.
>
> It may be partly due to the fact that the curves between the points don't
> start at the x axis and at z = 0 the way I meant them to.
>
> Any help for a beginner trying to figure out how to translate each set of
> points so that it starts with x and y coordinates of zero? That is, I just
> want to produce a new array for each set of points, where I subtract the x
> and y coordinates of the first point from each of those points.
>
> Thanks in advance for any help.
>
> Chris Young
> cy56 at comcast.net
>
>
> pts = {
>  {{1.796875, 1.34375, -9}, {2.15625, 1.34375, -9}, {2.296875,
>
> 1.359375, -9}, {2.375, 1.46875, -9}, {2.46875,
>    1.671875, -9}, {2.53125,
> 1.78125, -9}, {2.578125,
>    1.9375, -9}, {2.6875, 1.96875, -9}, {2.71875,
>    1.78125, -9}, {2.734375, 1.609375, -9}, {2.921875,
>    0.421875, -9},
> {3.03125, 0.125, -9}, {3.078125,
>    0.03125, -9}, {3.296875, 0.078125,
> -9}, {3.484375,
>    0.0625, -9}, {11.5625, 0, -9}},
>
>  {{1.625, 1.171875,
> -8}, {2.234375, 1.171875, -8}, {2.359375,
>    1.1875, -8}, {2.5, 1.296875,
> -8}, {2.765625,
>    1.421875, -8}, {2.828125, 2.015625, -8}, {2.9375,
>
> 2.328125, -8}, {3.1875, 2.34375, -8}, {3.234375,
>    2, -8}, {3.328125,
> 1.59375, -8}, {3.453125,
>    1.234375, -8}, {3.609375, 0.75, -8},
> {3.421875,
>    0.515625, -8}, {3.953125, 0.09375, -8}, {4.234375,
>
> 0.203125, -8}, {11.4375, 0.203125, -8}},
>
>  {{1.390625, 1.03125, -7},
> {2.234375, 1.015625, -7}, {2.46875,
>    1.0625, -7}, {2.59375, 1.15625,
> -7}, {2.890625,
>    1.5625, -7}, {3.15625, 2.1875, -7}, {3.359375,
>
> 2.796875, -7}, {3.625, 2.78125, -7}, {3.734375,
>    2.171875, -7},
> {3.90625, 1.46875, -7}, {4.15625,
>    0.59375, -7}, {4.359375, 0.03125,
> -7}, {4.453125,
>    0.15625, -7}, {4.5625, 0.328125, -7}, {5.09375,
>
> 0.421875, -7}, {11.171875, 0.390625, -7}},
>
>  {{1.203125, 0.875, -6},
> {2.328125, 0.84375, -6}, {2.578125,
>    0.875, -6}, {2.6875, 0.953125, -6},
> {3.140625,
>    1.515625, -6}, {3.4375, 2.15625, -6}, {3.84375,
>    3.0625,
> -6}, {4.25, 3.0625, -6}, {4.40625, 2.34375, -6}, {4.65625,
>     1.625, -6},
> {5.0625, 0.515625, -6}, {5.46875,
>    0.359375, -6}, {5.578125, 0.53125,
> -6}, {5.84375,
>    0.5625, -6}, {6.625, 0.59375, -6}, {10.96875, 0.5625,
> -6}},
>
>  {{1, 0.6875, -5}, {2.546875, 0.671875, -5}, {2.734375,
>
> 0.71875, -5}, {2.953125, 0.84375, -5}, {3.609375,
>    1.609375, -5},
> {4.0625, 2.578125, -5}, {4.359375,
>    3.359375, -5}, {4.890625, 3.375,
> -5}, {5.15625,
>    2.515625, -5}, {5.5, 1.734375, -5}, {6.0625,
>
> 0.484375, -5}, {6.625, 0.390625, -5}, {6.75,
>    0.59375, -5}, {6.9375,
> 0.703125, -5}, {8.03125,
>    0.75, -5}, {10.84375, 0.734375, -5}},
>
>
> {{0.75, 0.53125, -4}, {3.265625, 0.515625, -4}, {3.390625,
>    0.546875,
> -4}, {3.59375, 0.640625, -4}, {3.78125,
>    0.828125, -4}, {4.25, 1.625,
> -4}, {5.015625,
>    3.0625, -4}, {5.40625, 4.15625, -4}, {6.25,
>
> 4.140625, -4}, {6.640625, 3.0625, -4}, {7.578125,
>    1.21875, -4},
> {8.234375, 0.40625, -4}, {9.171875,
>    0.625, -4}, {9.390625, 0.765625,
> -4}, {9.703125,
>    0.890625, -4}, {10.546875, 0.875, -4}},
>
>
> {{0.484375, 0.390625, -3}, {2.984375, 0.34375, -3}, {3.734375,
>
> 0.34375, -3}, {3.890625, 0.359375, -3}, {4.046875,
>     0.375, -3},
> {4.265625, 0.453125, -3}, {5.609375,
>     1.875, -3}, {6.5625, 2.6875, -3},
> {6.78125,
>     2.828125, -3}, {6.984375, 2.890625, -3}, {7.203125,
>
> 2.96875, -3}, {8.34375, 3.09375, -3}, {7.46875,
>     3.046875, -3},
> {8.90625, 3.140625, -3}, {9.296875,
>     3.125, -3}, {10.03125, 3.109375,
> -3}}
>
>   {{0.28125, 0.234375, -2}, {1.75, 0.25, -2}, {2.796875,
>
> 0.203125, -2}, {3.84375, 0.265625, -2}, {4.625,
>     0.28125, -2}, {4.875,
> 0.28125, -2}, {5.046875,
>     0.328125, -2}, {5.234375, 0.484375, -2},
> {6.171875,
>     1.109375, -2}, {6.796875, 1.578125, -2}, {7.234375,
>
> 1.8125, -2}, {7.625, 1.984375, -2}, {7.921875,
>     2.015625, -2}, {8.1875,
> 2.046875, -2}, {9.28125,
>     2.015625, -2}, {9.84375, 2.015625, -2}},
>
>
> {{0.625, 0.1, -1}, {1.25, 0.1, -1}, {1.875, 0.1, -1}, {2.5,
>    0.1, -1},
> {3.125, 0.1, -1}, {3.75, 0.1, -1}, {4.375, 0.1, -1}, {5,
>     0.1, -1},
> {5.625, 0.1, -1}, {6.25, 0.1, -1}, {6.875,
>    0.1, -1}, {6.25, 0.1, -1},
> {8.125, 0.1, -1}, {8.75,
>    0.1, -1}, {9.375, 0.1, -1}, {10.265625,
> 0.109375, -1}}
>
>
> Show[
> ParametricPlot3D[
>  BezierFunction[pts][u, v], {u, 0, 1}, {v, 0, 1},
>
> MeshFunctions -> {#1 &, #3 &},
>  AxesLabel -> z]
> ]
>
>


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