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Graphics and Visualization

Problems with Translation

Michael Kyzar

Posted 10 years ago

For a class project, I am trying to make a 3D object which includes a fleet of ships heading toward an island. I was planning to make one ship and translate it to many locations. However I've run into a dilemma. The method I am using to show the translation of the copied ship object has run into a snag and I'm wondering what I'm doing wrong. This is what I used without including the translation: K1 = ParametricPlot3D[{(1 - 2 b) (7 + Cos[b]) Cos[ 8 Pia], (1 - a) (3 + Cos[4 b]) Sin[8Pia], 4 a + (1 - a) Cos[12Pib]}, {a, -1, 1}, {b, -1, 1}, PlotStyle -> Directive[Brown], MeshStyle -> {{Black, Thickness[0.001]}, {Black, Thickness[0.001]}}, Axes -> False, Boxed -> False]; K2 = {Blue, Polygon[{{-50, 50, -3}, {50, 50, -3}, {50, -50, -3}, {-50, -50, -3}}]}; K3 = {Black, Cylinder[{{15, 0, 0}, {15, 0, 15}}, .75]}; K4 = {Black, Cylinder[{{-15, 0, 0}, {-15, 0, 15}}, .75]}; K5 = {Black, Cylinder[{{0, 0, 0}, {0, 0, 30}}, .75]}; Show[{Graphics3D[{K2, K3, K4, K5}], K1}] This is what I used with the translation added: K1 = ParametricPlot3D[{(1 - 2 b) (7 + Cos[b]) Cos[ 8 Pia], (1 - a) (3 + Cos[4 b]) Sin[8Pia], 4 a + (1 - a) Cos[12Pib]}, {a, -1, 1}, {b, -1, 1}, PlotStyle -> Directive[Brown], MeshStyle -> {{Black, Thickness[0.001]}, {Black, Thickness[0.001]}}, Axes -> False, Boxed -> False]; K2 = {Blue, Polygon[{{-50, 50, -3}, {50, 50, -3}, {50, -50, -3}, {-50, -50, -3}}]}; K3 = {Black, Cylinder[{{15, 0, 0}, {15, 0, 15}}, .75]}; K4 = {Black, Cylinder[{{-15, 0, 0}, {-15, 0, 15}}, .75]}; K5 = {Black, Cylinder[{{0, 0, 0}, {0, 0, 30}}, .75]}; Show[{Graphics3D[{K2, K3, K4, K5}], K1, Translate[{Graphics3D[{K2, K3, K4, K5}], K1}, {50, 0, 0}]}] If anyone could add any clarification as to what I'm doing wrong, that would be greatly appreciated.

For a class project, I am trying to make a 3D object which includes a fleet of ships heading toward an island. I was planning to make one ship and translate it to many locations. However I've run into a dilemma. The method I am using to show the translation of the copied ship object has run into a snag and I'm wondering what I'm doing wrong. This is what I used without including the translation:

    K1 = ParametricPlot3D[{(1 - 2 b) (7 + Cos[b]) Cos[
          8 Pi*a], (1 - a) (3 + Cos[4 b]) Sin[8*Pi*a], 
        4 a + (1 - a) Cos[12*Pi*b]}, {a, -1, 1}, {b, -1, 1}, 
       PlotStyle -> Directive[Brown], 
       MeshStyle -> {{Black, Thickness[0.001]}, {Black, 
          Thickness[0.001]}}, Axes -> False, Boxed -> False];
    K2 = {Blue, 
       Polygon[{{-50, 50, -3}, {50, 
          50, -3}, {50, -50, -3}, {-50, -50, -3}}]};
    K3 = {Black, Cylinder[{{15, 0, 0}, {15, 0, 15}}, .75]};
    K4 = {Black, Cylinder[{{-15, 0, 0}, {-15, 0, 15}}, .75]};
    K5 = {Black, Cylinder[{{0, 0, 0}, {0, 0, 30}}, .75]};
    Show[{Graphics3D[{K2, K3, K4, K5}], K1}]

This is what I used with the translation added:

    K1 = ParametricPlot3D[{(1 - 2 b) (7 + Cos[b]) Cos[
          8 Pi*a], (1 - a) (3 + Cos[4 b]) Sin[8*Pi*a], 
        4 a + (1 - a) Cos[12*Pi*b]}, {a, -1, 1}, {b, -1, 1}, 
       PlotStyle -> Directive[Brown], 
       MeshStyle -> {{Black, Thickness[0.001]}, {Black, 
          Thickness[0.001]}}, Axes -> False, Boxed -> False];
    K2 = {Blue, 
       Polygon[{{-50, 50, -3}, {50, 
          50, -3}, {50, -50, -3}, {-50, -50, -3}}]};
    K3 = {Black, Cylinder[{{15, 0, 0}, {15, 0, 15}}, .75]};
    K4 = {Black, Cylinder[{{-15, 0, 0}, {-15, 0, 15}}, .75]};
    K5 = {Black, Cylinder[{{0, 0, 0}, {0, 0, 30}}, .75]};
    Show[{Graphics3D[{K2, K3, K4, K5}], K1, Translate[{Graphics3D[{K2, K3, K4, K5}], K1}, {50, 0, 0}]}]

If anyone could add any clarification as to what I'm doing wrong, that would be greatly appreciated.

POSTED BY: Michael Kyzar

3 Replies

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Xavier Roy

Xavier Roy, WOLFRAM

Posted 10 years ago

(I posted twice the answer, sorry.)

POSTED BY: Xavier Roy

Xavier Roy

Xavier Roy, WOLFRAM

Posted 10 years ago

Hi Michael, In case one of your graphics primitive is defined with more than two options, such as for instance K2 = {Blue, EdgeForm[], Polygon[{{-50, 50, -3}, {50, 50, -3}, {50, -50, -3}, {-50, -50, -3}}]}; (I added EdgeForm[] compared to your definition of K2 this removes the black edge of the sea), the code Graphics3D[Map[ {First[#], Translate[Last[#], {50, 0, 0}]} &, {K2, K3, K4, K5}] will not propagate the EdgeForm[] option. (EdgeForm[] is the second element of the list K2, and only its first and last element are considered.) In such a situation you can use directly Graphics3D[Translate[{K2}, {50, 0, 0}]] This way the graphics primitive is translated along with all its options. Using part of Craig's code, the alternative final code would read Show[{Graphics3D[{K2, K3, K4, K5}], K1, Graphics3D[Translate[{K2, K3, K4, K5}, {50, 0, 0}]], K1 /. GraphicsComplex[points_, a__] :> GraphicsComplex[Map[# + {50, 0, 0} &, points], a]}] which can be shorten into Show[{Graphics3D[{K2, K3, K4, K5, Translate[{K2, K3, K4, K5}, {50, 0, 0}]}], K1, K1 /. GraphicsComplex[points_, a__] :> GraphicsComplex[Map[# + {50, 0, 0} &, points], a]}] Cheers, Xavier

POSTED BY: Xavier Roy

W. Craig Carter

W. Craig Carter, MIT

Posted 10 years ago

Hello MIchael, You can Translate something that is not a graphics primitive. But, there is a way around this: Here, I use Map to only translate your primitives. Because your K1 is a GraphicsComplex, we can grab the points and then translate them the old-fashioned way: Show[ {Graphics3D[{K2, K3, K4, K5}], K1, Graphics3D[Map[ {First[#], Translate[Last[#], {50, 0, 0}]} &, {K2, K3, K4, K5}] ], K1 /. GraphicsComplex[points_, a__] :> GraphicsComplex[Map[# + {50, 0, 0} &, points], a]}]

POSTED BY: W. Craig Carter

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