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I am an absolute beginner in Mathematica. For a small test project, I am supposed to change the following code such that the corners of the polygon {0, 0, 0}, {1, 1, 1}, {0, 1, 0}, {1, 0, 1} can be manipulated. I did not find any satisfactory solution so far.

Manipulate[
  Graphics3D[
    Polygon[{{0, 0, 0}, {1, 1, 1}, {0, 1, 0}, {1, 0, 1}}, 
      VertexColors -> {a, b, c, d}], 
    ImageSize -> {600, 600}], 
  {{a, Red, "first corner"}, Red}, 
  {{b, Green, "second corner"}, Green},
  {{c, Blue, "third corner"}, Blue}, 
  {{d, Yellow, "fourth corner"}, Yellow}]
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  • $\begingroup$ What kind of manipulation to have in mind? What action should change invoke in the displayed polygon? Is it the position of the corners, or something else? $\endgroup$
    – m_goldberg
    Commented Apr 17, 2018 at 18:16

1 Answer 1

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Depending on how you want to manipulate the corners, you could do it a few ways.

  1. Inputting points as a list

    Manipulate[
 Graphics3D[Polygon[{p1, p2, p3, p4}, VertexColors -> {a, b, c, d}], 
   ImageSize -> {600, 600}], {{a, Red, "first corner"}, 
  Red}, {{b, Green, "second corner"}, 
  Green}, {{c, Blue, "third corner"}, 
  Blue}, {{d, Yellow, "fourth corner"}, Yellow},
 Column[{Control[{{p1, {0, 0, 0}}}], Control[{{p2, {1, 1, 1}}}], 
   Control[{{p3, {0, 1, 0}}}], Control[{{p4, {1, 0, 1}}}]}]]

Output: User inputs the corners as a list

1b. Prettier version of 1:

Manipulate[
 Graphics3D[Polygon[{p1, p2, p3, p4}, VertexColors -> {a, b, c, d}], 
  ImageSize -> {600, 600}], {{a, Red, "first corner"}, 
  Red}, {{b, Green, "second corner"}, 
  Green}, {{c, Blue, "third corner"}, 
  Blue}, {{d, Yellow, "fourth corner"}, Yellow},
 Control[{{p1, {0, 0, 0}}}], Control[{{p2, {1, 1, 1}}}], 
 Control[{{p3, {0, 1, 0}}}], Control[{{p4, {1, 0, 1}}}]]

Output: Prettier version of 1

  1. User could use sliders to slide the corners

    Manipulate[ Graphics3D[ Polygon[{{p1x, p1y, p1z}, {p2x, p2y, p2z}, {p3x, p3y, p3z}, {p4x, p4y, p4z}}, VertexColors -> {a, b, c, d}], ImageSize -> {600, 600}], {{a, Red, "first corner"}, Red}, {{b, Green, "second corner"}, Green}, {{c, Blue, "third corner"}, Blue}, {{d, Yellow, "fourth corner"}, Yellow}, Grid[{ {Control[{p1x, 0, 1}], Control[{p1y, 0, 1}], Control[{p1z, 0, 1}]}, {Control[{p2x, 0, 1}], Control[{p2y, 0, 1}], Control[{p2z, 0, 1}]}, {Control[{p3x, 0, 1}], Control[{p3y, 0, 1}], Control[{p3z, 0, 1}]}, {Control[{p4x, 0, 1}], Control[{p4y, 0, 1}], Control[{p4z, 0, 1}]}}]]

Output: Sliders

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  • 1
    $\begingroup$ thats exactly what I was looking for. Thank you! $\endgroup$
    – MARIUS
    Commented Apr 17, 2018 at 17:00
  • $\begingroup$ You're welcome! Make sure to mark this as the correct answer if it was sufficient!! $\endgroup$
    – Max Coplan
    Commented Apr 17, 2018 at 19:58

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