i am trying to draw a 3D-Rectangle that is rotated by say 45 degrees around its longitudinal axis. How can i achieve this? It is suprisingly difficult to draw such that it doesn't look akward.

enter image description here

  • It's impossible to make the rotated box (no scaling in any direction, only rotated as wanted) fit into the same grid because the vertices would be in points which have irrational number coordinates. You must allow some amount of scaling and proportion change. No shifting after rotating would move all vertices to the points in the grid.
    – user82991
    Feb 24, 2022 at 13:33
  • Something similar was my first idea. Create a second grid with adjusted angles. Let, e.g., the first grid be 30°, 30°. Then, the angles of the second grid somehow encode my relative rotation, say 45°, 30°. Then, drawing a second box in the second grid makes this magically work. Nope, not so easy.
    – Simon B
    Feb 24, 2022 at 13:53
  • Learn to use matrices to set the planes, and learn to use numeric input so you can get rid of the grid (illustrator example but similar things work in inkscape). And yes the 45 degree rotated box only shows 2 sides so yes it is awkward. Suggest you rotate it by 30 in z direction too
    – joojaa
    Feb 24, 2022 at 14:21

1 Answer 1


It can be drawn only approximately because the wanted rotation (no scaling nor shifting!) would require points which do not exist in the grid, no matter how much denser it was. There's irrational number coordinates.

If you allow a little scaling and changing the proportions + shifting to let a couple of edges to fit into the grid you may draw this (=the red one, green lines are only for help):

enter image description here

Essentially the squareroot of 2 is rounded to 1,5

You can move it 2 or 3 grid minor divisions leftwards to make it fit as closely as possible to the original and still keep the corners in grid points. I drew it too far right only because it was marginally easier.

  • Why would you need a grid? Just use numerical input.
    – joojaa
    Feb 24, 2022 at 14:43
  • @joojaa To avoid the need of numerical input.
    – user82991
    Feb 24, 2022 at 14:45
  • Normally you only need 2 or 3 numerical inputs in a drawing once you have that you can make the rest without one. By avoiding numerical input you limit yourself quite much but by using a few of them you release potential you would otherwise not have.
    – joojaa
    Feb 24, 2022 at 14:48
  • I do numerical inputs and even try to write formulas if I see they might help and the case is so simple that elementary math knowledge is enough. A recent example: graphicdesign.stackexchange.com/questions/155878/… I guess most of us do not want to use nor see even that amount.
    – user82991
    Feb 25, 2022 at 10:21

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