# Graphics 3D – manipulate

Basing on this code:

box1 = GeometricTransformation[Cuboid[{0, 0, 0}], ShearingMatrix[Pi/4, {1, 0, 0}, {-1, 1, 0}]]
box2 = GeometricTransformation[Cuboid[{1, 1, 0}], ShearingMatrix[-Pi/4, {1, 0, 0}, {-1, 1, 0}]]
Graphics3D@{box1, box2}

I would like to create a 3D figure (two joined cuboids) with adjustable bend angle and dimensions of cuboids {a,b,c} (Manipulate)

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And what problems did you find?
– Dr. belisarius
Sep 30 ’15 at 19:22

1) unable to set the adjustable {a,b,c} dimensions for both cuboids simulatneously 2) cuboids do not maintain “stuck” under the chang of bend angle
– ATomek
Sep 30 ’15 at 20:13

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2

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{gt, sc, sh, re} = {GeometricTransformation, ScalingTransform,
ShearingTransform, ReflectionTransform};
{x, y} = {{1, 0, 0}, {0, 1, 0}};

Manipulate[ t = gt[gt[Cuboid[{0, 0, 0}], sc[{a, b, c}]], sh[p, x, y]];
Graphics3D[{t, gt[t, re[y]]}, Axes -> True],
{a, 1, 2}, {b, 1, 2}, {c, 1, 2}, {p, 0, Pi}]

How would it look like if such parametrization for Cuboid was introduced: Cuboid[{0, 0, 0}], {Abs[-1/Sqrt[6] +a], Abs[-1/Sqrt[6] + a], Sqrt[2/3]}]
– ATomek
Sep 30 ’15 at 21:17

Manipulate[
box1 = GeometricTransformation[Cuboid[{0, 0, 0}],
ShearingMatrix[ Î¸, {1, 0, 0}, {-1, 1, 0}]];
box2 = GeometricTransformation[Cuboid[{1, 1, 0}],
ShearingMatrix[-Î¸, {1, 0, 0}, {-1, 1, 0}]];
Graphics3D@{box1, box2},
{{Î¸, 0}, -Ï€/4, Ï€/4}]

I am looking for constant operation that will not separate the cuboids when changing the bend angle.
– ATomek
Sep 30 ’15 at 20:12