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Rotate

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Rotate[g, Theta]
represents 2D graphics primitives or any other objects g rotated counterclockwise by Theta radians about the center of their bounding box.
Rotate[g, Theta, {x, y}]
rotates about the point {x, y}.
Rotate[g, {u, v}]
rotates around the origin, transforming the 2D or 3D vector u to v.
Rotate[g, Theta, w]
rotates 3D graphics primitives by Theta radians around the 3D vector w anchored at the origin.
Rotate[g, Theta, w, p]
rotates around the 3D vector w anchored at p.
Rotate[g, Theta, {u, v}]
rotates by angle Theta in the plane spanned by 3D vectors u and v.
  • Theta Degree or theta degrees specifies an angle in degrees.
  • If Rotate appears outside of a graphic, the object g in Rotate[g, Theta], etc. can be any expression.
  • You can specify special points such as {Left, Bottom} within the bounding box for g.
  • If Rotate appears within a graphic, the coordinates {x, y} are taken to be in the coordinate system of the graphic.
  • If Rotate appears outside of a graphic, the coordinates {x, y} are taken to run from -1 to +1 across the bounding box of the object being rotated.
  • For objects specified with scaled coordinates Scaled[{x, y}], Rotate effectively applies its transformation to the corresponding ordinary coordinates.
  • If Rotate appears inside a graphic, Normal[expr] if possible replaces all Rotate[gi, ...] constructs by versions of the gi in which the coordinates have explicitly been transformed.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Rotate a square by 30°:
Rotate a cuboid by 30° around the z axis:
Rotate text by 45°:
Rotate a square by 30°:
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Rotate a cuboid by 30° around the z axis:
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Rotate text by 45°:
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Scope   (8)
Transformation applied to a 2D shape:
Transformation applied to a 3D shape:
Rotation around the z axis keeping the point {1,1,1} fixed:
Rotation mapping vector {1,1,1} to vector {0,0,1}:
Rotation in the plane spanned by vectors {1,1,0} and {0,0,1}:
Rotate text:
Rotate objects with scaled coordinates:
Keep the lower-right corner of the rectangle fixed:
Applications   (2)
Grid with vertical text:
Diamond grid:
Properties & Relations   (1)
When possible, Normal will transform the coordinates explicitly:
Possible Issues   (3)
By default Rotate uses the center of the bounding box as the center of rotation:
Explicitly specify a center of rotation:
Transforming an object may move it out of view:
Adjust the PlotRange to display the transformed object:
The center of the baseline of rotated text aligns with the baseline of the surrounding text:
For a different alignment, specify an explicit center of rotation:
Neat Examples   (2)
Rotations of a regular polygon:
Nested, rotated square roots:
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