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In general pivot point rotation what is the correct sequence of transformations ?

  • A.Rotation, translation, rotation
  • B.Rotation, scaling, rotation
  • C.Scaling, rotation, translation
  • D.Translation, rotation, translation

Answer: D

The sequence is Translation, rotation, translation.

Basic rotation formulas turn a point about the origin. To rotate about any other pivot point (xr, yr), the object is first translated so that the pivot moves to the origin, then rotated about the origin, then translated back so the pivot returns to its original position. The composite matrix is \(T(x_r, y_r) \cdot R(\theta) \cdot T(-x_r, -y_r)\).

Scaling plays no part in a rotation, and rotating twice around a translation does not keep the pivot fixed, so the other three sequences are wrong.

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