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Homogenous Coordinate Transformations --2

• Consider

• The 2 x 2 submatrix columns:

  • are unit vectors (length=1)

  • are perpendicular (dot product = 0)

  • are vectors into which X-axis and Y-axis rotate

• The 2 x 2 submatrix rows:

  • are unit vectors

  • are perpendicular

  • rotate into X-axis and Y-axis

• These properties are "rigid body" and preserve lengths and angles

• These properties can be used to find the submatrix needed to produce a specific rotation.

Geometric Transformations - 09 MAY 95

Page 38 of 51

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