Page 65 - PowerPoint Presentation

Affine Transformations

x'  a b   c  x
Affine transformations are combinations of … y'  = d e   f  y

• Linear transformations, and  w   0 0 1     w 




• Translations
Properties of affine transformations:

• Origin does not necessarily map to origin

• Lines map to lines

• Parallel lines remain parallel

• Ratios are preserved

• Closed under composition

• Models change of basis

Will the last coordinate w always be 1?