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How is a shear different from a rotation?


A these transformations appear to be uniform or relatively easy to recognize a mathematical concept behind it (multiplying by a constant, adding a constant to each coordinate, etc.) How do we mathematically describe more complicated functions/transformations that aren't as obvious (such dripping water, crumpling a soda can, etc.)


How is a shear transformation represented (for example translation may be given a vector to move by, rotation given an angle to rotate) what information must be given to perform a shear transformation?


The shear transformation here looks like a rotation, despite the explanation later in the slides of how it is different; do shear transformations in 3D often look similar to rotations?


How is a shear different than a scaling along a diagonal axis?


Is there any other transformation that is also linear?


Why is it called a shear transformation?


Are there any other types of transformations?