Lecture 1 - Projections and Transformations (slides)

G translation matrix translation matrix 0 1 1 0 0 tx

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Unformatted text preview: an apply a general translation by (tx, ty, tz ) to the points of a scene by using the following matrix multiplication 0 10 1 0 1 1 0 0 tx px px + tx B 0 1 0 t y C B p y C B py + t y C B CB C = B C @ 0 0 1 t z A @ p z A @ pz + t z A 0001 1 1 Graphics Lecture 1: Slide 41! Inverting a translation Inverting a translation ! Since we know what a translation matrix physically does, we can •  Since its know what a translation matrix physically does, write down we inversion directly we can For example: write down its inversion directly, e.g.! ! Translation matrix Translation matrix 0 1 1 0 0 tx B0 1 0 t y C B C @0 0 1 t z A 0001 inverse ! inverse 0 1 B0 B @0 0 0 1 0 0 0 0 1 0 1 tx ty C C tz A 1 •  Can show that that the product of these matrices is the Can you you show the product of these matrices is the identity? identity? ! Graphics Lecture 1: Slide 42! 35 / 47 Scaling a matrix Scaling withwith a matrix ! •  Scaling simply multiplies each ordinate by a scaling factor. ! Scaling simply multiplies each ordinate by a scaling factor. It can •...
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