Lecture 1 - Projections and Transformations (slides)

Inverse inverse 1 0 0c c 0a 1 0 1sx 0 0 b0 1sy 0 b 0

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Unformatted text preview: It can be done with the following homogenous matrix: ! be done with the following homogenous matrix: 0 10 1 0 1 sx 0 0 0 px sx px B 0 sy 0 0C Bpy C Bsy py C B CB C = B C @ 0 0 sz 0A @pz A @ sz pz A 0001 1 1 Graphics Lecture 1: Slide 43! Inverting a scaling Inverting a scaling ! •  To invert a scaling we simply divide the individual ordinates by the scale factor. ! To invert a scaling we simply divide the individual ordinates by the scale factor. Scaling matrix Scaling matrix 0 sx 0 0 B 0 sy 0 B @ 0 0 sz 000 Graphics Lecture 1: Slide 44! inverse inverse ! 1 0 0C C 0A 1 0 1/sx 0 0 B0 1/sy 0 B @0 0 1/sz 0 0 0 1 0 0C C 0A 1 Combining transformations ! Combining transformations •  Suppose we want to make an object centred at the origin twice as big and then move it so that the centre is at (5, 5, Suppose! we want to make an object centred at the origin twice as 20). big and then move it so that the centre is at (5, 5, 20). •  The transformation is a scaling followed by a translation: ! The transformation is a scaling followed by a translation: ! 0 01 0 x...
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This document was uploaded on 03/26/2014.

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