Lecture 1 - Projections and Transformations (slides)

We can use to apply both 0 0 2 0 10 1 5 x 5 c by c cb

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Unformatted text preview: 1 B y 0 C B0 B C=B @ z 0 A @0 1 0 Graphics Lecture 1: Slide 45! 0 1 0 0 0 0 1 0 10 5 2 5 C B0 CB 20A @0 1 0 0 2 0 0 0 0 2 0 10 1 0 x 0C By C CB C 0A @ z A 1 1 Combined transformations! Combined transformations •  We can multiply out the transformation matrices ! We  can multiplyus a the transformation matrices • This gives out single matrix which we can use to apply both transformations to any point ! This gives us a single matrix which transformations to any point 0 01 0 x 20 By 0 C B0 2 B C=B @ z 0 A @0 0 1 00 Graphics Lecture 1: Slide 46! we can use to apply both 0 0 2 0 10 1 5 x 5 C By C CB C 20A @ z A 1 1 Careful: Transformations are not commutative! •  The order of applying transformations matters: ! •  In general ! T Ÿ༉ S is not the same as S Ÿ༉ T •  Check this for the transformation matrices on the last two slides ! Graphics Lecture 1: Slide 47! The order of transformations is significant ! The results at the end of each route are different. ! ! Graphics Lecture 1: Slide 48! Rotation ! •  To define a rotation we need an axis and an angle.! •  The simplest rotations are about the Cartesian axes. ! •  For example: ! ! –  Rx –  Ry –  Rz !Rotate about the x-axis ! !Rotate about the y-axis ! !Rotate about the z-axis ! Graphics Lecture 1: Slide 49! Rotation Matrices ! Rotation Matrices Rotation ma...
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