Lecture 2 - Transformations for animation (slides)

Homogenous co ordinates fall into two types

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Unformatted text preview: A z/s Graphics Lecture 2: Slide 23 ! 22 / 45 omogenous co-ordinates and vector omogenous co-ordinates and vector Homogenous coordinates and vectors! Homogenous co-ordinates fall into two types: •  Homogenous coordinates fall Homogenous co-ordinates fall into two types: into two types:! 1 0 0x1 1. Position vectors BxC By C 1.  with Position vectors! 1. Position vectorsnon-zero final ordinate (s > 0). I Those By C @A Bz C I Can bewith non-zero non-zero final (s > 0). (s > 0).! I Those –  Those with final ordinate ordinate normalised into Cartesian form. @z A s I Can be–  Can be normalised into Cartesian form.! normalised into Cartesian form. s 2. Direction  vectors 2. Direction vectors! 2. Direction vectors with zero in ordinate. ordinate. ! I Those with zero in the final the final –  Those I I I Have direction and magnitude. Those with zero in the final ordinate. ! –  Have direction and magnitude. Have direction and magnitude. Graphics Lecture 2: Slide 24 ! 01 0x1 BxC By C By C @A Bz C @z A 0 0 23 / 45 23 / 45 Adding direction vectors Adding direction vectors ! •  If we add two direction vectors we obtain a direction If we add two direction vectors we obtain a direction vector vector ! 01 01 0 1 xi xj xi + xj B y i C B yj C B y i + y j C B C+B C=B C @ zi A @ z j A @ z i + z j A 0 0 0 •  This is the normal vector addition rule. ! This is the normal vector addition rule. ! Graphics Lecture 2: Slide 25 ! 24 / 45 Adding position and direction vectors Adding position and direction vectors vectors ! Adding position and direction If we add a direction vector to a position vector we obtain a position vector: If •  If add a direction vectorvector to a positionwe obtain a obtain we we add a direction to a position vector vector we 01 1 positionosition vector: ! 0 1 0 a p vector: X x X +x B0 C1 B0C1 B0 + y C1 x x B Y X + By C = B Y X + C C @B AC @BAC @B + z AC ZY zy ZY + y B C+B C=B C 1 Z A @z A @ Z + z A 0 1 @ 1 0 1 Nice result. Nice! result. Nice result. ! Ties Ties in with definition of stra...
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This document was uploaded on 03/26/2014.

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