Lecture 2 - Transformations for animation (slides)

Unlike the previous analysis we now can control the

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Unformatted text preview: · w = P · w Or,  in matrix notation: • Or, in matrix notation: ! 0 t1 0 Or, in matrix notation: ! Px ux uy 0 t1 0 BPytC B vx vy B PxC = B ux uy @PztA @wx wy BPty C B vx vy B C=B 0 0 1t @Pz A @wx wy 0 0 1 Graphics Lecture 2: Slide 38 ! uz vzz u wz vz 0 wz 0 Cv C ·· w C·w 10 1 C·u Px 10 1 C ·· v C BPy C C uC B PxC C ··wA @PzyA C v C BP C CB C 1 · w A @ Pz A 1 C 1 1 37 / 45 Verticals revisited …! Verticals revisited . . . Unlike the previous analysis we now can control the vertical ! Unlike the previous analysis we now can control the vertical ! i.e. we can assumethe v-direction is the is the vertical and I.e. we can assume the v-direction vertical and constrain it constrain software to software to be upwards ! in the it in the be upwards Graphics Lecture 2: Slide 39 ! 38 / 45 Back to flying sequences Back to flying sequences We now return to the original problem Back to viewpoint point C and ! We I Given a flyingoriginal problema view direction d, we need to now return to the sequences I Given the transformationC and athat gives us the , we need to find a viewpoint point matrix view direction d canonical •  view.now return to the original gives us ! We find the transformation matrix thatproblem the canonical – view. Given a viewpoint point the vectors direction w. I We   do this by first finding C and a viewu, v and d, we need to find the transformation matrix that gives us the canonical view. ! I We do this by first finding the vectors u, v and w . –  We do this by first finding the vectors u, v and w. ! We knowknow that dthethe direction of thenew We that d is is direction of the new z that is can write immediately z knowso we dwe the direction of the ! We-axis,-axis, socan write immediately new z -axis, ! we can write immediately so d w= d d| | w= |d| 39 / 45 Graphics Lecture 2: Slide 40 ! 39 / 45 Now the horizontal direction the horizontal direction Now Now the horizontal direction ! We We write u in terms of some some vector horizontal • can can u in u in of s...
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This document was uploaded on 03/26/2014.

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