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2013 steve marschner 10 to take one recta le wind w

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Unformatted text preview: ti ut whi c ma st t u b ix [xp xh ]× yl yh × t , e ] to e e [yl y c × eq. zn]ez [Shirley3e,f.t 6-16; [we, 6-6] ss e ure 6.16. CS4620 Fall 2013 ngLectureo8 ) to the other, we first thie hhorrec-teft cornorf the result. 2013 Steve Marschner • 10 To take one recta • le (wind w sh f t e lo l r l h Cornell © x −x x x −x x he origin, then scale it to the new size, and then move the origin to the lower-left cornerh l lh h l Viewport transformation 1 ny – .5 –1 –1 –.5 –.5 1 ⇥ nx 2 xscreen ⇤ yscreen ⌅ = ⇤ 0 1 0 Cornell CS4620 Fall 2013 • Lecture 8 0 ny 2 0 nx – .5 ⇥ nx 1 ⇥ xcanonical 2 ny 1 ⌅ ⇤ ycanonical ⌅ 2 1 1 © 2013 Steve Marschner • 11 Viewport transformation • In 3D, carry along z for the ride – one extra row and column nx 2 Mvp Cornell CS4620 Fall 2013 • Lecture 8 ⇧0 =⇧ ⇤0 0 0 ny 2 0 0 0 0 1 0 nx 1 ⇥ 2 ny 1 ⌃ 2⌃ 0⌅ 1 © 2013 Steve Marschner • 12 Orthographic projection 7.1. Viewingeneralization: s • First g Transformation different view rectangle 149 – retain the minus-z view direction – specify view by left, right, top, bottom (as in RT) Figure 7.5. The or thographic view volume is along the negative z-axis, so f is a more – numbenear,nfar, thus n > f. also r tha n negative the bounding planes as follows: Cornell CS4620 Fall 2013 • Lecture 8 x = l ≡ left plane, © 2013 Steve Marschner • 13 Clipping planes • In object-order systems we always use at least two clipping planes that further constrain the view volume – near plane: parallel to view plane; things between it and the viewpoint will not be rendered – far plane: also parallel; things behind it will not be rendered • These planes are: – partly to remove unnecessary stuff (e.g. behind the camera) – but really to constrain the range of depths (we’ll see why later) Cornell CS4620 Fall 2013 • Lecture 8 © 2013 Steve Marschner • 14 0 0 1 ( 6 .6 ) Orthographic to some readers that the resulting matrix has the form It is perhaps not surprising projection it does, but the constructive process with the three matrices lea...
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This document was uploaded on 03/20/2014.

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