Lecture 1 - Projections and Transformations (slides)

Cartesian equations for each component gives gives p0

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Unformatted text preview: vector equation: T Substitute d = (0d0, (0,0,1)T intothe projector vector equation:! •  Substitute , = 1) into the projector vector equation: P = V + µd P = V + µd P = V + µd Gives Cartesian for each for each component Gives Cartesian Cartesianequations component equationsequations for each component ! •Cartesian equations for each component   Gives Gives ! += P0 Px = VxPx 0 Vx Py 0 Vy + y = Vy += Vz Pz = Vz += Pz 0 µ Px = V x + 0 Py = V y + 0 Pz = Vz µ •  plane is plane Projection z = 0 ) z 0 ) ProjectionProjectionplane is! zP= = 0 Pz = 0 Projection plane is z = 0 ) Pz = 0 So the projected on the screen is So the projected location location on the screen is So the projected location on the screen is 0 10 1 0x 1 Vx VV x PP = @V y A @V y A = @V y A P= 00 0 Graphics Lecture 1: Slide 24! i.e. we simply take the 3D x and y components of the vertex! µ Gives Cartesian equations for each component Px = V x + 0 Py = V y + 0 Pz = Vz µ Calculating an orthographic projection (cont.)! Projection plane is z...
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This document was uploaded on 03/26/2014.

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