Lecture 1 - Projections and Transformations (slides)

Point be value p point be p p pz vz f vz p pz vz

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Unformatted text preview: = µV ! because all projectors go through the origin. because projectors go go through the origin. At the because all all projectorsthrough the origin. projected point we have Pz = f.! At the projected point we have Pz = f , let the value of µ at this At the projectedof µ atwe have Pz be f ,p let the value of µ at this Let the µ † point this point = µ ! point be value p point be µp † ! µp = Pz /Vz = f /Vz µp = Pz /Vz = f /Vz and and ! and ! Px = µp Vx , Py = µp Vy Px = µp Vx , Py = µp Vy Therefore! Therefore Therefore Px = f Vx /Vz , Py = f Vy /Vz Px = f Vx /Vz , Py = f Vy /Vz Graphics Lecture 1: Slide 29! † The constant µp is sometimes called the ‘fore-shortening factor’ Perspective projections of a cube ! (a)  Viewing a face ! ! (b) Viewing a vertex ! ! (c) A general view ! Graphics Lecture 1: Slide 30! Problem break Problem break ! Given that the viewing plane is at z=5, = 5, what point on the Given that the viewing plane is at z What point on the viewplane corresponds to the 3D vertex view plane corresponds to the 3D vertex 01 ! 10 V = @10A ! 10 ! when we use the different projections:! When we use the di↵erent projections 1.  Perspective ! (a) Perspective 2.  Orthographic ! (b) Orthographi...
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