D focal distance y x projectio n plane pxy z ppxpypd

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Unformatted text preview: at the origin, Projection plane at z=-d. d: focal distance y x Projectio n Plane. P(x,y, z) Pp(xp,yp,d) z d Alternative formulation. d x z p P(x,y, z) z x y P(x,y, z) p y d Projection plane at z = 0, Centre of projection at z =d Now we can allow d→∞ Exercise: where will the two points be projected onto? Problems • After projection, the depth information is lost • We need to preserve the depth information for hidden surface removal • Objects behind the camera are projected to the front of the camera 3D View Volume • The volume in which the visible objects exist – For parallel projection, view volume is a box. – For perspective projection, view volume is a frustum. • The surfaces outside the view volume must be clipped Canonical View Volume • Checking if a point is within a frustum is costly • We can transform the frustum view volume into a normalized canonical view volume • By using the idea of perspective transformation • Much easier to clip surfaces and calculate hidden surfaces Transforming the View Frustum • Let us define parameters (l,r,b,t,n,f) that determines the shape of the frustum • The view frustum starts at z=-n and ends at z=-f, with 0<n<f • The rectangle at z=-n has the minimum corner at (l,b,-n) and the maximum corner at (r,t,-n) Transforming View Frustum into a Canonical view-volume • The perspective canonical view-volume can be transformed to t...
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