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 viewvolume
• The perspective canonical viewvolume can be transformed
to t...
View
Full
Document
This document was uploaded on 03/26/2014.
 Spring '14

Click to edit the document details