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Lecture11-Viewing-II

# Lecture11-Viewing-II - CS 455 Computer Graphics Viewing...

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CS 455 – Computer Graphics Viewing Transformations II

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Arbitrary Views Suppose we want to look at the environment from somewhere other than along the z-axis How do we do this? What is the perspective matrix? Where should an object project onto our new viewplane? Solution: set up our arbitrary view transform it into the situation we know how to handle (i.e., viewpoint on the +z axis looking at the origin) apply that transformation to the environment then apply the perspective computation
Specifying and Arbitrary View What do we need to specify and arbitrary view? 1. Projection plane (or View plane) - Specified with a point and a normal - We will call the point on the plane the “View Reference Point” or VRP - We will call the normal to the plane the “View Plane Normal” or VPN - We can define these anywhere in world space Viewplane VPN VRP

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Specifying and Arbitrary View What else? 2. A window in the infinite viewplane - We want to specify a subset of the viewplane that we will project onto the screen - Objects outside the window will not be seen - How do we define that window? Very difficult to do in world coordinates! Viewplane VPN VRP Window
Specifying the Window We would like to specify the window relative to the VRP (some number of units above, below, left and right) To do this, we must create a new coordinate system This will be called the “View-Reference Coordinate System” (VRC) The origin of the VRC is the VRP One axis is the VPN A second axis will be the “up” axis - This will need to be specified by the programmer - It is simply the direction that is to be “up” i.e. the up direction of the eye or camera

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Specifying the Window The “view up” vector (VUP) is projected onto the viewplane to get the second (V) axis This allows the programmer to specify any vector - not just a vector exactly perpendicular to N Viewplane VUP VRP (VRC origin) VPN (N axis) VUP projected onto Viewplane (V axis)
Specifying the Window The third axis (U) is obtained by taking the cross product of V and N Viewplane VRP (VRC origin) VPN (N axis) VUP projected onto Viewplane (V axis) U axis

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Computing the VRC system The actual way this is done is: VRP and VPN are specified N = VPN View Up is specified U = VUP X N V = N X U Viewplane N V U VUP
Specifying the Window With the VRC system defined, we can now specify the window Window = (u min , v min ) -> (u max , v max ) the Center of the Window (CW) is midway between (u min , v min ) and (u max , v max ) Viewplane N V U (u min , v min ) (u max , v max ) CW

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Back to specifying our arbitrary view What else do we need? 3.
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Lecture11-Viewing-II - CS 455 Computer Graphics Viewing...

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