Lecture11-Viewing-II

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

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 455 – Computer Graphics Viewing Transformations II
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 8
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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Back to specifying our arbitrary view What else do we need? 3.
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/02/2012 for the course C S 455 taught by Professor Jones,m during the Winter '08 term at BYU.

Page1 / 57

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

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online