# UT CS 354 - Viewing II: Camera,Projections and their Relations (18 pages)

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## Viewing II: Camera,Projections and their Relations

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## Viewing II: Camera,Projections and their Relations

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Pages:
18
School:
University of Texas at Austin
Course:
Cs 354 - Computer Graphics
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Department of Computer Sciences Graphics Fall 2005 Lecture 7 Viewing II Camera Projections and their Relations Positioning and Orienting the Camera Positioned VRP view reference point by set view reference point x y z Orientation VPN view plane normal and VUP view up vector by set view plane normal nx ny nz and set view up vup x vup y vup z The projection of the VUP onto the view plane is a up direction vector v u v x n a vector orthogonal to v and n The u v n and the VRP yields the viewing coordinate system Camera is usually located at a point e called the eye point and it is pointed at the at point a This defines VRP and VPN e a Finally use the OpenGL utitility function gluLookAt glMatrixMode GL MODELVIEW glLoadIdentity gluLookAt eyex eyey eyez atx aty atz upx upy upz The University of Texas at Austin 1 Department of Computer Sciences Graphics Fall 2005 Lecture 7 Projections Mapping from 3 dimensional space to 2 dimensional subspace Range of any projection P R3 R2 called a projection plane P maps lines to points The image of any point p under P is the intersection of a projection line through p with the projection plane The University of Texas at Austin 2 Department of Computer Sciences Graphics Fall 2005 Lecture 7 Taxonomy of Projections Parallel orthographic oblique Perspective 1 pt 2 pt 3 pt The University of Texas at Austin 3 Department of Computer Sciences Graphics Fall 2005 Lecture 7 Parallel Projections All projection lines are parallel An orthographic projection has projection lines orthogonal to projection plane Otherwise a parallel projection is an oblique projection Particularly interesting oblique projections are the cabinet projection and the cavalier projection The University of Texas at Austin 4 Department of Computer Sciences Graphics Fall 2005 Lecture 7 The OpenGL Orthographic Matrix 1 1 1 n 1 1 1 f The visible volume in world space is known as the viewing volume Specify with the call glOrtho l r b t n f In OpenGL the window is in the near plane l

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