This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 13 Operations in Graphics and Geometric Modeling I: Projection, Rotation, and Reflection ShangHua Teng Projection Projection onto an axis ( a,b ) x axis is a vector subspace Projection onto an Arbitrary Line Passing through 0 ( a , b ) Projection on to a Plane Projection on to a Line b a cos b a b a T = ( 29 ( 29 a a a b a a a a b a a a b p T T T = = = cos cos p Projection Matrix: on to a Line b a ( 29 ( 29 a a a b a a a a b a a a b p T T T = = = cos cos p What matrix P has the property p = P b = = = = = a a aa P b a a aa a a b a a p Pb a a a b a p T T T T T T T T Properties of Projection on to a Line b a p x a b x a p a a b a x b ax x a p b a p T T minimizes which , then , of ion approximat square least the is if ) ( ) ( Span = = =  p is the points in Span( a ) that is the closest to b Projection onto a Subspace Input: 1. Given a vector subspace V in R m 2. A vector b in R m Desirable Output: A vector in p in V that is closest to b The projection p of b in V A vector p in V such that ( bp ) is orthogonal to V How to Describe a Vector Subspace...
View
Full
Document
This note was uploaded on 03/08/2010 for the course CS 232 taught by Professor Bera during the Spring '09 term at BU.
 Spring '09
 BERA
 Algorithms

Click to edit the document details