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 Document
Unformatted text preview: on the circle C( P, PX ) such that ∠ XPX' ≅ ∠ ABC = θ . θ . ∠ WPW' ≅ ∠ XPX' ≅ ∠ YPY' ≅ ∠ ZPZ' ≅ ∠ ABC = θ The Four Isometry Types III. Rotations R P , θ Given directed angle θ = ∠ ABC and point P: Inverse: ( R P , θ )1 = ( R P ,  θ ) = ( R P , 360 ° θ ) The Rotation about point P through directed angle θ = ∠ ABC is R P , θ . Z ' Y ' W' X ' B C A X W Y Z P K ' Mirror line m C' = T AB ( Z ) Given a mirror line m and a vector AB which is parallel to m : The Four Isometry Types IV. Glide Reflections GL AB , m Z = R m ( C ) Inverse: ( GL AB , m )1 = R m ° T BA Thus, for any point X, X' = GL AB , m (X) = T AB ( R m (X) ) = R m ( T AB (X) ) The Glide Reflection about mirror line m through vector AB (parallel to the mirror line) is GL AB , m , where GL AB , m = T AB ° R m . Also, GL AB , m = R m ° T AB . M J ' H ' G ' F ' E ' D ' C ' L' Z A L C D E F G H J K B...
View
Full
Document
This note was uploaded on 11/02/2010 for the course MATH modern geo taught by Professor Shirley during the Spring '10 term at University of Texas.
 Spring '10
 Shirley
 Vectors

Click to edit the document details