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CS250_Review_Questions

# CS250_Review_Questions - CS250 Review Questions Notes a...

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1 CS250 Review Questions Notes: a. Unless otherwise specified, assume two-dimensional points and vectors are described in right-handed reference frame [ ] d d W d W d j i O f 2 2 2 2 ˆ , ˆ , = whose reference point is ( ) 0 , 0 2 = W d O while vectors ( ) 0 , 1 ˆ 2 = d i and ( ) 1 , 0 ˆ 2 = d j represent an ortho-normal basis. Basis vector d i 2 ˆ represents X axis and is horizontally oriented; while d j 2 ˆ represents Y axis and is vertically oriented. b. Unless otherwise specified, assume three-dimensional points and vectors are described in right-handed reference frame [ ] k j i O f W W ˆ , ˆ , ˆ , = whose reference point is ( ) 0 , 0 , 0 = W O while vectors ( ) 0 , 0 , 1 ˆ = i , ( ) 0 , 1 , 0 ˆ = j , and ( ) 1 , 0 , 0 ˆ = k represent an ortho-normal basis. Basis vector i ˆ represents X axis and is oriented right; j ˆ represents Y axis and is oriented into the paper; while k ˆ represents Z axis and is oriented up. c. v r represents a vector with arbitrary length while v ˆ represents a unit-length vector. d. As in class, points and vectors are represented using column matrices. 1) In W d f 2 , compute the 3 3 × matrix that aligns d i 2 ˆ to d j 2 ˆ . 2) In W d f 2 , compute the 3 3 × matrix that aligns d i 2 ˆ along vector ( ) 1 , 1 . 3) In W d f 2 , find the 3 3 × matrix that aligns ( ) y x d v v v , 2 = r along ( ) y x d w w w , 2 = r . 4) Reflection transform generates the mirror image of an object. In two-dimensional reflection, the mirror image is generated relative to an axis of reflection by rotating a vector (or, an object) o 180 about the reflection axis. In a two-dimensional reference frame, the axis of reflection can be a vector in Y X plane or a vector orthogonal to Y X plane. In W d f 2 , find 3 3 × matrices for the following common reflections: a. Reflection about line 0 = y . b. Reflection about line 0 = x . c. Reflection about line perpendicular to Y X plane and passing through origin W d O 2 . d.

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CS250_Review_Questions - CS250 Review Questions Notes a...

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