points are expressed in homogeneous coordinates). You want to uniformly scale point P2 by 1/2 and then rotate point p2 by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 2 location of the point p2 is p'2 a. Consider the two 2D points: p₁ = |1| and p₂ = |2 (please note that these 121 b. C. = You will need four 3 x 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. Show the result of each matrix multiplication.
points are expressed in homogeneous coordinates). You want to uniformly scale point P2 by 1/2 and then rotate point p2 by 45 degrees. Though, you want to perform these two operations about point p₁, i.e., not the origin. After this transformation, the new 1 2+√2 2 location of the point p2 is p'2 a. Consider the two 2D points: p₁ = |1| and p₂ = |2 (please note that these 121 b. C. = You will need four 3 x 3 transformation matrices to perform the above transformation. Clearly write the contents of each of these four matrices and indicate the name of the affine transformation for each. Entries in all matrices must have numeric values. Write the four transformation matrices in part (a) as a sequence of multiplications that would correctly perform the transformation. Add the point p2 to the matrix sequence in part (b) and complete the multiplication. Your final answer should be point p'2. Show the result of each matrix multiplication.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:2)
points are expressed in homogeneous coordinates). You want to uniformly scale point
P2 by 1/2 and then rotate point p2 by 45 degrees. Though, you want to perform these
two operations about point p₁, i.e., not the origin. After this transformation, the new
1
2+√2
location of the point p₂ is p'2
a.
Consider the two 2D points: p₁ = 1 and P2
-1-
=
b.
C.
=
121
2 (please note that these
2
1
You will need four 3 x 3 transformation matrices to perform
the above transformation. Clearly write the contents of each of these four
matrices and indicate the name of the affine transformation for each.
Entries in all matrices must have numeric values.
Write the four transformation matrices in part (a) as a
sequence of multiplications that would correctly perform the
transformation.
Show
Add the point p2 to the matrix sequence in part (b) and
complete the multiplication. Your final answer should be point p'2.
the result of each matrix multiplication.
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