Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:In 2-D geometric transformations, some of the common transformations including rotation, scaling, shearing,
reflection, and orthogonal projection. A 2 x 2 rotation matrix (R) that is used to perform a rotation in
Euclidean space is given by:
EECS 1560
The matrix R rotates points or 2 x 1 vectors in the xy-Cartesian plane counter-clockwise through an angle 0.
For example, the new coordinates for the point (xo, yo) after the transformation is:
4
3
2
1
0
-1
-2
-3
X new
The following points (x₁ to xg) sketch a hexagon as shown in Fig. 1: x₁ = (0, 1), x2 = (1, 1), x3 = (2, 2), X4 = (1,
3), x5 = (0, 3), x6 = (-1,3), x7= (-2, 2), xs = (-1, 1). Suppose we want to rotate the hexagon counter-clockwise
+150 degree.
-4
y new.
Plot both the original and the rotated hexagon on the same graph with different colours for -4≤x≤4 and -4
Sy≤ 4. Provide proper legend. Plot only the data points.
-4
Note: any conditional statements (if-else statement, for and while loops) are NOT allowed to use for this
question
R=
-3
= R
R(x) = (
(1
O
-2
cos
sin
Introduction to Computing for Mathematics and Statistics
cos
O
cos
sin0x₂
sinᎾ cose yo
()
Yo
O
-1
sin 0
O
O
0
Fig. 1
O
O
1
O
3| Page
2
3
4
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