3. Given is the equation below for a so-called horizontal shear, one type of an affine geometric transformation: (X1,0) = (x,,0) X1 X-x+sy y = y y
3. Given is the equation below for a so-called horizontal shear, one type of an affine geometric transformation: (X1,0) = (x,,0) X1 X-x+sy y = y y
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 39E
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D1
![3. Given is the equation below for a so-called
horizontal shear, one type of an affine
geometric transformation:
(x1,0)%3D(x",0)
X1
x =x+ sy
y y
In this equation (x,y) are coordinates in the
source image; (x y) are the corresponding
coordinates in the new (sheared) image. In the
figure at the right for one point (xI,0) in the
source image the corresponderending
transformed point is given: the source point
and the transformed point coincide.
• Construct, in the figure, the shear of two different points. The x-coordinates of
these two point should be similar to that of the given point (so the source points
lie somewhere on the vertical dashed line). Choose as shear factor s = 1,5. Show
your construction method.
%3D
What would happen when a line parallel to the dashed line would be sheared with
the same shear factor?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F720a8abc-3aca-4255-9305-1933a12ae53c%2F96793e85-a191-46b7-a44d-c41111e8f81f%2Fvgsir8o_processed.png&w=3840&q=75)
Transcribed Image Text:3. Given is the equation below for a so-called
horizontal shear, one type of an affine
geometric transformation:
(x1,0)%3D(x",0)
X1
x =x+ sy
y y
In this equation (x,y) are coordinates in the
source image; (x y) are the corresponding
coordinates in the new (sheared) image. In the
figure at the right for one point (xI,0) in the
source image the corresponderending
transformed point is given: the source point
and the transformed point coincide.
• Construct, in the figure, the shear of two different points. The x-coordinates of
these two point should be similar to that of the given point (so the source points
lie somewhere on the vertical dashed line). Choose as shear factor s = 1,5. Show
your construction method.
%3D
What would happen when a line parallel to the dashed line would be sheared with
the same shear factor?
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