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Unit 10: Shearing

This is illustrated by Figure 10.3. Notes

Figure 10.3: The Z-shear Transformation

This transform can be implemented by the following 4 × 4 matrix:
 
u
È 1 000˘ È ˘ È u ˘

Í 01 00 ˙ Í ˙ Í v  ˙
v
Í ˙ Í ˙ = Í    ˙

Í ab 10˙ Í ˙ Í au + v + w˙
w
bv
Í ˙ Í ˙ Í ˙
O
Î 000 1 ˚ Î ˚ Î O ˚
and so we define the z-shear transformation by
È 1 000˘
Í 01 00 ˙
H z;a,b = Í ˙
Í ab 10˙
Í ˙
Î 000 1 ˚
If this transformation is applied to the point (u, v, w), we obtain
È 1 000˘
Í 01 00 ˙
[u v w 1] Í ˙ = [v + aw v bw + w 1]
Í ab 10˙
Í ˙
Î 000 1 ˚
and thus objects can be sheared by applying this matrix to all points of the object.
10.1.4 2D Transformations

To write a C program to perform 2D transformations such as shearing Algorithm:
(a) Input the shearing factors shx and shy.
(b) Shearing related to x axis: Transform coordinates x 1 =x+shx*y and y 1 =y.

(c) Shearing related to y axis: Transform coordinates x 1 =x and y 1 =y+shy*x.
(d) Input the x ref and y ref values.
(e) X axis shear related to the reference line y–y ref is:

x 1 = x + shx(y – y ref) and y 1 = y.
(f) Y axis shear related to the reference line x = x ref is x 1 = x and
(g) Display the object after shearing.

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