Computer Graphics Tutorial

Introduction of Computer Graphics History of Computer Graphics Types of Computer Graphics Application of Computer Graphics Input Devices Output Devices Display Devices Display Processor Image Representation Color Model Animation Projection Transformation 2D Translation 2D Rotation 2D Scaling 2D Reflection 2D Shearing 3D Translation 3D Rotation 3D Scaling 3D Reflection 3D Shearing Computer Graphics Window Panning Zooming Clipping Line Clipping Point Clipping Text Clipping Polygon Clipping Scan Conversion Line Drawing Algorithm DDA Line Drawing Algorithm Bresenham’s Line Drawing Algorithm Mid-Point Line Drawing Algorithm Scan Conversion of a circle Bresenham’s Circle Drawing Algorithm Midpoint Circle Drawing Algorithm Scan Conversion of an Ellipse Pointing and positioning Techniques Filled Area Primitives

Misc

2D Transformation in Computer Graphics Types of Computer Graphics Resolution in Computer Graphics Anti-aliasing in Computer Graphics Aspect Ratio in Computer Graphics Composite Transformation in Computer Graphics Homogeneous Coordinates in Computer Graphics Illumination Model in Computer Graphics Rendering in Computer Graphics DPI Meaning in Computer What is Double Buffering?

2D Shearing
2022-03-26 14:22:27

2D Shearing

We can denote shearing with ‘SHx’ and ‘SHy.’ These ‘SHx’ and ‘SHy’ are called “Shearing factor.”

We can perform shearing on the object in two ways-

  • Shearing along x-axis: In this, we can store the y coordinate and only change the x coordinate. It is also called “Horizontal Shearing.”

We can represent Horizontal Shearing by the following equation-

X1 = X0 + SHx. Y0

Y1 = Y0

We can represent Horizontal shearing in the form of matrix-

2D Shearing

Homogeneous Coordinate Representation: The 3 x 3 matrix for Horizontal Shearing is given below-

2D Shearing 2D Shearing
  • Shearing along y-axis: In this, we can store the x coordinate and only change the y coordinate. It is also called “Vertical Shearing.”

We can represent Vertical Shearing by the following equation-

X1 = X0

Y1 = Y0 + SHy. X0

We can represent Vertical Shearing in the form of matrix-

2D Shearing

Homogeneous Coordinate Representation: The 3x3 matrix for Vertical Shearing is given below-

2D Shearing 2D Shearing

Example: A Triangle with (2, 2), (0, 0) and (2, 0). Apply Shearing factor 2 on X-axis and 2 on Y-axis. Find out the new coordinates of the triangle?     

Solution: We have,

The coordinates of triangle = P (2, 2), Q (0, 0), R (2, 0)

Shearing Factor for X-axis = 2

Shearing Factor for Y-axis = 2

Now, apply the equation to find the new coordinates.

Shearing for X-axis:

For Coordinate P (2, 2)-

Let the new coordinate for P = (X1, Y1)

X1 = X0 + SHx. Y0 = 2 + 2 x 2 = 6

Y1 = Y0 = 2

The New Coordinates = (6, 2)

For Coordinate Q (0, 0)-

Let the new coordinate for Q = (X1, Y1)

X1 = X0 + SHx. Y0 = 0 + 2 x 0 = 0

Y1 = Y0 = 0

The New Coordinates = (0, 0)

For Coordinate R (2, 0)-

Let the new coordinate for R = (X1, Y1)

X1 = X­0 + SHx. Y0 = 2 + 2 x 0 = 2

Y1 = Y0 = 0

The New Coordinates = (2, 0)

The New coordinates of triangle for x-axis = (6, 2), (0, 0), (2, 0)

2D Shearing 2D Shearing

Shearing for y-axis: 

For Coordinate P (2, 2)-

Let the new coordinate for P = (X1, Y1)

X1 = X0 = 2

Y1 = Y0 + Shy.X0 = 2 + 2 x 2 = 6

The New Coordinates = (2, 6)

For Coordinate Q (0, 0)-

Let the new coordinate for Q = (X1, Y1)

X1 = X0 = 0

Y1 = Y0 +Shy. X0 = 0 + 2 x 0 =0

The New Coordinates = (0, 0)

For Coordinate R (2, 0)-

Let the new coordinate for R = (X1, Y1)

X1 = X0 = 2

Y1 = Y0 + Shy. X0 = 0 +2 x 2 = 4

The New Coordinates = (2, 4)

The New coordinates of triangle for y-axis = (2, 6), (0, 0), (2, 4)

2D Shearing