Computer graphics are pictures and movies created using computers - usually referring to image data created by a computer specifically with help from specialized graphical hardware and software. It is a vast and recent area in computer science.The phrase was coined by computer graphics researchers Verne Hudson and William Fetter of Boeing in 1960. Another name for the field is computer-generated imagery, or simply CGI. Important topics in computer graphics include user interface design, sprite graphics, vector graphics, 3D modeling, shaders, GPU design, and computer vision, among others. The overall methodology depends heavily on the underlying sciences of geometry, optics, and physics. Computer graphics is responsible for displaying art and image data effectively and beautifully to the user, and processing image data received from the physical world. The interaction and understanding of computers and interpretation of data has been made easier because of computer graphics. Computer graphic development has had a significant impact on many types of media and has revolutionized animation, movies, advertising, video games, and graphic design generally.

1. Computer Graphics : Linear Algebra
Created By- Mydul Islam

2. Linear Algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear
mappings between such spaces. It includes the study of lines, planes, and subspaces,
but is also concerned with properties common to all vector spaces. There are much
more application in Linear Algebra. Computer Graphics in the one of Team.
In the simplest sense computer graphics are images viewable on a computer screen.
The images are generated using computers and likewise, are manipulated by
computers. Underlying the representation of the images on the computer screen is
the mathematics of Linear Algebra.

3. 2-Dimensional Computer Graphics
Examples of computer graphics are those of
which belong to 2 dimensions. Common 2D
graphics include text. For example the vertices of
the letter H can be represented by the following
data matrix D:
3-Dimensional Computer Graphics
3-Dimensional graphics live in R3 versus 2-Dimensional graphics
which live in R2. 3-Dimensional graphics have a vast deal more
applications in comparison to 2-Dimensional graphics, and are,
likewise, more complicated. We will now work with the variable Z, in
addition to X and Y, to fully represent coordinates on the X, Y, and Z
axes, or simply space. For example we can represent a cube with the
following data matrix D:

4. Scaling in 2-Dimensions
The scaling transformation is given by the matrix S=
The transformation is given by the multiplication of the matrices S and A: = =
Scaling in 3-Dimensions
In 3-Dimensions, scaling moves the coordinates (X,Y,Z) to new coordinates (C1, C2,
C3) where the Ci’s are scalars. Scaling in 3-Dimensions is exactly like scaling in 2-
Dimensions, except that the scaling occurs along 3 axes, rather than 2.
Note that if we view strictly from the XY-plane the scaling in the Z-direction can not be
seen, if we view strictly from the XZ-plane the scaling in the Y-direction can not be
seen, and if we view strictly from the YZ-plane then the scaling in the X-direction can
not be seen.
XY-plane
XZ-plane
YZ-plane

5. Translation in 2-Dimensions
Mathematically speaking translation in 2-Dimensons is represented by:
Where e1 and e2 are the first two columns of the Identity Matrix, and X0 and Y0 are the coordinates of the
translation vector T.
Translation in 3-Dimensions
Mathematically speaking we can represent the 3-Dimensional translation transformation with:
Where e1, e2, and e3 are the first three columns of the Identity Matrix, and X0,Y0, & Z0 are the coordinates of the
translation vector T.

6. Rotation in 2-Dimensions
• Counter-Clockwise Rotation Matrix:
• Clockwise Rotation Matrix:
Rotation in 3-Dimensions
• Rotation about the x-axis:
• Rotation about the y-axis:
• Rotation about the z-axis:

7. Thank You