1. Computer graphics (Assignment) By: Farwa Abdul Hannan (12 – CS – 13)
Zubaid Khalil (12 – CS – 22)
Hassan Ali Khan (12 – CS – 28)
Scaling:
Scaling is the process of changing the size of a picture or object. It can be done in either
compression or expansion. It consists of three scale factors
1. Sx – for scaling of x-coordinates
2. Sy – for scaling of y-coordinates
3. Sz – for scaling of z-coordinates
If the scaling factors are greater than 1 then the expansion in size will occur and if they are less
than 1 then the compression in length will occur. If the values for Sx and Sy are negative then the
mirror image can be created.
For scaling, at the backend the scaled values for x and y coordinates are computed by using matrix
multiplication. The matrix is known as scaling matrix and is like
---------- (1)
2D Scaling:
For 2D scaling x and y components are used for scaling of x and y coordinates and scaling
matrix for 2D scaling is
---------- (2)
Here x and y are the values of the x-axis and y-axis where the object is placed and the Sx and Sy
are the scaled values that is the value we want the object to be scaled at. These values are multiplied
by using the matrix multiplication property and the computed values will be given out as x’ and
y’.
Example:
Consider the values of x and y are 1 and 1 respectively for a rectangular object as shown
below.
And suppose the values of Sx & Sy are 3 & -2 respectively then putting them in eq. (2)
2. And after computation we’ve got new scaled values which are 3 and -2 so the shape will look like
the following.
3D Scaling:
For 3D scaling x, y and z components are used for scaling of x, y and z coordinates and
scaling matrix for 3D scaling is
---------- (3)
Here x, y and z are the values of the x-axis, y-axis and z-axis where the object is placed and the
Sx, Sy and Sz are the scaled values that is the value we want the object to be scaled at. These
values are multiplied by using the matrix multiplication property and the computed values will be
given out as x’, y’ and z’.
Example:
Consider the values of x, y and z are 3, 2 and 2 respectively for a rectangular object as shown
below.
And suppose the values of Sx, Sy & Sz are 1, 2 & 1 respectively then putting them in eq. (3)
And after computation we’ve got new scaled values which are 3, 4 and -2 so the shape will look
like the following.
Uniform & non-uniform scaling:
If the values of Sx, Sy and Sz are same then the scaling is known as uniform scaling or
pure reflection and if both the values are not same then the scaling is known as non-uniform scaling
or differential scaling.
