Transformation matrix

[FurqanKhalil]

Could someone please tell me how to calculate a transformation matrix?

 

[intelnehalem]

I suggest you remember the transformation matrices your teacher has given you !
Otherwise you have to do this:
(coordinate matrix of object) x (transformation matrix) = (coordinate matrix of image_
ex:
0 2 x a c = 0 4
1 0 , b d _ 2 0

matrix on LHS simplified :
2b 2d = 0 4
a _ c __ 2 0
corresponding elements in a matrix are equal!
so 2b=0 ; 2d=4 ; a=2; c=0
finally:
b=0; d=2; a=2;c=0
re-arrange them in matrix form:

2 0
0 2
This is the transformation matrix for the above (it is an enlargement , scale factor 2)

Hope this helped!
EDIT: arghhh my matrices aren't being shown here properly

 

[FurqanKhalil]

Thanks. But exactly how do you obtain a coordinate matrix? A point has only two elements.

 

[intelnehalem]

Thanks. But exactly how do you obtain a coordinate matrix? A point has only two elements.

Yes. If an object has more than one point, you arrange the x coordinates in the first row of the matrix and the corresponding y coordinates on the bottom row
ex: For a triangle, (x1,y1) (x2,y2) and (x3,y3) are the vertices so the matrix is-
x1 x2 x3
y1 y2 y3

 

[Sanaiqbal]

The smartest thing to do about Transformation Matrix is to check out the unsolved Topic By Topics (Elementery Mathematics). In the Transformation Topics where explanation is given, there you will find all the necessary transformation matrices for all the transformation. Memorize them. Those are special transformation matrices. Constructing all matrices manually is NOT part of the syllabus.