MAKING TRANSFORMATIONS USING BORLAND C++

Hi,

All these transformations i.e. translation,scaling and rotation have standard matrices that
are used.
Just do a Google for :2D transformations "computer graphics"

U'll get plenty of links and there are a number of standard matrices that are used by dif.
authors.

Some represent the matrices as row matrices,some as column matrices.

In my program ,i have used the fol. matrix format
x' and y' are the co-ordinates after tranformations
x and y are the co-ordinates before tranformations.

Matrices of 3 columns(why the extra 1?u could have asked) have been used for 2D to make the co-ordinates homogeneous i.e. all the operations can be represented as matrix multiplications


[x' y' 1]=[x y 1][1 0 0
                         0 1 0
                        tx ty 1]

For translation where tx and ty are the translation displacements respectively.

[x' y' 1]=[x y 1][sx  0 0
                         0  sy 0
                         0   0  1]

For scaling where sx and sy are the scale ratios in x and y respectively.

[x' y' 1]=[x y 1][cos a  sin a  0
                         -sin a cos a  0
                           0        0      1]

For rotation where a is the angle in degrees and this is rotation anti-clockwise.
For clockwise,replace a by -a

So,if u have a number of points say 3 points,
store them in matrix as:
[x1 y1 1
 x2 y2 1
 x3 y3 1]
and multiply this matrix with the appropriate transformation matrix to get the new co-ordinates.


HTH

HI,

I WNTA TO SAY THANKS FOR ANKURATUB & AVIK77
 FOR HELPING ME "MANY THANKS".

ARSSES

Glad to be of help.