Transformation matrix for a plane- can rotation be performed using translation itself? ?

Question

Hello,

given the vertices's of initial and resultant plane.

I need to transform a plane(i.e. triangle) from one plane to other in which rotation, scaling and translation has to occur. I just need that transformation matrix if applied to the initial plane it will give resultant plane.

i am trying to

1> rotate the plane first to the normal of the resultant plane.

2> scale the matrix requred

3> translate the points...

dont know the approach is correct upto what extent? also it would be to know that can the rotation o the plane be replaced by transalation.

Answer 1

The transformation equations look like:

a x + b y + c = x'

d x + e y + f = y'

For each of the three points in your triangle you know the initial coordinates (x and y) and the final coordinates( x' and y') so you have 6 equations in 6 unknowns (a, b, c, d, e, and f) so you can solve them. (If you are working in three dimension, then you have 9 equations in 9 unknowns)

If you really want to compute the operations separately, then:

http://en.wikipedia.org/wiki/Coordinate_...

http://en.wikipedia.org/wiki/Rotation_ma...

http://en.wikipedia.org/wiki/Affine_tran...