[CSC 315] Re: CSC315 homework question

[Andrew J. Pounds]

Basically you are asking the following question -- should you move the 
origin, the mid-point, or the end-point to the origin before operating 
on the vector with a 2-d scaling matrix.  I'll answer your question in 
the following way -- to the person doing the rotating it should appear 
that the vector is growing relative to the rotation point.   The whole 
process should require four 3-D matrices (the 3rd dimension if required 
for homogeneous coordinates in 2-D):

1. Translation of rotation point to origin
2. Rotation
3. Scaling
4. Translation of rotation point back to original coordinates


David Thomas wrote:
> Hi Dr. Pounds.
>
> Homework 2 #7 says "Derive the transformation matrices needed to rotate a line 
> segment starting at the point (2,2) and ending at the point (5,2) about the 
> point (3,2) by 30 degrees and to increase its length by a factor of 1.75." It 
> then asks for the starting and ending coordinates of the line.
>
> My question deals with the scaling part. "Increase its length" is ambiguous; 
> there are many ways to do so. Should the starting point extend to increase the 
> length? Or the ending point? Or should they both extend an equal amount (i.e. 
> scale about the midpoint)? All of these possibilities would yield different 
> results, but they would all increase its length by a factor of 1.75. Could you 
> clarify what you want us to do?
>
> Thanks,
> ~David
>   


-- 
Andrew J. Pounds, Ph.D.  (pounds at theochem.mercer.edu)
Associate Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627