he4rty wrote:
Don't know how I missed this thread but somehow I did.
Could somebody explain the maths behind the scaling factor please.
The "
Final scale factor in X direction" represents the value by which the width of the original layer has to be multiplied so that obtaining what will be the width of the last duplicate.
For instance, supposing that the original layer features a width of 200 px, if we set the "
Final scale factor in X direction" to 1.25, then the width of the last duplicate will be: 1.25 * 200 = 250 px.
As for the intermediate copies (if any), their widths will vary linearly between the width of the original layer and the one of the last duplicate.
In general, if
n is the number of copies and
a is the integer number representing the stage of duplication from which the scaling process must begin (as specified through the "
Step to start transforming from" slider), we can express the width
w(k) of the generic
k-th duplicate by means of the following formula:
/ w(0) , 1 = k < a
/
w(k) = <
\
\ w(0) + [(k - (a - 1)) / (n - (a - 1))] * (w(n) - w(0)) , a ≤ k ≤ n - 1 where
w(0) and
w(n) respectively symbolize the width of the original layer and the width of the last namely the
n-th duplicate, while the latter value is obtained by multiplying the former by
Sx , that is the final scale factor in X direction:
w(n) = sX * w(0)For
a = 1, we simply get:
w(k) = w(0) + (k / n) * (w(n) - w(0)) , 1 ≤ k ≤ n - 1With appropriate change of symbols, identical remarks apply to the "
Final scale factor in Y direction".