On Fri, 23 Dec 2005, c wrote:
sqrt(pow(($b0+$b1*cos($w)+$b2*cos(2*$w)),2)+pow(($b1*sin($w)+$b2*sin(2*$w)),2))/sqrt(pow(($a0+$a1*cos($w)+$a2*cos(2*$w)),2)+pow(($a1*sin($w)+$a2*sin(2*$w)),2))
This scary-looking formula is less scary reformatted like this:
sqrt(pow(($b0+$b1*cos($w)+$b2*cos(2*$w)),2) +pow(( $b1*sin($w)+$b2*sin(2*$w)),2))/ sqrt(pow(($a0+$a1*cos($w)+$a2*cos(2*$w)),2) +pow(( $a1*sin($w)+$a2*sin(2*$w)),2))
And then using slightly more advanced math concepts it can be further simplified like this:
norm(($b0,0)+($b1,$b2)*M)/ norm(($a0,0)+($a1,$a2)*M) where M is the matrix (cos($w), cos(2*$w); sin($w), sin(2*$w))
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada