Expression 3: 0 equals left bracket, left parenthesis, "x" minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, "K" , Baseline times sin left parenthesis, 2 times pi times "L" times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, "y" minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, "K" , Baseline times cos left parenthesis, 2 times pi times "L" times "c" to the negative 1st power , right parenthesis , right parenthesis squared minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, 2 times "K" , Baseline times StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared left brace, left parenthesis, "x" plus 0 , right parenthesis squared plus left parenthesis, "y" plus 0 , right parenthesis squared less than or equal to left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, 2 times "K" , Baseline , right brace for "K" equals left bracket, 0... "r" Subscript, "e" "p" "i" "t" "i" "t" "i" "o" "n" "s" , Baseline , right bracket , "L" equals left bracket, 1... "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline , right bracket , right bracket0=x−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2πK·sin2·π·L·c−1orners2+y−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2πK·cos2·π·L·c−1orners2−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2π2·K·sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22x+02+y+02≤−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2π2·KforK=0...repititions,L=1...corners
3
Expression 4: 0 equals left bracket, left parenthesis, "x" minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, "K" , Baseline times sin left parenthesis, 2 times pi times "L" times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, "y" minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, "K" , Baseline times cos left parenthesis, 2 times pi times "L" times "c" to the negative 1st power , right parenthesis , right parenthesis squared minus left parenthesis, negative StartRoot, StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared minus sin squared left parenthesis, 2 pi , right parenthesis , EndRoot plus cos left parenthesis, 2 pi , right parenthesis , right parenthesis Superscript, 2 times "K" , Baseline times StartRoot, left parenthesis, sin left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus sin left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared plus left parenthesis, cos left parenthesis, 2 times pi times "c" to the negative 1st power , right parenthesis minus cos left parenthesis, 2 times pi times StartFraction, "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline plus 1 Over 2 , EndFraction times "c" to the negative 1st power , right parenthesis , right parenthesis squared , EndRoot squared for "K" equals left bracket, 0... "r" Subscript, "e" "p" "i" "t" "i" "t" "i" "o" "n" "s" , Baseline , right bracket , "L" equals left bracket, 1... "c" Subscript, "o" "r" "n" "e" "r" "s" , Baseline , right bracket , right bracket0=x−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2πK·sin2·π·L·c−1orners2+y−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2πK·cos2·π·L·c−1orners2−−sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22−sin22π+cos2π2·K·sin2·π·c−1orners−sin2·π·corners+12·c−1orners2+cos2·π·c−1orners−cos2·π·corners+12·c−1orners22forK=0...repititions,L=1...corners
