Expression 15: left parenthesis, "x" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 0 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis cos left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 1 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared plus left parenthesis, "y" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 0 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis sin left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 1 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared equals left parenthesis, "r" Superscript, 0 , Baseline min left parenthesis, 1 , "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline , right parenthesis undefined , right parenthesis squared left brace, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline greater than 0 , right bracex−min0,ceilIteration−1∑n1=0minIteration−n1,1cos2πmodfloorl1nn1,nnorn102+y−min0,ceilIteration−1∑n1=0minIteration−n1,1sin2πmodfloorl1nn1,nnorn102=rmin1,Iteration02Iteration>0
15
Expression 16: left parenthesis, "x" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 1 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis cos left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 2 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared plus left parenthesis, "y" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 1 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis sin left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 2 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared less than left parenthesis, "r" Superscript, 0 , Baseline min left parenthesis, 2 , "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline , right parenthesis undefined , right parenthesis squared left brace, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline greater than 1 , right bracex−min1,ceilIteration−1∑n1=0minIteration−n1,1cos2πmodfloorl2nn1,nnorn102+y−min1,ceilIteration−1∑n1=0minIteration−n1,1sin2πmodfloorl2nn1,nnorn102<rmin2,Iteration02Iteration>1
16
Expression 17: left parenthesis, "x" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 2 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis cos left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 3 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared plus left parenthesis, "y" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 2 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis sin left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 3 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared equals left parenthesis, "r" Superscript, 0 , Baseline min left parenthesis, 3 , "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline , right parenthesis undefined , right parenthesis squared left brace, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline greater than 2 , right bracex−min2,ceilIteration−1∑n1=0minIteration−n1,1cos2πmodfloorl3nn1,nnorn102+y−min2,ceilIteration−1∑n1=0minIteration−n1,1sin2πmodfloorl3nn1,nnorn102=rmin3,Iteration02Iteration>2
17
Expression 18: left parenthesis, "x" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 3 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis cos left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 4 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared plus left parenthesis, "y" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 3 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis sin left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 4 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared equals left parenthesis, "r" Superscript, 0 , Baseline min left parenthesis, 4 , "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline , right parenthesis undefined , right parenthesis squared left brace, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline greater than 3 , right bracex−min3,ceilIteration−1∑n1=0minIteration−n1,1cos2πmodfloorl4nn1,nnorn102+y−min3,ceilIteration−1∑n1=0minIteration−n1,1sin2πmodfloorl4nn1,nnorn102=rmin4,Iteration02Iteration>3
18
Expression 19: left parenthesis, "x" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 4 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis cos left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 5 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared plus left parenthesis, "y" minus Start sum from "n" Subscript, 1 , Baseline equals 0 to min left parenthesis, 4 , ceil left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus 1 , right parenthesis , right parenthesis , end sum, min left parenthesis, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline minus "n" Subscript, 1 , Baseline , 1 , right parenthesis sin left parenthesis, StartFraction, 2 pi mod left parenthesis, floor left parenthesis, StartNestedFraction, "l" Subscript, 5 , Baseline NestedOver "n" Superscript, "n" Subscript, 1 , Baseline , Baseline , EndNestedFraction , right parenthesis , "n" , right parenthesis Over "n" , EndFraction , right parenthesis "o" "r" Superscript, 0 , Baseline left parenthesis, "n" Subscript, 1 , Baseline , right parenthesis undefined , right parenthesis squared equals left parenthesis, "r" Superscript, 0 , Baseline min left parenthesis, 5 , "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline , right parenthesis undefined , right parenthesis squared left brace, "I" Subscript, "t" "e" "r" "a" "t" "i" "o" "n" , Baseline greater than 4 , right bracex−min4,ceilIteration−1∑n1=0minIteration−n1,1cos2πmodfloorl5nn1,nnorn102+y−min4,ceilIteration−1∑n1=0minIteration−n1,1sin2πmodfloorl5nn1,nnorn102=rmin5,Iteration02Iteration>4
