~v300 200 y#hYWm]hV\b\Dlg[D\Xj yzw$PSSjTgMNRWWRZ]YdTQ ~w178 4 393 797 0 483 0 0 ~f? 14 12 10 ? 2 1 1 0 ? ? ? "Arial" ? ? ? 0 ? 0 0 "Times" 12 ? ? 7 0 c n 105 0 0 0 k 288 i"" ? 1 26177 26178 26115 26178 0 1 1 1 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 0 1 1 0 2 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b'4" *|: ;bP:&c0!)TLS Cylinder ,H| |Gauss,MNewton Method,I}% b!( b"0 b#8 b$@ b%H!WW}]|[~p1 0 ~Ie(x,y,z,X_k,Y_k,Z_k,u,v,w)~p0 1 ~V?m0 (Result)~p0 1 ~V?m0 (Circle)~p0 1 ~V?m0 (Axis)~p0 1 ~V?m0 (B)~p0 1 ~V?m0 (N)~p0 1 ~V?m0 (T)~p0 1 ~V?m0 (P)~p0 1 ~V?m0 (D)~p0 1 ~V?f0 (Gauss)~p0 1 ~V?f0 (F)~p0 1 ~V?f0 (J)~p0 1 ~V?f0 (r)~p0 1 ~V?f0 (d)~p0 1 ~V?f256 (sin)~p0 1 ~V?f257 (cos)~p0 1 ~V?f0 (Objective)~p0 1 ~V?v0 (Gradient)~p0 1 ~V?v0 (Iterations)~p0 1 ~V?v0 (Radius)~p0 1 ~V?v0 (Center)~p0 1 ~V?v0 ('q)~p0 1 ~V?v0 (t)~p0 1 ~V?v0 (w)~p0 1 ~V?v0 (v)~p0 1 ~V?v0 (u)~p0 1 ~V?v0 (z)~p0 1 ~V?v0 (y)~p0 1 ~V?v0 (x)~p0 1 ~V?v0 (k)~p0 1 ~V?c0 (Y)~p0 1 ~V?c0 (Z)~p0 1 ~V?c0 (X)~p0 1 ~V?c0 (n)~p0 1 ~V?c0 (m)~p0 1 ~V?c0 ('e)~p0 1 ~V?c1 ('p)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$@`f }["! `f#}) # b$@| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b$@" *|: ;bP8&c0!*Data| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})## b$@" *|: ;bP8&c0!*xyz data| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(X=(0.69999999999999996;3.2999999999999998;5.5999999999999996;~ 7.5;6.4000000000000004;4.4000000000000004;0.29999999999999999;~ -1.1000000000000001))~p0 2 ~d~A(Y=(6;4.7000000000000002;4;1.3;-1.1000000000000001;~ -3;-2.5;1.3))~p0 255 ~d~A(Z=(5;1;4;3;2;3;1;5))~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#\[%! )b B# b#\" *|: ;bP8&c0!*The| | cylinder axis must intersect the plane z ,] $^z^0_ and have | |a nonzero z component $^w^0_,N}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b#\| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b#\}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b#\}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b#\| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 255 ~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})'# b"0" *|: ;bP8&c0!*number of data| | points}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(n=8)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*convergence| | criterion}& b!( b!L b"0 b#8 b%H b&P!WW}]|[~p0 1 ~A('e=10^(-8))~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*maximum iterations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(m=30)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}`f#})## b"0" *|: ;bP8&c0!*starting point| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(x_0=3)~p0 255 ~d~A(y_0=2)~p0 255 ~d~A(z_0=3)~p0 255 ~d~A(u_0=0)~p0 255 ~d~A(v_0=0)~p0 255 ~d~A(w_0=1)~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b$@" *|: ;bP8&c0!*Algorithm| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b$@" *|: ;bP8&c0!*objective vector| | and cylinder radius}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(F(x,y,u,v)=(r(x,y,u,v)-d(x,y,u,v,1);r(x,y,u,~ v)-d(x,y,u,v,2);r(x,y,u,v)-d(x,y,u,v,3);r(x,y,~ u,v)-d(x,y,u,v,4);r(x,y,u,v)-d(x,y,u,v,5);r(x,~ y,u,v)-d(x,y,u,v,6);r(x,y,u,v)-d(x,y,u,v,7);r(~ x,y,u,v)-d(x,y,u,v,8)))~p1 2 ~A(F(x,y,u,v)=(1/8*Summation(k):(1):(8)*sqrt((~ -(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)/sqrt(w_0^2+u^~ 2+v^2)-sqrt((-(-y+Y_1)*u+(-x+X_1)*v)^2+(-(-x+X_~ 1)*w_0+(-z_0+Z_1)*u)^2+((-y+Y_1)*w_0-(-z_0+Z_1)*~ v)^2)/sqrt(w_0^2+u^2+v^2);1/8*Summation(k):(1):(~ 8)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+~ (Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)/sqrt(~ w_0^2+u^2+v^2)-sqrt((-(-y+Y_2)*u+(-x+X_2)*v)^2+~ (-(-x+X_2)*w_0+(-z_0+Z_2)*u)^2+((-y+Y_2)*w_0-(~ -z_0+Z_2)*v)^2)/sqrt(w_0^2+u^2+v^2);1/8*Summation(~ k):(1):(8)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)/sqrt(w_0^2+u^2+v^2)-sqrt((-(-y+Y_3)*u+(-~ x+X_3)*v)^2+(-(-x+X_3)*w_0+(-z_0+Z_3)*u)^2+((-~ y+Y_3)*w_0-(-z_0+Z_3)*v)^2)/sqrt(w_0^2+u^2+v^2);~ 1/8*Summation(k):(1):(8)*sqrt((-(Y_k-y)*u+(X_k-~ x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*~ w_0-(Z_k-z_0)*v)^2)/sqrt(w_0^2+u^2+v^2)-sqrt((~ -(-y+Y_4)*u+(-x+X_4)*v)^2+(-(-x+X_4)*w_0+(-z_0+~ Z_4)*u)^2+((-y+Y_4)*w_0-(-z_0+Z_4)*v)^2)/sqrt(~ w_0^2+u^2+v^2);1/8*Summation(k):(1):(8)*sqrt((~ -(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)/sqrt(w_0^2+u^~ 2+v^2)-sqrt((-(-y+Y_5)*u+(-x+X_5)*v)^2+(-(-x+X_~ 5)*w_0+(-z_0+Z_5)*u)^2+((-y+Y_5)*w_0-(-z_0+Z_5)*~ v)^2)/sqrt(w_0^2+u^2+v^2);1/8*Summation(k):(1):(~ 8)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+~ (Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)/sqrt(~ w_0^2+u^2+v^2)-sqrt((-(-y+Y_6)*u+(-x+X_6)*v)^2+~ (-(-x+X_6)*w_0+(-z_0+Z_6)*u)^2+((-y+Y_6)*w_0-(~ -z_0+Z_6)*v)^2)/sqrt(w_0^2+u^2+v^2);1/8*Summation(~ k):(1):(8)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)/sqrt(w_0^2+u^2+v^2)-sqrt((-(-y+Y_7)*u+(-~ x+X_7)*v)^2+(-(-x+X_7)*w_0+(-z_0+Z_7)*u)^2+((-~ y+Y_7)*w_0-(-z_0+Z_7)*v)^2)/sqrt(w_0^2+u^2+v^2);~ 1/8*Summation(k):(1):(8)*sqrt((-(Y_k-y)*u+(X_k-~ x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*~ w_0-(Z_k-z_0)*v)^2)/sqrt(w_0^2+u^2+v^2)-sqrt((~ -(-y+Y_8)*u+(-x+X_8)*v)^2+(-(-x+X_8)*w_0+(-z_0+~ Z_8)*u)^2+((-y+Y_8)*w_0-(-z_0+Z_8)*v)^2)/sqrt(~ w_0^2+u^2+v^2)))~p0 3 ~sb/_!! } b00(! c#T"_c/__c/__! ""} ^ _~A(F(~ ?x,?y,?u,?v)=(1/8*Summation(k):(1):(8)*sqrt((-~ (X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_~ k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2)-sqrt((-(-?x+X_1)*w_0+(-z_0+Z_~ 1)*?u)^2+((-?y+Y_1)*w_0-(-z_0+Z_1)*?v)^2+(-(-?y+~ Y_1)*?u+(-?x+X_1)*?v)^2)/sqrt(w_0^2+?u^2+?v^2);~ 1/8*Summation(k):(1):(8)*sqrt((-(X_k-?x)*w_0+(~ Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(~ -(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(w_0^2+?u^2+?v^~ 2)-sqrt((-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+((-?y+~ Y_2)*w_0-(-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+(-?x+~ X_2)*?v)^2)/sqrt(w_0^2+?u^2+?v^2);1/8*Summation(~ k):(1):(8)*sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+~ ((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_~ k-?x)*?v)^2)/sqrt(w_0^2+?u^2+?v^2)-sqrt((-(-?x+~ X_3)*w_0+(-z_0+Z_3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+~ Z_3)*?v)^2+(-(-?y+Y_3)*?u+(-?x+X_3)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2);1/8*Summation(k):(1):(8)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2)-sqrt((-(-?x+X_4)*w_0+(-z_0+Z_~ 4)*?u)^2+((-?y+Y_4)*w_0-(-z_0+Z_4)*?v)^2+(-(-?y+~ Y_4)*?u+(-?x+X_4)*?v)^2)/sqrt(w_0^2+?u^2+?v^2);~ 1/8*Summation(k):(1):(8)*sqrt((-(X_k-?x)*w_0+(~ Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(~ -(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(w_0^2+?u^2+?v^~ 2)-sqrt((-(-?x+X_5)*w_0+(-z_0+Z_5)*?u)^2+((-?y+~ Y_5)*w_0-(-z_0+Z_5)*?v)^2+(-(-?y+Y_5)*?u+(-?x+~ X_5)*?v)^2)/sqrt(w_0^2+?u^2+?v^2);1/8*Summation(~ k):(1):(8)*sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+~ ((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_~ k-?x)*?v)^2)/sqrt(w_0^2+?u^2+?v^2)-sqrt((-(-?x+~ X_6)*w_0+(-z_0+Z_6)*?u)^2+((-?y+Y_6)*w_0-(-z_0+~ Z_6)*?v)^2+(-(-?y+Y_6)*?u+(-?x+X_6)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2);1/8*Summation(k):(1):(8)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2)-sqrt((-(-?x+X_7)*w_0+(-z_0+Z_~ 7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+Z_7)*?v)^2+(-(-?y+~ Y_7)*?u+(-?x+X_7)*?v)^2)/sqrt(w_0^2+?u^2+?v^2);~ 1/8*Summation(k):(1):(8)*sqrt((-(X_k-?x)*w_0+(~ Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(~ -(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(w_0^2+?u^2+?v^~ 2)-sqrt((-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+((-?y+~ Y_8)*w_0-(-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+(-?x+~ X_8)*?v)^2)/sqrt(w_0^2+?u^2+?v^2)))~p0 4 ~d~sb/_!! } b00,! c#T"_c/__c/__! " # $"} ^ _~ ~A(x=?x)~p0 2 ~A(y=?y)~p0 255 ~A(z=z_0)~p0 255 ~A(D=(u,v,w))~p0 255 ~A(u=?u)~p0 2 ~A(v=?v)~p0 255 ~A(w=w_0)~p0 255 ~A(k=?k)~p0 255 ~A(d(x,y,u,v,k)=abs(((X_k;Y_k;Z_k)-(x;y;z))*#D)/~ abs(D))~p1 2 ~A(d(x,y,u,v,k)=abs(((X_k;Y_k;Z_k)-(x;y;z_0))*#~ (u,v,w))/abs(u,v,w))~p0 3 ~sb/_!! } b00(! c#T"_c/__c/__! ""} ^ _~A(d(~ x,y,u,v,k)=abs(((X_k;Y_k;Z_k)-(x;y;z_0))*#(u,v,~ w_0))/abs(u,v,w_0))~p0 4 ~sb/_!! } b00(! c#T"!c"\"_c/__c/__!"} ^ _~A(~ d(x,y,u,v,k)=sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(~ X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_~ 0)*v)^2)/sqrt(w_0^2+u^2+v^2))~p0 5 ~sb/_!! } "&! c#T"!c"\"_c/__c/__} ^ _~A(d(?x,~ ?y,?u,?v,?k)=sqrt((-(-?x+X_?k)*w_0+(-z_0+Z_?k)*~ ?u)^2+((-?y+Y_?k)*w_0-(-z_0+Z_?k)*?v)^2+(-(-?y+~ Y_?k)*?u+(-?x+X_?k)*?v)^2)/sqrt(w_0^2+?u^2+?v^~ 2))~p0 6 ~d~sb/_!! } b00.! c#T"_c/__c/__! " # $ %"} ^ _~ ~A(r(x,y,u,v)=1/n*Summation(k):(1):(n)*d(x,y,u,~ v,k))~p1 2 ~A(r(x,y,u,v)=1/8*Summation(k):(1):(8)*d(x,y,u,~ v,k))~p0 3 ~sb/_!! } $*! c#T"!c"H#!c',#"c'8 _c/__c/__} $*! c#T"!c"H# c"\"!c'8 _c/__c/__} ^ _~ ~A(r(x,y,u,v)=1/8*Summation(k):(1):(8)*sqrt((-~ (Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)/sqrt(w_0^2+u^~ 2+v^2))~p0 4 ~sb/_!! } b00*! c#T"!c"H#"c#L"_c/__c/__!"} ^ _~ ~A(r(?x,?y,?u,?v)=1/8*Summation(k):(1):(8)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)/sqrt(~ w_0^2+?u^2+?v^2))~p0 5 ~d~sb/_!! } b00,! c#T"_c/__c/__! " # $"} ^ _~ ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$@" *|: ;bP8&c0!*Jacobian matrix| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(J(x,y,u,v)=(Diff(x)*(F(x,y,u,v))_1,Diff(y)*~ (F(x,y,u,v))_1,Diff(u)*(F(x,y,u,v))_1,Diff(v)*~ (F(x,y,u,v))_1;Diff(x)*(F(x,y,u,v))_2,Diff(y)*~ (F(x,y,u,v))_2,Diff(u)*(F(x,y,u,v))_2,Diff(v)*~ (F(x,y,u,v))_2;Diff(x)*(F(x,y,u,v))_3,Diff(y)*~ (F(x,y,u,v))_3,Diff(u)*(F(x,y,u,v))_3,Diff(v)*~ (F(x,y,u,v))_3;Diff(x)*(F(x,y,u,v))_4,Diff(y)*~ (F(x,y,u,v))_4,Diff(u)*(F(x,y,u,v))_4,Diff(v)*~ (F(x,y,u,v))_4;Diff(x)*(F(x,y,u,v))_5,Diff(y)*~ (F(x,y,u,v))_5,Diff(u)*(F(x,y,u,v))_5,Diff(v)*~ (F(x,y,u,v))_5;Diff(x)*(F(x,y,u,v))_6,Diff(y)*~ (F(x,y,u,v))_6,Diff(u)*(F(x,y,u,v))_6,Diff(v)*~ (F(x,y,u,v))_6;Diff(x)*(F(x,y,u,v))_7,Diff(y)*~ (F(x,y,u,v))_7,Diff(u)*(F(x,y,u,v))_7,Diff(v)*~ (F(x,y,u,v))_7;Diff(x)*(F(x,y,u,v))_8,Diff(y)*~ (F(x,y,u,v))_8,Diff(u)*(F(x,y,u,v))_8,Diff(v)*~ (F(x,y,u,v))_8))~p1 2 ~A(J(x,y,u,v)=(1/16*Summation(k):(1):(8)*(2*(-~ (X_k-x)*w_0+(Z_k-z_0)*u)*w_0-2*(-(Y_k-y)*u+(X_~ k-x)*v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*~ u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((~ Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*(2*(-(-x+X_1)*~ w_0+(-z_0+Z_1)*u)*w_0-2*(-(-y+Y_1)*u+(-x+X_1)*~ v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(-y+Y_1)*u+(~ -x+X_1)*v)^2+(-(-x+X_1)*w_0+(-z_0+Z_1)*u)^2+((~ -y+Y_1)*w_0-(-z_0+Z_1)*v)^2)),1/16*Summation(k):(~ 1):(8)*(-2*((Y_k-y)*w_0-(Z_k-z_0)*v)*w_0+2*(-(~ Y_k-y)*u+(X_k-x)*v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*(-2*~ ((-y+Y_1)*w_0-(-z_0+Z_1)*v)*w_0+2*(-(-y+Y_1)*u+~ (-x+X_1)*v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(-y+~ Y_1)*u+(-x+X_1)*v)^2+(-(-x+X_1)*w_0+(-z_0+Z_1)*~ u)^2+((-y+Y_1)*w_0-(-z_0+Z_1)*v)^2)),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(Y_k-~ y)*(-(Y_k-y)*u+(X_k-x)*v)+2*(Z_k-z_0)*(-(X_k-x)*~ w_0+(Z_k-z_0)*u)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^~ 2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_~ k-z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-~ (X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_~ 0)*v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^~ 2)-(1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(-y+Y_1)*(-(-~ y+Y_1)*u+(-x+X_1)*v)+2*(-z_0+Z_1)*(-(-x+X_1)*w_~ 0+(-z_0+Z_1)*u)))/sqrt((-(-y+Y_1)*u+(-x+X_1)*v)^~ 2+(-(-x+X_1)*w_0+(-z_0+Z_1)*u)^2+((-y+Y_1)*w_0-~ (-z_0+Z_1)*v)^2)-(sqrt((-(-y+Y_1)*u+(-x+X_1)*v)^~ 2+(-(-x+X_1)*w_0+(-z_0+Z_1)*u)^2+((-y+Y_1)*w_0-~ (-z_0+Z_1)*v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(2*(X_k-x)*(-(Y_k-y)*u+(X_k-x)*~ v)-2*(Z_k-z_0)*((Y_k-y)*w_0-(Z_k-z_0)*v)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*v)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(2*(-x+X_1)*(-(-y+Y_1)*u+(-x+X_1)*v)-2*~ (-z_0+Z_1)*((-y+Y_1)*w_0-(-z_0+Z_1)*v)))/sqrt(~ (-(-y+Y_1)*u+(-x+X_1)*v)^2+(-(-x+X_1)*w_0+(-z_~ 0+Z_1)*u)^2+((-y+Y_1)*w_0-(-z_0+Z_1)*v)^2)-(sqrt(~ (-(-y+Y_1)*u+(-x+X_1)*v)^2+(-(-x+X_1)*w_0+(-z_~ 0+Z_1)*u)^2+((-y+Y_1)*w_0-(-z_0+Z_1)*v)^2)*v)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2);1/16*Summation(~ k):(1):(8)*(2*(-(X_k-x)*w_0+(Z_k-z_0)*u)*w_0-2*~ (-(Y_k-y)*u+(X_k-x)*v)*v)/(sqrt(w_0^2+u^2+v^2)*~ sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_~ k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*~ (2*(-(-x+X_2)*w_0+(-z_0+Z_2)*u)*w_0-2*(-(-y+Y_~ 2)*u+(-x+X_2)*v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt(~ (-(-y+Y_2)*u+(-x+X_2)*v)^2+(-(-x+X_2)*w_0+(-z_~ 0+Z_2)*u)^2+((-y+Y_2)*w_0-(-z_0+Z_2)*v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-y)*w_0-(Z_k-~ z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_k-x)*v)*u)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(~ -(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2))-1/2*(-2*((-y+Y_2)*w_0-(-z_0+Z_2)*v)*~ w_0+2*(-(-y+Y_2)*u+(-x+X_2)*v)*u)/(sqrt(w_0^2+~ u^2+v^2)*sqrt((-(-y+Y_2)*u+(-x+X_2)*v)^2+(-(-x+~ X_2)*w_0+(-z_0+Z_2)*u)^2+((-y+Y_2)*w_0-(-z_0+Z_~ 2)*v)^2)),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(-2*(Y_k-y)*(-(Y_k-y)*u+(X_k-x)*~ v)+2*(Z_k-z_0)*(-(X_k-x)*w_0+(Z_k-z_0)*u)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*u)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(-2*(-y+Y_2)*(-(-y+Y_2)*u+(-x+X_2)*v)+2*~ (-z_0+Z_2)*(-(-x+X_2)*w_0+(-z_0+Z_2)*u)))/sqrt(~ (-(-y+Y_2)*u+(-x+X_2)*v)^2+(-(-x+X_2)*w_0+(-z_~ 0+Z_2)*u)^2+((-y+Y_2)*w_0-(-z_0+Z_2)*v)^2)-(sqrt(~ (-(-y+Y_2)*u+(-x+X_2)*v)^2+(-(-x+X_2)*w_0+(-z_~ 0+Z_2)*u)^2+((-y+Y_2)*w_0-(-z_0+Z_2)*v)^2)*u)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(2*(X_k-x)*~ (-(Y_k-y)*u+(X_k-x)*v)-2*(Z_k-z_0)*((Y_k-y)*w_~ 0-(Z_k-z_0)*v)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(2*(-x+X_2)*(-(-y+Y_~ 2)*u+(-x+X_2)*v)-2*(-z_0+Z_2)*((-y+Y_2)*w_0-(-~ z_0+Z_2)*v)))/sqrt((-(-y+Y_2)*u+(-x+X_2)*v)^2+~ (-(-x+X_2)*w_0+(-z_0+Z_2)*u)^2+((-y+Y_2)*w_0-(~ -z_0+Z_2)*v)^2)-(sqrt((-(-y+Y_2)*u+(-x+X_2)*v)^~ 2+(-(-x+X_2)*w_0+(-z_0+Z_2)*u)^2+((-y+Y_2)*w_0-~ (-z_0+Z_2)*v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2);1/16*Summation(k):(1):(8)*(2*(-(X_k-~ x)*w_0+(Z_k-z_0)*u)*w_0-2*(-(Y_k-y)*u+(X_k-x)*~ v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_~ k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*~ w_0-(Z_k-z_0)*v)^2))-1/2*(2*(-(-x+X_3)*w_0+(-z_~ 0+Z_3)*u)*w_0-2*(-(-y+Y_3)*u+(-x+X_3)*v)*v)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(-y+Y_3)*u+(-x+X_3)*v)^2+~ (-(-x+X_3)*w_0+(-z_0+Z_3)*u)^2+((-y+Y_3)*w_0-(~ -z_0+Z_3)*v)^2)),1/16*Summation(k):(1):(8)*(-2*~ ((Y_k-y)*w_0-(Z_k-z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_~ k-x)*v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*~ u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((~ Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*(-2*((-y+Y_3)*~ w_0-(-z_0+Z_3)*v)*w_0+2*(-(-y+Y_3)*u+(-x+X_3)*~ v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(-y+Y_3)*u+(~ -x+X_3)*v)^2+(-(-x+X_3)*w_0+(-z_0+Z_3)*u)^2+((~ -y+Y_3)*w_0-(-z_0+Z_3)*v)^2)),1/8*Summation(k):(~ 1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(Y_k-y)*(~ -(Y_k-y)*u+(X_k-x)*v)+2*(Z_k-z_0)*(-(X_k-x)*w_~ 0+(Z_k-z_0)*u)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(-y+Y_3)*(-(-y+Y_~ 3)*u+(-x+X_3)*v)+2*(-z_0+Z_3)*(-(-x+X_3)*w_0+(~ -z_0+Z_3)*u)))/sqrt((-(-y+Y_3)*u+(-x+X_3)*v)^2+~ (-(-x+X_3)*w_0+(-z_0+Z_3)*u)^2+((-y+Y_3)*w_0-(~ -z_0+Z_3)*v)^2)-(sqrt((-(-y+Y_3)*u+(-x+X_3)*v)^~ 2+(-(-x+X_3)*w_0+(-z_0+Z_3)*u)^2+((-y+Y_3)*w_0-~ (-z_0+Z_3)*v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(2*(X_k-x)*(-(Y_k-y)*u+(X_k-x)*~ v)-2*(Z_k-z_0)*((Y_k-y)*w_0-(Z_k-z_0)*v)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*v)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(2*(-x+X_3)*(-(-y+Y_3)*u+(-x+X_3)*v)-2*~ (-z_0+Z_3)*((-y+Y_3)*w_0-(-z_0+Z_3)*v)))/sqrt(~ (-(-y+Y_3)*u+(-x+X_3)*v)^2+(-(-x+X_3)*w_0+(-z_~ 0+Z_3)*u)^2+((-y+Y_3)*w_0-(-z_0+Z_3)*v)^2)-(sqrt(~ (-(-y+Y_3)*u+(-x+X_3)*v)^2+(-(-x+X_3)*w_0+(-z_~ 0+Z_3)*u)^2+((-y+Y_3)*w_0-(-z_0+Z_3)*v)^2)*v)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2);1/16*Summation(~ k):(1):(8)*(2*(-(X_k-x)*w_0+(Z_k-z_0)*u)*w_0-2*~ (-(Y_k-y)*u+(X_k-x)*v)*v)/(sqrt(w_0^2+u^2+v^2)*~ sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_~ k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*~ (2*(-(-x+X_4)*w_0+(-z_0+Z_4)*u)*w_0-2*(-(-y+Y_~ 4)*u+(-x+X_4)*v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt(~ (-(-y+Y_4)*u+(-x+X_4)*v)^2+(-(-x+X_4)*w_0+(-z_~ 0+Z_4)*u)^2+((-y+Y_4)*w_0-(-z_0+Z_4)*v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-y)*w_0-(Z_k-~ z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_k-x)*v)*u)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(~ -(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2))-1/2*(-2*((-y+Y_4)*w_0-(-z_0+Z_4)*v)*~ w_0+2*(-(-y+Y_4)*u+(-x+X_4)*v)*u)/(sqrt(w_0^2+~ u^2+v^2)*sqrt((-(-y+Y_4)*u+(-x+X_4)*v)^2+(-(-x+~ X_4)*w_0+(-z_0+Z_4)*u)^2+((-y+Y_4)*w_0-(-z_0+Z_~ 4)*v)^2)),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(-2*(Y_k-y)*(-(Y_k-y)*u+(X_k-x)*~ v)+2*(Z_k-z_0)*(-(X_k-x)*w_0+(Z_k-z_0)*u)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*u)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(-2*(-y+Y_4)*(-(-y+Y_4)*u+(-x+X_4)*v)+2*~ (-z_0+Z_4)*(-(-x+X_4)*w_0+(-z_0+Z_4)*u)))/sqrt(~ (-(-y+Y_4)*u+(-x+X_4)*v)^2+(-(-x+X_4)*w_0+(-z_~ 0+Z_4)*u)^2+((-y+Y_4)*w_0-(-z_0+Z_4)*v)^2)-(sqrt(~ (-(-y+Y_4)*u+(-x+X_4)*v)^2+(-(-x+X_4)*w_0+(-z_~ 0+Z_4)*u)^2+((-y+Y_4)*w_0-(-z_0+Z_4)*v)^2)*u)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(2*(X_k-x)*~ (-(Y_k-y)*u+(X_k-x)*v)-2*(Z_k-z_0)*((Y_k-y)*w_~ 0-(Z_k-z_0)*v)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(2*(-x+X_4)*(-(-y+Y_~ 4)*u+(-x+X_4)*v)-2*(-z_0+Z_4)*((-y+Y_4)*w_0-(-~ z_0+Z_4)*v)))/sqrt((-(-y+Y_4)*u+(-x+X_4)*v)^2+~ (-(-x+X_4)*w_0+(-z_0+Z_4)*u)^2+((-y+Y_4)*w_0-(~ -z_0+Z_4)*v)^2)-(sqrt((-(-y+Y_4)*u+(-x+X_4)*v)^~ 2+(-(-x+X_4)*w_0+(-z_0+Z_4)*u)^2+((-y+Y_4)*w_0-~ (-z_0+Z_4)*v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2);1/16*Summation(k):(1):(8)*(2*(-(X_k-~ x)*w_0+(Z_k-z_0)*u)*w_0-2*(-(Y_k-y)*u+(X_k-x)*~ v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_~ k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*~ w_0-(Z_k-z_0)*v)^2))-1/2*(2*(-(-x+X_5)*w_0+(-z_~ 0+Z_5)*u)*w_0-2*(-(-y+Y_5)*u+(-x+X_5)*v)*v)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(-y+Y_5)*u+(-x+X_5)*v)^2+~ (-(-x+X_5)*w_0+(-z_0+Z_5)*u)^2+((-y+Y_5)*w_0-(~ -z_0+Z_5)*v)^2)),1/16*Summation(k):(1):(8)*(-2*~ ((Y_k-y)*w_0-(Z_k-z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_~ k-x)*v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*~ u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((~ Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*(-2*((-y+Y_5)*~ w_0-(-z_0+Z_5)*v)*w_0+2*(-(-y+Y_5)*u+(-x+X_5)*~ v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(-y+Y_5)*u+(~ -x+X_5)*v)^2+(-(-x+X_5)*w_0+(-z_0+Z_5)*u)^2+((~ -y+Y_5)*w_0-(-z_0+Z_5)*v)^2)),1/8*Summation(k):(~ 1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(Y_k-y)*(~ -(Y_k-y)*u+(X_k-x)*v)+2*(Z_k-z_0)*(-(X_k-x)*w_~ 0+(Z_k-z_0)*u)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(-y+Y_5)*(-(-y+Y_~ 5)*u+(-x+X_5)*v)+2*(-z_0+Z_5)*(-(-x+X_5)*w_0+(~ -z_0+Z_5)*u)))/sqrt((-(-y+Y_5)*u+(-x+X_5)*v)^2+~ (-(-x+X_5)*w_0+(-z_0+Z_5)*u)^2+((-y+Y_5)*w_0-(~ -z_0+Z_5)*v)^2)-(sqrt((-(-y+Y_5)*u+(-x+X_5)*v)^~ 2+(-(-x+X_5)*w_0+(-z_0+Z_5)*u)^2+((-y+Y_5)*w_0-~ (-z_0+Z_5)*v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(2*(X_k-x)*(-(Y_k-y)*u+(X_k-x)*~ v)-2*(Z_k-z_0)*((Y_k-y)*w_0-(Z_k-z_0)*v)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*v)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(2*(-x+X_5)*(-(-y+Y_5)*u+(-x+X_5)*v)-2*~ (-z_0+Z_5)*((-y+Y_5)*w_0-(-z_0+Z_5)*v)))/sqrt(~ (-(-y+Y_5)*u+(-x+X_5)*v)^2+(-(-x+X_5)*w_0+(-z_~ 0+Z_5)*u)^2+((-y+Y_5)*w_0-(-z_0+Z_5)*v)^2)-(sqrt(~ (-(-y+Y_5)*u+(-x+X_5)*v)^2+(-(-x+X_5)*w_0+(-z_~ 0+Z_5)*u)^2+((-y+Y_5)*w_0-(-z_0+Z_5)*v)^2)*v)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2);1/16*Summation(~ k):(1):(8)*(2*(-(X_k-x)*w_0+(Z_k-z_0)*u)*w_0-2*~ (-(Y_k-y)*u+(X_k-x)*v)*v)/(sqrt(w_0^2+u^2+v^2)*~ sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_~ k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*~ (2*(-(-x+X_6)*w_0+(-z_0+Z_6)*u)*w_0-2*(-(-y+Y_~ 6)*u+(-x+X_6)*v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt(~ (-(-y+Y_6)*u+(-x+X_6)*v)^2+(-(-x+X_6)*w_0+(-z_~ 0+Z_6)*u)^2+((-y+Y_6)*w_0-(-z_0+Z_6)*v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-y)*w_0-(Z_k-~ z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_k-x)*v)*u)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(~ -(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2))-1/2*(-2*((-y+Y_6)*w_0-(-z_0+Z_6)*v)*~ w_0+2*(-(-y+Y_6)*u+(-x+X_6)*v)*u)/(sqrt(w_0^2+~ u^2+v^2)*sqrt((-(-y+Y_6)*u+(-x+X_6)*v)^2+(-(-x+~ X_6)*w_0+(-z_0+Z_6)*u)^2+((-y+Y_6)*w_0-(-z_0+Z_~ 6)*v)^2)),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(-2*(Y_k-y)*(-(Y_k-y)*u+(X_k-x)*~ v)+2*(Z_k-z_0)*(-(X_k-x)*w_0+(Z_k-z_0)*u)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*u)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(-2*(-y+Y_6)*(-(-y+Y_6)*u+(-x+X_6)*v)+2*~ (-z_0+Z_6)*(-(-x+X_6)*w_0+(-z_0+Z_6)*u)))/sqrt(~ (-(-y+Y_6)*u+(-x+X_6)*v)^2+(-(-x+X_6)*w_0+(-z_~ 0+Z_6)*u)^2+((-y+Y_6)*w_0-(-z_0+Z_6)*v)^2)-(sqrt(~ (-(-y+Y_6)*u+(-x+X_6)*v)^2+(-(-x+X_6)*w_0+(-z_~ 0+Z_6)*u)^2+((-y+Y_6)*w_0-(-z_0+Z_6)*v)^2)*u)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(2*(X_k-x)*~ (-(Y_k-y)*u+(X_k-x)*v)-2*(Z_k-z_0)*((Y_k-y)*w_~ 0-(Z_k-z_0)*v)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(2*(-x+X_6)*(-(-y+Y_~ 6)*u+(-x+X_6)*v)-2*(-z_0+Z_6)*((-y+Y_6)*w_0-(-~ z_0+Z_6)*v)))/sqrt((-(-y+Y_6)*u+(-x+X_6)*v)^2+~ (-(-x+X_6)*w_0+(-z_0+Z_6)*u)^2+((-y+Y_6)*w_0-(~ -z_0+Z_6)*v)^2)-(sqrt((-(-y+Y_6)*u+(-x+X_6)*v)^~ 2+(-(-x+X_6)*w_0+(-z_0+Z_6)*u)^2+((-y+Y_6)*w_0-~ (-z_0+Z_6)*v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2);1/16*Summation(k):(1):(8)*(2*(-(X_k-~ x)*w_0+(Z_k-z_0)*u)*w_0-2*(-(Y_k-y)*u+(X_k-x)*~ v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_~ k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*~ w_0-(Z_k-z_0)*v)^2))-1/2*(2*(-(-x+X_7)*w_0+(-z_~ 0+Z_7)*u)*w_0-2*(-(-y+Y_7)*u+(-x+X_7)*v)*v)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(-y+Y_7)*u+(-x+X_7)*v)^2+~ (-(-x+X_7)*w_0+(-z_0+Z_7)*u)^2+((-y+Y_7)*w_0-(~ -z_0+Z_7)*v)^2)),1/16*Summation(k):(1):(8)*(-2*~ ((Y_k-y)*w_0-(Z_k-z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_~ k-x)*v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*~ u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((~ Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*(-2*((-y+Y_7)*~ w_0-(-z_0+Z_7)*v)*w_0+2*(-(-y+Y_7)*u+(-x+X_7)*~ v)*u)/(sqrt(w_0^2+u^2+v^2)*sqrt((-(-y+Y_7)*u+(~ -x+X_7)*v)^2+(-(-x+X_7)*w_0+(-z_0+Z_7)*u)^2+((~ -y+Y_7)*w_0-(-z_0+Z_7)*v)^2)),1/8*Summation(k):(~ 1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(Y_k-y)*(~ -(Y_k-y)*u+(X_k-x)*v)+2*(Z_k-z_0)*(-(X_k-x)*w_~ 0+(Z_k-z_0)*u)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(-2*(-y+Y_7)*(-(-y+Y_~ 7)*u+(-x+X_7)*v)+2*(-z_0+Z_7)*(-(-x+X_7)*w_0+(~ -z_0+Z_7)*u)))/sqrt((-(-y+Y_7)*u+(-x+X_7)*v)^2+~ (-(-x+X_7)*w_0+(-z_0+Z_7)*u)^2+((-y+Y_7)*w_0-(~ -z_0+Z_7)*v)^2)-(sqrt((-(-y+Y_7)*u+(-x+X_7)*v)^~ 2+(-(-x+X_7)*w_0+(-z_0+Z_7)*u)^2+((-y+Y_7)*w_0-~ (-z_0+Z_7)*v)^2)*u)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(2*(X_k-x)*(-(Y_k-y)*u+(X_k-x)*~ v)-2*(Z_k-z_0)*((Y_k-y)*w_0-(Z_k-z_0)*v)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*v)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(2*(-x+X_7)*(-(-y+Y_7)*u+(-x+X_7)*v)-2*~ (-z_0+Z_7)*((-y+Y_7)*w_0-(-z_0+Z_7)*v)))/sqrt(~ (-(-y+Y_7)*u+(-x+X_7)*v)^2+(-(-x+X_7)*w_0+(-z_~ 0+Z_7)*u)^2+((-y+Y_7)*w_0-(-z_0+Z_7)*v)^2)-(sqrt(~ (-(-y+Y_7)*u+(-x+X_7)*v)^2+(-(-x+X_7)*w_0+(-z_~ 0+Z_7)*u)^2+((-y+Y_7)*w_0-(-z_0+Z_7)*v)^2)*v)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2);1/16*Summation(~ k):(1):(8)*(2*(-(X_k-x)*w_0+(Z_k-z_0)*u)*w_0-2*~ (-(Y_k-y)*u+(X_k-x)*v)*v)/(sqrt(w_0^2+u^2+v^2)*~ sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_~ k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2))-1/2*~ (2*(-(-x+X_8)*w_0+(-z_0+Z_8)*u)*w_0-2*(-(-y+Y_~ 8)*u+(-x+X_8)*v)*v)/(sqrt(w_0^2+u^2+v^2)*sqrt(~ (-(-y+Y_8)*u+(-x+X_8)*v)^2+(-(-x+X_8)*w_0+(-z_~ 0+Z_8)*u)^2+((-y+Y_8)*w_0-(-z_0+Z_8)*v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-y)*w_0-(Z_k-~ z_0)*v)*w_0+2*(-(Y_k-y)*u+(X_k-x)*v)*u)/(sqrt(~ w_0^2+u^2+v^2)*sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(~ -(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2))-1/2*(-2*((-y+Y_8)*w_0-(-z_0+Z_8)*v)*~ w_0+2*(-(-y+Y_8)*u+(-x+X_8)*v)*u)/(sqrt(w_0^2+~ u^2+v^2)*sqrt((-(-y+Y_8)*u+(-x+X_8)*v)^2+(-(-x+~ X_8)*w_0+(-z_0+Z_8)*u)^2+((-y+Y_8)*w_0-(-z_0+Z_~ 8)*v)^2)),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+u^2+v^2)*(-2*(Y_k-y)*(-(Y_k-y)*u+(X_k-x)*~ v)+2*(Z_k-z_0)*(-(X_k-x)*w_0+(Z_k-z_0)*u)))/sqrt(~ (-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_~ 0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)-(sqrt((-(~ Y_k-y)*u+(X_k-x)*v)^2+(-(X_k-x)*w_0+(Z_k-z_0)*~ u)^2+((Y_k-y)*w_0-(Z_k-z_0)*v)^2)*u)/sqrt(w_0^~ 2+u^2+v^2))/(w_0^2+u^2+v^2)-(1/2*(sqrt(w_0^2+u^~ 2+v^2)*(-2*(-y+Y_8)*(-(-y+Y_8)*u+(-x+X_8)*v)+2*~ (-z_0+Z_8)*(-(-x+X_8)*w_0+(-z_0+Z_8)*u)))/sqrt(~ (-(-y+Y_8)*u+(-x+X_8)*v)^2+(-(-x+X_8)*w_0+(-z_~ 0+Z_8)*u)^2+((-y+Y_8)*w_0-(-z_0+Z_8)*v)^2)-(sqrt(~ (-(-y+Y_8)*u+(-x+X_8)*v)^2+(-(-x+X_8)*w_0+(-z_~ 0+Z_8)*u)^2+((-y+Y_8)*w_0-(-z_0+Z_8)*v)^2)*u)/~ sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+u^2+v^2)*(2*(X_k-x)*~ (-(Y_k-y)*u+(X_k-x)*v)-2*(Z_k-z_0)*((Y_k-y)*w_~ 0-(Z_k-z_0)*v)))/sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+~ (-(X_k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-~ z_0)*v)^2)-(sqrt((-(Y_k-y)*u+(X_k-x)*v)^2+(-(X_~ k-x)*w_0+(Z_k-z_0)*u)^2+((Y_k-y)*w_0-(Z_k-z_0)*~ v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^2+u^2+v^2)-~ (1/2*(sqrt(w_0^2+u^2+v^2)*(2*(-x+X_8)*(-(-y+Y_~ 8)*u+(-x+X_8)*v)-2*(-z_0+Z_8)*((-y+Y_8)*w_0-(-~ z_0+Z_8)*v)))/sqrt((-(-y+Y_8)*u+(-x+X_8)*v)^2+~ (-(-x+X_8)*w_0+(-z_0+Z_8)*u)^2+((-y+Y_8)*w_0-(~ -z_0+Z_8)*v)^2)-(sqrt((-(-y+Y_8)*u+(-x+X_8)*v)^~ 2+(-(-x+X_8)*w_0+(-z_0+Z_8)*u)^2+((-y+Y_8)*w_0-~ (-z_0+Z_8)*v)^2)*v)/sqrt(w_0^2+u^2+v^2))/(w_0^~ 2+u^2+v^2)))~p0 3 ~sb/_!! } b00&! c#T"_c/__c/__!"} ^ _~A(J(?x,~ ?y,?u,?v)=(1/16*Summation(k):(1):(8)*(2*(-(X_k-~ ?x)*w_0+(Z_k-z_0)*?u)*w_0-2*(-(Y_k-?y)*?u+(X_k-~ ?x)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-~ ?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*~ ?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(2*(-~ (-?x+X_1)*w_0+(-z_0+Z_1)*?u)*w_0-2*(-(-?y+Y_1)*~ ?u+(-?x+X_1)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(-?x+X_1)*w_0+(-z_0+Z_1)*?u)^2+((-?y+Y_1)*w_~ 0-(-z_0+Z_1)*?v)^2+(-(-?y+Y_1)*?u+(-?x+X_1)*?v)^~ 2)),1/16*Summation(k):(1):(8)*(-2*((Y_k-?y)*w_~ 0-(Z_k-z_0)*?v)*w_0+2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*~ ?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+~ (Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+~ (-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(-2*((-?y+Y_~ 1)*w_0-(-z_0+Z_1)*?v)*w_0+2*(-(-?y+Y_1)*?u+(-?x+~ X_1)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_1)*w_0+(-z_0+Z_1)*?u)^2+((-?y+Y_1)*w_0-(-z_0+~ Z_1)*?v)^2+(-(-?y+Y_1)*?u+(-?x+X_1)*?v)^2)),1/~ 8*Summation(k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^~ 2)*(2*(Z_k-z_0)*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)-2*~ (Y_k-?y)*(-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(~ X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?u)/~ sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*~ (sqrt(w_0^2+?u^2+?v^2)*(2*(-z_0+Z_1)*(-(-?x+X_~ 1)*w_0+(-z_0+Z_1)*?u)-2*(-?y+Y_1)*(-(-?y+Y_1)*~ ?u+(-?x+X_1)*?v)))/sqrt((-(-?x+X_1)*w_0+(-z_0+~ Z_1)*?u)^2+((-?y+Y_1)*w_0-(-z_0+Z_1)*?v)^2+(-(~ -?y+Y_1)*?u+(-?x+X_1)*?v)^2)-(sqrt((-(-?x+X_1)*~ w_0+(-z_0+Z_1)*?u)^2+((-?y+Y_1)*w_0-(-z_0+Z_1)*~ ?v)^2+(-(-?y+Y_1)*?u+(-?x+X_1)*?v)^2)*?u)/sqrt(~ w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(Z_~ k-z_0)*((Y_k-?y)*w_0-(Z_k-z_0)*?v)+2*(X_k-?x)*~ (-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(X_k-?x)*w_~ 0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?v)/sqrt(w_0^2+~ ?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+~ ?u^2+?v^2)*(-2*(-z_0+Z_1)*((-?y+Y_1)*w_0-(-z_0+~ Z_1)*?v)+2*(-?x+X_1)*(-(-?y+Y_1)*?u+(-?x+X_1)*~ ?v)))/sqrt((-(-?x+X_1)*w_0+(-z_0+Z_1)*?u)^2+((~ -?y+Y_1)*w_0-(-z_0+Z_1)*?v)^2+(-(-?y+Y_1)*?u+(~ -?x+X_1)*?v)^2)-(sqrt((-(-?x+X_1)*w_0+(-z_0+Z_~ 1)*?u)^2+((-?y+Y_1)*w_0-(-z_0+Z_1)*?v)^2+(-(-?y+~ Y_1)*?u+(-?x+X_1)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^~ 2))/(w_0^2+?u^2+?v^2);1/16*Summation(k):(1):(8)*~ (2*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)*w_0-2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(2*(-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)*w_0-2*(-~ (-?y+Y_2)*?u+(-?x+X_2)*?v)*?v)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+~ ((-?y+Y_2)*w_0-(-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+~ (-?x+X_2)*?v)^2)),1/16*Summation(k):(1):(8)*(-~ 2*((Y_k-?y)*w_0-(Z_k-z_0)*?v)*w_0+2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(-2*((-?y+Y_2)*w_0-(-z_0+Z_2)*?v)*w_0+2*(-~ (-?y+Y_2)*?u+(-?x+X_2)*?v)*?u)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+~ ((-?y+Y_2)*w_0-(-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+~ (-?x+X_2)*?v)^2)),1/8*Summation(k):(1):(8)*(1/~ 2*(sqrt(w_0^2+?u^2+?v^2)*(2*(Z_k-z_0)*(-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)-2*(Y_k-?y)*(-(Y_k-?y)*?u+(X_~ k-?x)*?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^~ 2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+~ (X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*~ ?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/~ (w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*~ (2*(-z_0+Z_2)*(-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)-2*~ (-?y+Y_2)*(-(-?y+Y_2)*?u+(-?x+X_2)*?v)))/sqrt(~ (-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+((-?y+Y_2)*w_~ 0-(-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+(-?x+X_2)*?v)^~ 2)-(sqrt((-(-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+((-?y+~ Y_2)*w_0-(-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+(-?x+~ X_2)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+~ ?u^2+?v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+?u^2+?v^2)*(-2*(Z_k-z_0)*((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)+2*(X_k-?x)*(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_~ k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((~ Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-~ ?x)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^~ 2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(-z_0+~ Z_2)*((-?y+Y_2)*w_0-(-z_0+Z_2)*?v)+2*(-?x+X_2)*~ (-(-?y+Y_2)*?u+(-?x+X_2)*?v)))/sqrt((-(-?x+X_2)*~ w_0+(-z_0+Z_2)*?u)^2+((-?y+Y_2)*w_0-(-z_0+Z_2)*~ ?v)^2+(-(-?y+Y_2)*?u+(-?x+X_2)*?v)^2)-(sqrt((-~ (-?x+X_2)*w_0+(-z_0+Z_2)*?u)^2+((-?y+Y_2)*w_0-~ (-z_0+Z_2)*?v)^2+(-(-?y+Y_2)*?u+(-?x+X_2)*?v)^~ 2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2);~ 1/16*Summation(k):(1):(8)*(2*(-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)*w_0-2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?v)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(2*(-(-?x+X_3)*~ w_0+(-z_0+Z_3)*?u)*w_0-2*(-(-?y+Y_3)*?u+(-?x+X_~ 3)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_3)*w_0+(-z_0+Z_3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+~ Z_3)*?v)^2+(-(-?y+Y_3)*?u+(-?x+X_3)*?v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)*w_0+2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?u)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(-2*((-?y+Y_3)*~ w_0-(-z_0+Z_3)*?v)*w_0+2*(-(-?y+Y_3)*?u+(-?x+X_~ 3)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_3)*w_0+(-z_0+Z_3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+~ Z_3)*?v)^2+(-(-?y+Y_3)*?u+(-?x+X_3)*?v)^2)),1/~ 8*Summation(k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^~ 2)*(2*(Z_k-z_0)*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)-2*~ (Y_k-?y)*(-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(~ X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?u)/~ sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*~ (sqrt(w_0^2+?u^2+?v^2)*(2*(-z_0+Z_3)*(-(-?x+X_~ 3)*w_0+(-z_0+Z_3)*?u)-2*(-?y+Y_3)*(-(-?y+Y_3)*~ ?u+(-?x+X_3)*?v)))/sqrt((-(-?x+X_3)*w_0+(-z_0+~ Z_3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+Z_3)*?v)^2+(-(~ -?y+Y_3)*?u+(-?x+X_3)*?v)^2)-(sqrt((-(-?x+X_3)*~ w_0+(-z_0+Z_3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+Z_3)*~ ?v)^2+(-(-?y+Y_3)*?u+(-?x+X_3)*?v)^2)*?u)/sqrt(~ w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(Z_~ k-z_0)*((Y_k-?y)*w_0-(Z_k-z_0)*?v)+2*(X_k-?x)*~ (-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(X_k-?x)*w_~ 0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?v)/sqrt(w_0^2+~ ?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+~ ?u^2+?v^2)*(-2*(-z_0+Z_3)*((-?y+Y_3)*w_0-(-z_0+~ Z_3)*?v)+2*(-?x+X_3)*(-(-?y+Y_3)*?u+(-?x+X_3)*~ ?v)))/sqrt((-(-?x+X_3)*w_0+(-z_0+Z_3)*?u)^2+((~ -?y+Y_3)*w_0-(-z_0+Z_3)*?v)^2+(-(-?y+Y_3)*?u+(~ -?x+X_3)*?v)^2)-(sqrt((-(-?x+X_3)*w_0+(-z_0+Z_~ 3)*?u)^2+((-?y+Y_3)*w_0-(-z_0+Z_3)*?v)^2+(-(-?y+~ Y_3)*?u+(-?x+X_3)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^~ 2))/(w_0^2+?u^2+?v^2);1/16*Summation(k):(1):(8)*~ (2*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)*w_0-2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(2*(-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)*w_0-2*(-~ (-?y+Y_4)*?u+(-?x+X_4)*?v)*?v)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)^2+~ ((-?y+Y_4)*w_0-(-z_0+Z_4)*?v)^2+(-(-?y+Y_4)*?u+~ (-?x+X_4)*?v)^2)),1/16*Summation(k):(1):(8)*(-~ 2*((Y_k-?y)*w_0-(Z_k-z_0)*?v)*w_0+2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(-2*((-?y+Y_4)*w_0-(-z_0+Z_4)*?v)*w_0+2*(-~ (-?y+Y_4)*?u+(-?x+X_4)*?v)*?u)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)^2+~ ((-?y+Y_4)*w_0-(-z_0+Z_4)*?v)^2+(-(-?y+Y_4)*?u+~ (-?x+X_4)*?v)^2)),1/8*Summation(k):(1):(8)*(1/~ 2*(sqrt(w_0^2+?u^2+?v^2)*(2*(Z_k-z_0)*(-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)-2*(Y_k-?y)*(-(Y_k-?y)*?u+(X_~ k-?x)*?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^~ 2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+~ (X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*~ ?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/~ (w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*~ (2*(-z_0+Z_4)*(-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)-2*~ (-?y+Y_4)*(-(-?y+Y_4)*?u+(-?x+X_4)*?v)))/sqrt(~ (-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)^2+((-?y+Y_4)*w_~ 0-(-z_0+Z_4)*?v)^2+(-(-?y+Y_4)*?u+(-?x+X_4)*?v)^~ 2)-(sqrt((-(-?x+X_4)*w_0+(-z_0+Z_4)*?u)^2+((-?y+~ Y_4)*w_0-(-z_0+Z_4)*?v)^2+(-(-?y+Y_4)*?u+(-?x+~ X_4)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+~ ?u^2+?v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+?u^2+?v^2)*(-2*(Z_k-z_0)*((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)+2*(X_k-?x)*(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_~ k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((~ Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-~ ?x)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^~ 2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(-z_0+~ Z_4)*((-?y+Y_4)*w_0-(-z_0+Z_4)*?v)+2*(-?x+X_4)*~ (-(-?y+Y_4)*?u+(-?x+X_4)*?v)))/sqrt((-(-?x+X_4)*~ w_0+(-z_0+Z_4)*?u)^2+((-?y+Y_4)*w_0-(-z_0+Z_4)*~ ?v)^2+(-(-?y+Y_4)*?u+(-?x+X_4)*?v)^2)-(sqrt((-~ (-?x+X_4)*w_0+(-z_0+Z_4)*?u)^2+((-?y+Y_4)*w_0-~ (-z_0+Z_4)*?v)^2+(-(-?y+Y_4)*?u+(-?x+X_4)*?v)^~ 2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2);~ 1/16*Summation(k):(1):(8)*(2*(-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)*w_0-2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?v)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(2*(-(-?x+X_5)*~ w_0+(-z_0+Z_5)*?u)*w_0-2*(-(-?y+Y_5)*?u+(-?x+X_~ 5)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_5)*w_0+(-z_0+Z_5)*?u)^2+((-?y+Y_5)*w_0-(-z_0+~ Z_5)*?v)^2+(-(-?y+Y_5)*?u+(-?x+X_5)*?v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)*w_0+2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?u)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(-2*((-?y+Y_5)*~ w_0-(-z_0+Z_5)*?v)*w_0+2*(-(-?y+Y_5)*?u+(-?x+X_~ 5)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_5)*w_0+(-z_0+Z_5)*?u)^2+((-?y+Y_5)*w_0-(-z_0+~ Z_5)*?v)^2+(-(-?y+Y_5)*?u+(-?x+X_5)*?v)^2)),1/~ 8*Summation(k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^~ 2)*(2*(Z_k-z_0)*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)-2*~ (Y_k-?y)*(-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(~ X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?u)/~ sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*~ (sqrt(w_0^2+?u^2+?v^2)*(2*(-z_0+Z_5)*(-(-?x+X_~ 5)*w_0+(-z_0+Z_5)*?u)-2*(-?y+Y_5)*(-(-?y+Y_5)*~ ?u+(-?x+X_5)*?v)))/sqrt((-(-?x+X_5)*w_0+(-z_0+~ Z_5)*?u)^2+((-?y+Y_5)*w_0-(-z_0+Z_5)*?v)^2+(-(~ -?y+Y_5)*?u+(-?x+X_5)*?v)^2)-(sqrt((-(-?x+X_5)*~ w_0+(-z_0+Z_5)*?u)^2+((-?y+Y_5)*w_0-(-z_0+Z_5)*~ ?v)^2+(-(-?y+Y_5)*?u+(-?x+X_5)*?v)^2)*?u)/sqrt(~ w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(Z_~ k-z_0)*((Y_k-?y)*w_0-(Z_k-z_0)*?v)+2*(X_k-?x)*~ (-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(X_k-?x)*w_~ 0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?v)/sqrt(w_0^2+~ ?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+~ ?u^2+?v^2)*(-2*(-z_0+Z_5)*((-?y+Y_5)*w_0-(-z_0+~ Z_5)*?v)+2*(-?x+X_5)*(-(-?y+Y_5)*?u+(-?x+X_5)*~ ?v)))/sqrt((-(-?x+X_5)*w_0+(-z_0+Z_5)*?u)^2+((~ -?y+Y_5)*w_0-(-z_0+Z_5)*?v)^2+(-(-?y+Y_5)*?u+(~ -?x+X_5)*?v)^2)-(sqrt((-(-?x+X_5)*w_0+(-z_0+Z_~ 5)*?u)^2+((-?y+Y_5)*w_0-(-z_0+Z_5)*?v)^2+(-(-?y+~ Y_5)*?u+(-?x+X_5)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^~ 2))/(w_0^2+?u^2+?v^2);1/16*Summation(k):(1):(8)*~ (2*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)*w_0-2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(2*(-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)*w_0-2*(-~ (-?y+Y_6)*?u+(-?x+X_6)*?v)*?v)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)^2+~ ((-?y+Y_6)*w_0-(-z_0+Z_6)*?v)^2+(-(-?y+Y_6)*?u+~ (-?x+X_6)*?v)^2)),1/16*Summation(k):(1):(8)*(-~ 2*((Y_k-?y)*w_0-(Z_k-z_0)*?v)*w_0+2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(-2*((-?y+Y_6)*w_0-(-z_0+Z_6)*?v)*w_0+2*(-~ (-?y+Y_6)*?u+(-?x+X_6)*?v)*?u)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)^2+~ ((-?y+Y_6)*w_0-(-z_0+Z_6)*?v)^2+(-(-?y+Y_6)*?u+~ (-?x+X_6)*?v)^2)),1/8*Summation(k):(1):(8)*(1/~ 2*(sqrt(w_0^2+?u^2+?v^2)*(2*(Z_k-z_0)*(-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)-2*(Y_k-?y)*(-(Y_k-?y)*?u+(X_~ k-?x)*?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^~ 2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+~ (X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*~ ?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/~ (w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*~ (2*(-z_0+Z_6)*(-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)-2*~ (-?y+Y_6)*(-(-?y+Y_6)*?u+(-?x+X_6)*?v)))/sqrt(~ (-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)^2+((-?y+Y_6)*w_~ 0-(-z_0+Z_6)*?v)^2+(-(-?y+Y_6)*?u+(-?x+X_6)*?v)^~ 2)-(sqrt((-(-?x+X_6)*w_0+(-z_0+Z_6)*?u)^2+((-?y+~ Y_6)*w_0-(-z_0+Z_6)*?v)^2+(-(-?y+Y_6)*?u+(-?x+~ X_6)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+~ ?u^2+?v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+?u^2+?v^2)*(-2*(Z_k-z_0)*((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)+2*(X_k-?x)*(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_~ k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((~ Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-~ ?x)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^~ 2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(-z_0+~ Z_6)*((-?y+Y_6)*w_0-(-z_0+Z_6)*?v)+2*(-?x+X_6)*~ (-(-?y+Y_6)*?u+(-?x+X_6)*?v)))/sqrt((-(-?x+X_6)*~ w_0+(-z_0+Z_6)*?u)^2+((-?y+Y_6)*w_0-(-z_0+Z_6)*~ ?v)^2+(-(-?y+Y_6)*?u+(-?x+X_6)*?v)^2)-(sqrt((-~ (-?x+X_6)*w_0+(-z_0+Z_6)*?u)^2+((-?y+Y_6)*w_0-~ (-z_0+Z_6)*?v)^2+(-(-?y+Y_6)*?u+(-?x+X_6)*?v)^~ 2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2);~ 1/16*Summation(k):(1):(8)*(2*(-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)*w_0-2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?v)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(2*(-(-?x+X_7)*~ w_0+(-z_0+Z_7)*?u)*w_0-2*(-(-?y+Y_7)*?u+(-?x+X_~ 7)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_7)*w_0+(-z_0+Z_7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+~ Z_7)*?v)^2+(-(-?y+Y_7)*?u+(-?x+X_7)*?v)^2)),1/~ 16*Summation(k):(1):(8)*(-2*((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)*w_0+2*(-(Y_k-?y)*?u+(X_k-?x)*?v)*?u)/~ (sqrt(w_0^2+?u^2+?v^2)*sqrt((-(X_k-?x)*w_0+(Z_~ k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(~ Y_k-?y)*?u+(X_k-?x)*?v)^2))-1/2*(-2*((-?y+Y_7)*~ w_0-(-z_0+Z_7)*?v)*w_0+2*(-(-?y+Y_7)*?u+(-?x+X_~ 7)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt((-(-?x+~ X_7)*w_0+(-z_0+Z_7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+~ Z_7)*?v)^2+(-(-?y+Y_7)*?u+(-?x+X_7)*?v)^2)),1/~ 8*Summation(k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^~ 2)*(2*(Z_k-z_0)*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)-2*~ (Y_k-?y)*(-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(~ X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-~ z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?u)/~ sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*~ (sqrt(w_0^2+?u^2+?v^2)*(2*(-z_0+Z_7)*(-(-?x+X_~ 7)*w_0+(-z_0+Z_7)*?u)-2*(-?y+Y_7)*(-(-?y+Y_7)*~ ?u+(-?x+X_7)*?v)))/sqrt((-(-?x+X_7)*w_0+(-z_0+~ Z_7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+Z_7)*?v)^2+(-(~ -?y+Y_7)*?u+(-?x+X_7)*?v)^2)-(sqrt((-(-?x+X_7)*~ w_0+(-z_0+Z_7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+Z_7)*~ ?v)^2+(-(-?y+Y_7)*?u+(-?x+X_7)*?v)^2)*?u)/sqrt(~ w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2),1/8*Summation(~ k):(1):(8)*(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(Z_~ k-z_0)*((Y_k-?y)*w_0-(Z_k-z_0)*?v)+2*(X_k-?x)*~ (-(Y_k-?y)*?u+(X_k-?x)*?v)))/sqrt((-(X_k-?x)*w_~ 0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^~ 2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2)*?v)/sqrt(w_0^2+~ ?u^2+?v^2))/(w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+~ ?u^2+?v^2)*(-2*(-z_0+Z_7)*((-?y+Y_7)*w_0-(-z_0+~ Z_7)*?v)+2*(-?x+X_7)*(-(-?y+Y_7)*?u+(-?x+X_7)*~ ?v)))/sqrt((-(-?x+X_7)*w_0+(-z_0+Z_7)*?u)^2+((~ -?y+Y_7)*w_0-(-z_0+Z_7)*?v)^2+(-(-?y+Y_7)*?u+(~ -?x+X_7)*?v)^2)-(sqrt((-(-?x+X_7)*w_0+(-z_0+Z_~ 7)*?u)^2+((-?y+Y_7)*w_0-(-z_0+Z_7)*?v)^2+(-(-?y+~ Y_7)*?u+(-?x+X_7)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^~ 2))/(w_0^2+?u^2+?v^2);1/16*Summation(k):(1):(8)*~ (2*(-(X_k-?x)*w_0+(Z_k-z_0)*?u)*w_0-2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?v)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(2*(-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)*w_0-2*(-~ (-?y+Y_8)*?u+(-?x+X_8)*?v)*?v)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+~ ((-?y+Y_8)*w_0-(-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+~ (-?x+X_8)*?v)^2)),1/16*Summation(k):(1):(8)*(-~ 2*((Y_k-?y)*w_0-(Z_k-z_0)*?v)*w_0+2*(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)*?u)/(sqrt(w_0^2+?u^2+?v^2)*sqrt(~ (-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*?v)^2))-~ 1/2*(-2*((-?y+Y_8)*w_0-(-z_0+Z_8)*?v)*w_0+2*(-~ (-?y+Y_8)*?u+(-?x+X_8)*?v)*?u)/(sqrt(w_0^2+?u^~ 2+?v^2)*sqrt((-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+~ ((-?y+Y_8)*w_0-(-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+~ (-?x+X_8)*?v)^2)),1/8*Summation(k):(1):(8)*(1/~ 2*(sqrt(w_0^2+?u^2+?v^2)*(2*(Z_k-z_0)*(-(X_k-?x)*~ w_0+(Z_k-z_0)*?u)-2*(Y_k-?y)*(-(Y_k-?y)*?u+(X_~ k-?x)*?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^~ 2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+~ (X_k-?x)*?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*~ ?u)^2+((Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*~ ?u+(X_k-?x)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/~ (w_0^2+?u^2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*~ (2*(-z_0+Z_8)*(-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)-2*~ (-?y+Y_8)*(-(-?y+Y_8)*?u+(-?x+X_8)*?v)))/sqrt(~ (-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+((-?y+Y_8)*w_~ 0-(-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+(-?x+X_8)*?v)^~ 2)-(sqrt((-(-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+((-?y+~ Y_8)*w_0-(-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+(-?x+~ X_8)*?v)^2)*?u)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+~ ?u^2+?v^2),1/8*Summation(k):(1):(8)*(1/2*(sqrt(~ w_0^2+?u^2+?v^2)*(-2*(Z_k-z_0)*((Y_k-?y)*w_0-(~ Z_k-z_0)*?v)+2*(X_k-?x)*(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)))/sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((Y_~ k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-?x)*~ ?v)^2)-(sqrt((-(X_k-?x)*w_0+(Z_k-z_0)*?u)^2+((~ Y_k-?y)*w_0-(Z_k-z_0)*?v)^2+(-(Y_k-?y)*?u+(X_k-~ ?x)*?v)^2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^~ 2+?v^2)-(1/2*(sqrt(w_0^2+?u^2+?v^2)*(-2*(-z_0+~ Z_8)*((-?y+Y_8)*w_0-(-z_0+Z_8)*?v)+2*(-?x+X_8)*~ (-(-?y+Y_8)*?u+(-?x+X_8)*?v)))/sqrt((-(-?x+X_8)*~ w_0+(-z_0+Z_8)*?u)^2+((-?y+Y_8)*w_0-(-z_0+Z_8)*~ ?v)^2+(-(-?y+Y_8)*?u+(-?x+X_8)*?v)^2)-(sqrt((-~ (-?x+X_8)*w_0+(-z_0+Z_8)*?u)^2+((-?y+Y_8)*w_0-~ (-z_0+Z_8)*?v)^2+(-(-?y+Y_8)*?u+(-?x+X_8)*?v)^~ 2)*?v)/sqrt(w_0^2+?u^2+?v^2))/(w_0^2+?u^2+?v^2)))~p0 4 ~d~sb/_!! } b00,! c#T"_c/__c/__! " # $"} ^ _~ ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$@" *|: ;bP8&c0!*Gauss,MNewton method| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(Gauss(?x,?y,?u,?v,?m)=Conditional((?x,?y,?u,~ ?v,m-?m),(abs((J(?x,?y,?u,?v))^**F(?x,?y,?u,?v))<~ 'e)+(?m=0);Gauss(((?x;?y;?u;?v)-((J(?x,?y,?u,?v))^**~ J(?x,?y,?u,?v))^(-1)*((J(?x,?y,?u,?v))^**F(?x,~ ?y,?u,?v)))_1,((?x;?y;?u;?v)-((J(?x,?y,?u,?v))^**~ J(?x,?y,?u,?v))^(-1)*((J(?x,?y,?u,?v))^**F(?x,~ ?y,?u,?v)))_2,((?x;?y;?u;?v)-((J(?x,?y,?u,?v))^**~ J(?x,?y,?u,?v))^(-1)*((J(?x,?y,?u,?v))^**F(?x,~ ?y,?u,?v)))_3,((?x;?y;?u;?v)-((J(?x,?y,?u,?v))^**~ J(?x,?y,?u,?v))^(-1)*((J(?x,?y,?u,?v))^**F(?x,~ ?y,?u,?v)))_4,?m-1),(1>0)))~p0 2 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$@}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Result=Gauss(x_0,y_0,u_0,v_0,m))~p0 1 ~A(Result=(2.9603330243513502,1.1914074015664153,~ -0.12789240914955474,0.40775288802295351,8))~p0 2 ~d~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$@" *|: ;bP8&c0!*point on cylinder| | axis}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(P=(Result_1,Result_2,z_0))~p0 255 ~d~A(P=(2.9603330243513502,1.1914074015664153,~ 3))~p0 2 ~sb/_!! } $&! c#T"!c&T#_c/__c/_^} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})## b$@" *|: ;bP8&c0!*axis direction| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(T=(Result_3,Result_4,w_0))~p0 255 ~d~A(T=(-0.12789240914955474,0.40775288802295351,~ 1))~p0 2 ~sb/_!! } $&! c#T"!c&T#_c/__c/_^} ^ _~A(Radius=~ r(P_1,P_2,T_1,T_2))~p0 1 ~d~A(Radius=3.9854100217399044)~p0 255 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(Iterations=~ Result_5)~p0 1 ~A(Iterations=8)~p0 255 ~sb/_!! } $&! c#T"!c%\"_c/__c/__} ^ _~A(Objective(~ ?x,?y,?a,?b)=1/2*abs(F(?x,?y,?a,?b))^2)~p0 1 ~d~A(Objective(P_1,P_2,T_1,T_2))~p0 1 ~A(Objective(P_1,P_2,T_1,T_2)=0.28510842091467309)~p0 255 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(abs(~ Gradient)=abs((J(P_1,P_2,T_1,T_2))^**F(P_1,P_2,~ T_1,T_2)))~p0 1 ~A(abs(Gradient)=6.1727702531173332e-9)~p0 2 ~sb/_!! } $&! c#T"!c'P!_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@| |}& b!( b"0 b#8 b$@ b%H b&P!WW})## b$@" *|: ;bP8&c0!*Tube plot| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~A(Axis=P+t*T/abs(T))~p0 1 ~d~A(N=(1,0,0)*#T)~p0 255 ~d~A(B=T*#N)~p0 255 ~d~A(Circle=Radius*(N/abs(N)*cos('q)+B/abs(B)*~ sin('q)))~p0 1 ~d~Z1 1 337 514 0 0.51209 0.85895 0.00000 0.83187 -0.49594 -0.24907 -0.21396 0.12755 -0.96847 2 4 4 4 10 0 0 ? ? 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