#Nathan Fox
#Homework 24
#I give permission for this work to be posted online

#Read procedures from class
read(`C25.txt`):

Help:=proc():
    print(` InsP(P,x,y) , TgT(N) , TgC(N) `):
end:

##PROBLEM 1##

#InsP(P,x,y): P is a list of vertices, describing, in
#counterclockwise way, the vertices of a polygon assumed to be
#convex, and outputs the conditions for a point to be inside.
InsP:=proc(P, x, y) local C, L, i:
    C:=add(P[i], i=1..nops(P))/nops(P):
    #C:=convert(P,`+`)/nops(P): didn't work for some reason
    L:=[seq(Le(P[i],P[i+1],x,y), i=1..nops(P)-1),
        Le(P[nops(P)], P[1],x,y)]:
    return convert([seq(expand(sign(subs({x=C[1],y=C[2]},L[i]))*
        L[i])>0, i=1..nops(P))], `and`):
end:

##PROBLEM 2##

#TgT(N): inputs a positive integer N and outputs a natural
#triangulation of the equilateral triangle whose vertices are at 
#[0,0],[1,0],[1/2,sqrt(3)/2] 
#into equilateral triangles of side-length 1/N.
TgT:=proc(N) local i, j:
    return {seq(seq({[(j/N)*(1/2)+i/N, (j/N)*(sqrt(3)/2)],
        [(j/N)*(1/2)+(i+1)/N, (j/N)*(sqrt(3)/2)],
        [(j/N)*(1/2)+(i+1/2)/N, ((j+1)/N)*(sqrt(3)/2)]},
        i=0..N-1-j), j=0..N-1)}:
end:

#TgT(2) returned {{[0, 0], [1/2, 0], [1/4, 1/4*3^(1/2)]}, {[1, 0], [1/2, 0], [3/4, 1/4*3^(1/2)]}, {[1/2, 1/2*3^(1/2)], [1/4, 1/4*3^(1/2)], [3/4, 1/4*3^(1/2)]}}
#TgT(4) returned {{[0, 0], [1/4, 0], [1/8, 1/8*3^(1/2)]}, {[1, 0], [3/4, 0], [7/8, 1/8*3^(1/2)]}, {[1/2, 0], [1/4, 0], [3/8, 1/8*3^(1/2)]}, {[1/2, 0], [3/4, 0], [5/8, 1/8*3^(1/2)]}, {[1/2, 1/2*3^(1/2)], [3/8, 3/8*3^(1/2)], [5/8, 3/8*3^(1/2)]}, {[1/2, 1/4*3^(1/2)], [1/4, 1/4*3^(1/2)], [3/8, 3/8*3^(1/2)]}, {[1/2, 1/4*3^(1/2)], [3/4, 1/4*3^(1/2)], [5/8, 3/8*3^(1/2)]}, {[1/2, 1/4*3^(1/2)], [3/8, 1/8*3^(1/2)], [5/8, 1/8*3^(1/2)]}, {[1/4, 1/4*3^(1/2)], [1/8, 1/8*3^(1/2)], [3/8, 1/8*3^(1/2)]}, {[3/4, 1/4*3^(1/2)], [5/8, 1/8*3^(1/2)], [7/8, 1/8*3^(1/2)]}}

##PROBLEM 3##

#TgC(N): inputs a positive integer N and outputs a natural
#triangulation APPROXIMATING the unit circle, centered at the
#origin, into right-angled triangles of side-length 1/N
TgC:=proc(N) local T, i, j:
    T:={}:
    #Do the first quadrant
    #Replicate for all other quadrants
    for i from 0 to N-1 do
        for j from 0 to floor(sqrt(N^2-i^2))-1 do
            if (i+1)^2+j^2<=N^2 then
                T:=T union {{[i,j]/N, [i,j+1]/N, [i+1, j]/N}}:
                T:=T union {{[i,-j]/N, [i,-j-1]/N, [i+1, -j]/N}}:
                T:=T union {{[-i,j]/N, [-i,j+1]/N, [-i-1, j]/N}}:
                T:=T union {{[-i,-j]/N, [-i,-j-1]/N, [-i-1, -j]/N}}:
            fi:
            if (i+1)^2+(j+1)^2<=N^2 then
                T:=T union {{[i+1,j+1]/N, [i,j+1]/N, [i+1, j]/N}}:
                T:=T union {{[i+1,-j-1]/N, [i,-j-1]/N, [i+1, -j]/N}}:
                T:=T union {{[-i-1,j+1]/N, [-i,j+1]/N, [-i-1, j]/N}}:
                T:=T union {{[-i-1,-j-1]/N, [-i,-j-1]/N, [-i-1, -j]/N}}:
            fi:
        od:
    od:
    return T:
end:

#TgC(2) returns {{[-1, 0], [-1/2, 0], [-1/2, -1/2]}, {[-1, 0], [-1/2, 0], [-1/2, 1/2]}, {[0, -1], [0, -1/2], [-1/2, -1/2]}, {[0, -1], [0, -1/2], [1/2, -1/2]}, {[0, 0], [0, -1/2], [-1/2, 0]}, {[0, 0], [0, -1/2], [1/2, 0]}, {[0, 0], [0, 1/2], [-1/2, 0]}, {[0, 0], [0, 1/2], [1/2, 0]}, {[0, 1], [0, 1/2], [-1/2, 1/2]}, {[0, 1], [0, 1/2], [1/2, 1/2]}, {[0, -1/2], [-1/2, 0], [-1/2, -1/2]}, {[0, -1/2], [1/2, 0], [1/2, -1/2]}, {[0, 1/2], [-1/2, 0], [-1/2, 1/2]}, {[0, 1/2], [1/2, 0], [1/2, 1/2]}, {[1, 0], [1/2, 0], [1/2, -1/2]}, {[1, 0], [1/2, 0], [1/2, 1/2]}}
#TgC(8) returns {{[-1, 0], [-7/8, 0], [-7/8, -1/8]}, {[-1, 0], [-7/8, 0], [-7/8, 1/8]}, {[0, -1], [0, -7/8], [-1/8, -7/8]}, {[0, -1], [0, -7/8], [1/8, -7/8]}, {[0, 0], [0, -1/8], [-1/8, 0]}, {[0, 0], [0, -1/8], [1/8, 0]}, {[0, 0], [0, 1/8], [-1/8, 0]}, {[0, 0], [0, 1/8], [1/8, 0]}, {[0, 1], [0, 7/8], [-1/8, 7/8]}, {[0, 1], [0, 7/8], [1/8, 7/8]}, {[0, -7/8], [0, -3/4], [-1/8, -3/4]}, {[0, -7/8], [0, -3/4], [1/8, -3/4]}, {[0, -7/8], [-1/8, -7/8], [-1/8, -3/4]}, {[0, -7/8], [1/8, -7/8], [1/8, -3/4]}, {[0, -5/8], [0, -3/4], [-1/8, -5/8]}, {[0, -5/8], [0, -3/4], [1/8, -5/8]}, {[0, -5/8], [0, -1/2], [-1/8, -1/2]}, {[0, -5/8], [0, -1/2], [1/8, -1/2]}, {[0, -5/8], [-1/8, -5/8], [-1/8, -1/2]}, {[0, -5/8], [1/8, -5/8], [1/8, -1/2]}, {[0, -3/4], [-1/8, -5/8], [-1/8, -3/4]}, {[0, -3/4], [1/8, -5/8], [1/8, -3/4]}, {[0, -3/8], [0, -1/2], [-1/8, -3/8]}, {[0, -3/8], [0, -1/2], [1/8, -3/8]}, {[0, -3/8], [0, -1/4], [-1/8, -1/4]}, {[0, -3/8], [0, -1/4], [1/8, -1/4]}, {[0, -3/8], [-1/8, -3/8], [-1/8, -1/4]}, {[0, -3/8], [1/8, -3/8], [1/8, -1/4]}, {[0, -1/2], [-1/8, -3/8], [-1/8, -1/2]}, {[0, -1/2], [1/8, -3/8], [1/8, -1/2]}, {[0, -1/4], [0, -1/8], [-1/8, -1/8]}, {[0, -1/4], [0, -1/8], [1/8, -1/8]}, {[0, -1/4], [-1/8, -1/4], [-1/8, -1/8]}, {[0, -1/4], [1/8, -1/4], [1/8, -1/8]}, {[0, -1/8], [-1/8, 0], [-1/8, -1/8]}, {[0, -1/8], [1/8, 0], [1/8, -1/8]}, {[0, 1/2], [0, 3/8], [-1/8, 3/8]}, {[0, 1/2], [0, 3/8], [1/8, 3/8]}, {[0, 1/2], [0, 5/8], [-1/8, 1/2]}, {[0, 1/2], [0, 5/8], [1/8, 1/2]}, {[0, 1/2], [-1/8, 1/2], [-1/8, 3/8]}, {[0, 1/2], [1/8, 1/2], [1/8, 3/8]}, {[0, 1/4], [0, 1/8], [-1/8, 1/8]}, {[0, 1/4], [0, 1/8], [1/8, 1/8]}, {[0, 1/4], [0, 3/8], [-1/8, 1/4]}, {[0, 1/4], [0, 3/8], [1/8, 1/4]}, {[0, 1/4], [-1/8, 1/4], [-1/8, 1/8]}, {[0, 1/4], [1/8, 1/4], [1/8, 1/8]}, {[0, 1/8], [-1/8, 0], [-1/8, 1/8]}, {[0, 1/8], [1/8, 0], [1/8, 1/8]}, {[0, 3/4], [0, 5/8], [-1/8, 5/8]}, {[0, 3/4], [0, 5/8], [1/8, 5/8]}, {[0, 3/4], [0, 7/8], [-1/8, 3/4]}, {[0, 3/4], [0, 7/8], [1/8, 3/4]}, {[0, 3/4], [-1/8, 3/4], [-1/8, 5/8]}, {[0, 3/4], [1/8, 3/4], [1/8, 5/8]}, {[0, 3/8], [-1/8, 1/4], [-1/8, 3/8]}, {[0, 3/8], [1/8, 1/4], [1/8, 3/8]}, {[0, 5/8], [-1/8, 1/2], [-1/8, 5/8]}, {[0, 5/8], [1/8, 1/2], [1/8, 5/8]}, {[0, 7/8], [-1/8, 3/4], [-1/8, 7/8]}, {[0, 7/8], [1/8, 3/4], [1/8, 7/8]}, {[1, 0], [7/8, 0], [7/8, -1/8]}, {[1, 0], [7/8, 0], [7/8, 1/8]}, {[-7/8, 0], [-7/8, -1/8], [-3/4, -1/8]}, {[-7/8, 0], [-7/8, 1/8], [-3/4, 1/8]}, {[-7/8, 0], [-3/4, 0], [-3/4, -1/8]}, {[-7/8, 0], [-3/4, 0], [-3/4, 1/8]}, {[-7/8, -3/8], [-7/8, -1/4], [-3/4, -3/8]}, {[-7/8, -3/8], [-3/4, -3/8], [-3/4, -1/2]}, {[-7/8, -1/4], [-7/8, -1/8], [-3/4, -1/4]}, {[-7/8, -1/4], [-3/4, -3/8], [-3/4, -1/4]}, {[-7/8, -1/8], [-3/4, -1/4], [-3/4, -1/8]}, {[-7/8, 1/4], [-7/8, 1/8], [-3/4, 1/4]}, {[-7/8, 1/4], [-7/8, 3/8], [-3/4, 3/8]}, {[-7/8, 1/4], [-3/4, 1/4], [-3/4, 3/8]}, {[-7/8, 1/8], [-3/4, 1/4], [-3/4, 1/8]}, {[-7/8, 3/8], [-3/4, 1/2], [-3/4, 3/8]}, {[-5/8, 0], [-5/8, -1/8], [-3/4, 0]}, {[-5/8, 0], [-5/8, -1/8], [-1/2, -1/8]}, {[-5/8, 0], [-5/8, 1/8], [-3/4, 0]}, {[-5/8, 0], [-5/8, 1/8], [-1/2, 1/8]}, {[-5/8, 0], [-1/2, 0], [-1/2, -1/8]}, {[-5/8, 0], [-1/2, 0], [-1/2, 1/8]}, {[-5/8, -5/8], [-5/8, -3/4], [-3/4, -5/8]}, {[-5/8, -5/8], [-5/8, -3/4], [-1/2, -3/4]}, {[-5/8, -5/8], [-5/8, -1/2], [-3/4, -1/2]}, {[-5/8, -5/8], [-5/8, -1/2], [-1/2, -5/8]}, {[-5/8, -5/8], [-3/4, -5/8], [-3/4, -1/2]}, {[-5/8, -5/8], [-1/2, -5/8], [-1/2, -3/4]}, {[-5/8, -3/8], [-5/8, -1/2], [-3/4, -3/8]}, {[-5/8, -3/8], [-5/8, -1/2], [-1/2, -1/2]}, {[-5/8, -3/8], [-5/8, -1/4], [-3/4, -1/4]}, {[-5/8, -3/8], [-5/8, -1/4], [-1/2, -3/8]}, {[-5/8, -3/8], [-3/4, -3/8], [-3/4, -1/4]}, {[-5/8, -3/8], [-1/2, -3/8], [-1/2, -1/2]}, {[-5/8, -1/2], [-3/4, -3/8], [-3/4, -1/2]}, {[-5/8, -1/2], [-1/2, -5/8], [-1/2, -1/2]}, {[-5/8, -1/4], [-5/8, -1/8], [-3/4, -1/8]}, {[-5/8, -1/4], [-5/8, -1/8], [-1/2, -1/4]}, {[-5/8, -1/4], [-3/4, -1/4], [-3/4, -1/8]}, {[-5/8, -1/4], [-1/2, -3/8], [-1/2, -1/4]}, {[-5/8, -1/8], [-3/4, 0], [-3/4, -1/8]}, {[-5/8, -1/8], [-1/2, -1/4], [-1/2, -1/8]}, {[-5/8, 1/2], [-5/8, 3/8], [-3/4, 3/8]}, {[-5/8, 1/2], [-5/8, 3/8], [-1/2, 1/2]}, {[-5/8, 1/2], [-5/8, 5/8], [-3/4, 1/2]}, {[-5/8, 1/2], [-5/8, 5/8], [-1/2, 5/8]}, {[-5/8, 1/2], [-3/4, 1/2], [-3/4, 3/8]}, {[-5/8, 1/2], [-1/2, 1/2], [-1/2, 5/8]}, {[-5/8, 1/4], [-5/8, 1/8], [-3/4, 1/8]}, {[-5/8, 1/4], [-5/8, 1/8], [-1/2, 1/4]}, {[-5/8, 1/4], [-5/8, 3/8], [-3/4, 1/4]}, {[-5/8, 1/4], [-5/8, 3/8], [-1/2, 3/8]}, {[-5/8, 1/4], [-3/4, 1/4], [-3/4, 1/8]}, {[-5/8, 1/4], [-1/2, 1/4], [-1/2, 3/8]}, {[-5/8, 1/8], [-3/4, 0], [-3/4, 1/8]}, {[-5/8, 1/8], [-1/2, 1/4], [-1/2, 1/8]}, {[-5/8, 3/4], [-5/8, 5/8], [-3/4, 5/8]}, {[-5/8, 3/4], [-5/8, 5/8], [-1/2, 3/4]}, {[-5/8, 3/8], [-3/4, 1/4], [-3/4, 3/8]}, {[-5/8, 3/8], [-1/2, 1/2], [-1/2, 3/8]}, {[-5/8, 5/8], [-3/4, 1/2], [-3/4, 5/8]}, {[-5/8, 5/8], [-1/2, 3/4], [-1/2, 5/8]}, {[-3/8, 0], [-3/8, -1/8], [-1/2, 0]}, {[-3/8, 0], [-3/8, -1/8], [-1/4, -1/8]}, {[-3/8, 0], [-3/8, 1/8], [-1/2, 0]}, {[-3/8, 0], [-3/8, 1/8], [-1/4, 1/8]}, {[-3/8, 0], [-1/4, 0], [-1/4, -1/8]}, {[-3/8, 0], [-1/4, 0], [-1/4, 1/8]}, {[-3/8, -7/8], [-3/8, -3/4], [-1/2, -3/4]}, {[-3/8, -7/8], [-3/8, -3/4], [-1/4, -7/8]}, {[-3/8, -5/8], [-3/8, -3/4], [-1/2, -5/8]}, {[-3/8, -5/8], [-3/8, -3/4], [-1/4, -3/4]}, {[-3/8, -5/8], [-3/8, -1/2], [-1/2, -1/2]}, {[-3/8, -5/8], [-3/8, -1/2], [-1/4, -5/8]}, {[-3/8, -5/8], [-1/2, -5/8], [-1/2, -1/2]}, {[-3/8, -5/8], [-1/4, -5/8], [-1/4, -3/4]}, {[-3/8, -3/4], [-1/2, -5/8], [-1/2, -3/4]}, {[-3/8, -3/4], [-1/4, -7/8], [-1/4, -3/4]}, {[-3/8, -3/8], [-3/8, -1/2], [-1/2, -3/8]}, {[-3/8, -3/8], [-3/8, -1/2], [-1/4, -1/2]}, {[-3/8, -3/8], [-3/8, -1/4], [-1/2, -1/4]}, {[-3/8, -3/8], [-3/8, -1/4], [-1/4, -3/8]}, {[-3/8, -3/8], [-1/2, -3/8], [-1/2, -1/4]}, {[-3/8, -3/8], [-1/4, -3/8], [-1/4, -1/2]}, {[-3/8, -1/2], [-1/2, -3/8], [-1/2, -1/2]}, {[-3/8, -1/2], [-1/4, -5/8], [-1/4, -1/2]}, {[-3/8, -1/4], [-3/8, -1/8], [-1/2, -1/8]}, {[-3/8, -1/4], [-3/8, -1/8], [-1/4, -1/4]}, {[-3/8, -1/4], [-1/2, -1/4], [-1/2, -1/8]}, {[-3/8, -1/4], [-1/4, -3/8], [-1/4, -1/4]}, {[-3/8, -1/8], [-1/2, 0], [-1/2, -1/8]}, {[-3/8, -1/8], [-1/4, -1/4], [-1/4, -1/8]}, {[-3/8, 1/2], [-3/8, 3/8], [-1/2, 3/8]}, {[-3/8, 1/2], [-3/8, 3/8], [-1/4, 1/2]}, {[-3/8, 1/2], [-3/8, 5/8], [-1/2, 1/2]}, {[-3/8, 1/2], [-3/8, 5/8], [-1/4, 5/8]}, {[-3/8, 1/2], [-1/2, 1/2], [-1/2, 3/8]}, {[-3/8, 1/2], [-1/4, 1/2], [-1/4, 5/8]}, {[-3/8, 1/4], [-3/8, 1/8], [-1/2, 1/8]}, {[-3/8, 1/4], [-3/8, 1/8], [-1/4, 1/4]}, {[-3/8, 1/4], [-3/8, 3/8], [-1/2, 1/4]}, {[-3/8, 1/4], [-3/8, 3/8], [-1/4, 3/8]}, {[-3/8, 1/4], [-1/2, 1/4], [-1/2, 1/8]}, {[-3/8, 1/4], [-1/4, 1/4], [-1/4, 3/8]}, {[-3/8, 1/8], [-1/2, 0], [-1/2, 1/8]}, {[-3/8, 1/8], [-1/4, 1/4], [-1/4, 1/8]}, {[-3/8, 3/4], [-3/8, 5/8], [-1/2, 5/8]}, {[-3/8, 3/4], [-3/8, 5/8], [-1/4, 3/4]}, {[-3/8, 3/4], [-3/8, 7/8], [-1/2, 3/4]}, {[-3/8, 3/4], [-3/8, 7/8], [-1/4, 7/8]}, {[-3/8, 3/4], [-1/2, 3/4], [-1/2, 5/8]}, {[-3/8, 3/4], [-1/4, 3/4], [-1/4, 7/8]}, {[-3/8, 3/8], [-1/2, 1/4], [-1/2, 3/8]}, {[-3/8, 3/8], [-1/4, 1/2], [-1/4, 3/8]}, {[-3/8, 5/8], [-1/2, 1/2], [-1/2, 5/8]}, {[-3/8, 5/8], [-1/4, 3/4], [-1/4, 5/8]}, {[-1/4, 0], [-1/4, -1/8], [-1/8, -1/8]}, {[-1/4, 0], [-1/4, 1/8], [-1/8, 1/8]}, {[-1/4, 0], [-1/8, 0], [-1/8, -1/8]}, {[-1/4, 0], [-1/8, 0], [-1/8, 1/8]}, {[-1/4, -7/8], [-1/4, -3/4], [-1/8, -7/8]}, {[-1/4, -5/8], [-1/4, -3/4], [-1/8, -3/4]}, {[-1/4, -5/8], [-1/4, -1/2], [-1/8, -5/8]}, {[-1/4, -5/8], [-1/8, -5/8], [-1/8, -3/4]}, {[-1/4, -3/4], [-1/8, -7/8], [-1/8, -3/4]}, {[-1/4, -3/8], [-1/4, -1/2], [-1/8, -1/2]}, {[-1/4, -3/8], [-1/4, -1/4], [-1/8, -3/8]}, {[-1/4, -3/8], [-1/8, -3/8], [-1/8, -1/2]}, {[-1/4, -1/2], [-1/8, -5/8], [-1/8, -1/2]}, {[-1/4, -1/4], [-1/4, -1/8], [-1/8, -1/4]}, {[-1/4, -1/4], [-1/8, -3/8], [-1/8, -1/4]}, {[-1/4, -1/8], [-1/8, -1/4], [-1/8, -1/8]}, {[-1/4, 1/2], [-1/4, 3/8], [-1/8, 1/2]}, {[-1/4, 1/2], [-1/4, 5/8], [-1/8, 5/8]}, {[-1/4, 1/2], [-1/8, 1/2], [-1/8, 5/8]}, {[-1/4, 1/4], [-1/4, 1/8], [-1/8, 1/4]}, {[-1/4, 1/4], [-1/4, 3/8], [-1/8, 3/8]}, {[-1/4, 1/4], [-1/8, 1/4], [-1/8, 3/8]}, {[-1/4, 1/8], [-1/8, 1/4], [-1/8, 1/8]}, {[-1/4, 3/4], [-1/4, 5/8], [-1/8, 3/4]}, {[-1/4, 3/4], [-1/4, 7/8], [-1/8, 7/8]}, {[-1/4, 3/4], [-1/8, 3/4], [-1/8, 7/8]}, {[-1/4, 3/8], [-1/8, 1/2], [-1/8, 3/8]}, {[-1/4, 5/8], [-1/8, 3/4], [-1/8, 5/8]}, {[1/2, 0], [1/2, -1/8], [3/8, -1/8]}, {[1/2, 0], [1/2, -1/8], [5/8, 0]}, {[1/2, 0], [1/2, 1/8], [3/8, 1/8]}, {[1/2, 0], [1/2, 1/8], [5/8, 0]}, {[1/2, 0], [3/8, 0], [3/8, -1/8]}, {[1/2, 0], [3/8, 0], [3/8, 1/8]}, {[1/2, -5/8], [1/2, -3/4], [3/8, -3/4]}, {[1/2, -5/8], [1/2, -3/4], [5/8, -5/8]}, {[1/2, -5/8], [1/2, -1/2], [3/8, -5/8]}, {[1/2, -5/8], [1/2, -1/2], [5/8, -1/2]}, {[1/2, -5/8], [3/8, -5/8], [3/8, -3/4]}, {[1/2, -5/8], [5/8, -5/8], [5/8, -1/2]}, {[1/2, -3/4], [3/8, -7/8], [3/8, -3/4]}, {[1/2, -3/4], [5/8, -5/8], [5/8, -3/4]}, {[1/2, -3/8], [1/2, -1/2], [3/8, -1/2]}, {[1/2, -3/8], [1/2, -1/2], [5/8, -3/8]}, {[1/2, -3/8], [1/2, -1/4], [3/8, -3/8]}, {[1/2, -3/8], [1/2, -1/4], [5/8, -1/4]}, {[1/2, -3/8], [3/8, -3/8], [3/8, -1/2]}, {[1/2, -3/8], [5/8, -3/8], [5/8, -1/4]}, {[1/2, -1/2], [3/8, -5/8], [3/8, -1/2]}, {[1/2, -1/2], [5/8, -3/8], [5/8, -1/2]}, {[1/2, -1/4], [1/2, -1/8], [3/8, -1/4]}, {[1/2, -1/4], [1/2, -1/8], [5/8, -1/8]}, {[1/2, -1/4], [3/8, -3/8], [3/8, -1/4]}, {[1/2, -1/4], [5/8, -1/4], [5/8, -1/8]}, {[1/2, -1/8], [3/8, -1/4], [3/8, -1/8]}, {[1/2, -1/8], [5/8, 0], [5/8, -1/8]}, {[1/2, 1/2], [1/2, 3/8], [3/8, 1/2]}, {[1/2, 1/2], [1/2, 3/8], [5/8, 3/8]}, {[1/2, 1/2], [1/2, 5/8], [3/8, 5/8]}, {[1/2, 1/2], [1/2, 5/8], [5/8, 1/2]}, {[1/2, 1/2], [3/8, 1/2], [3/8, 5/8]}, {[1/2, 1/2], [5/8, 1/2], [5/8, 3/8]}, {[1/2, 1/4], [1/2, 1/8], [3/8, 1/4]}, {[1/2, 1/4], [1/2, 1/8], [5/8, 1/8]}, {[1/2, 1/4], [1/2, 3/8], [3/8, 3/8]}, {[1/2, 1/4], [1/2, 3/8], [5/8, 1/4]}, {[1/2, 1/4], [3/8, 1/4], [3/8, 3/8]}, {[1/2, 1/4], [5/8, 1/4], [5/8, 1/8]}, {[1/2, 1/8], [3/8, 1/4], [3/8, 1/8]}, {[1/2, 1/8], [5/8, 0], [5/8, 1/8]}, {[1/2, 3/4], [1/2, 5/8], [3/8, 3/4]}, {[1/2, 3/4], [1/2, 5/8], [5/8, 5/8]}, {[1/2, 3/4], [3/8, 3/4], [3/8, 7/8]}, {[1/2, 3/4], [5/8, 3/4], [5/8, 5/8]}, {[1/2, 3/8], [3/8, 1/2], [3/8, 3/8]}, {[1/2, 3/8], [5/8, 1/4], [5/8, 3/8]}, {[1/2, 5/8], [3/8, 3/4], [3/8, 5/8]}, {[1/2, 5/8], [5/8, 1/2], [5/8, 5/8]}, {[1/4, 0], [1/4, -1/8], [1/8, -1/8]}, {[1/4, 0], [1/4, -1/8], [3/8, 0]}, {[1/4, 0], [1/4, 1/8], [1/8, 1/8]}, {[1/4, 0], [1/4, 1/8], [3/8, 0]}, {[1/4, 0], [1/8, 0], [1/8, -1/8]}, {[1/4, 0], [1/8, 0], [1/8, 1/8]}, {[1/4, -7/8], [1/4, -3/4], [1/8, -7/8]}, {[1/4, -7/8], [1/4, -3/4], [3/8, -3/4]}, {[1/4, -7/8], [3/8, -7/8], [3/8, -3/4]}, {[1/4, -5/8], [1/4, -3/4], [1/8, -3/4]}, {[1/4, -5/8], [1/4, -3/4], [3/8, -5/8]}, {[1/4, -5/8], [1/4, -1/2], [1/8, -5/8]}, {[1/4, -5/8], [1/4, -1/2], [3/8, -1/2]}, {[1/4, -5/8], [1/8, -5/8], [1/8, -3/4]}, {[1/4, -5/8], [3/8, -5/8], [3/8, -1/2]}, {[1/4, -3/4], [1/8, -7/8], [1/8, -3/4]}, {[1/4, -3/4], [3/8, -5/8], [3/8, -3/4]}, {[1/4, -3/8], [1/4, -1/2], [1/8, -1/2]}, {[1/4, -3/8], [1/4, -1/2], [3/8, -3/8]}, {[1/4, -3/8], [1/4, -1/4], [1/8, -3/8]}, {[1/4, -3/8], [1/4, -1/4], [3/8, -1/4]}, {[1/4, -3/8], [1/8, -3/8], [1/8, -1/2]}, {[1/4, -3/8], [3/8, -3/8], [3/8, -1/4]}, {[1/4, -1/2], [1/8, -5/8], [1/8, -1/2]}, {[1/4, -1/2], [3/8, -3/8], [3/8, -1/2]}, {[1/4, -1/4], [1/4, -1/8], [1/8, -1/4]}, {[1/4, -1/4], [1/4, -1/8], [3/8, -1/8]}, {[1/4, -1/4], [1/8, -3/8], [1/8, -1/4]}, {[1/4, -1/4], [3/8, -1/4], [3/8, -1/8]}, {[1/4, -1/8], [1/8, -1/4], [1/8, -1/8]}, {[1/4, -1/8], [3/8, 0], [3/8, -1/8]}, {[1/4, 1/2], [1/4, 3/8], [1/8, 1/2]}, {[1/4, 1/2], [1/4, 3/8], [3/8, 3/8]}, {[1/4, 1/2], [1/4, 5/8], [1/8, 5/8]}, {[1/4, 1/2], [1/4, 5/8], [3/8, 1/2]}, {[1/4, 1/2], [1/8, 1/2], [1/8, 5/8]}, {[1/4, 1/2], [3/8, 1/2], [3/8, 3/8]}, {[1/4, 1/4], [1/4, 1/8], [1/8, 1/4]}, {[1/4, 1/4], [1/4, 1/8], [3/8, 1/8]}, {[1/4, 1/4], [1/4, 3/8], [1/8, 3/8]}, {[1/4, 1/4], [1/4, 3/8], [3/8, 1/4]}, {[1/4, 1/4], [1/8, 1/4], [1/8, 3/8]}, {[1/4, 1/4], [3/8, 1/4], [3/8, 1/8]}, {[1/4, 1/8], [1/8, 1/4], [1/8, 1/8]}, {[1/4, 1/8], [3/8, 0], [3/8, 1/8]}, {[1/4, 3/4], [1/4, 5/8], [1/8, 3/4]}, {[1/4, 3/4], [1/4, 5/8], [3/8, 5/8]}, {[1/4, 3/4], [1/4, 7/8], [1/8, 7/8]}, {[1/4, 3/4], [1/4, 7/8], [3/8, 3/4]}, {[1/4, 3/4], [1/8, 3/4], [1/8, 7/8]}, {[1/4, 3/4], [3/8, 3/4], [3/8, 5/8]}, {[1/4, 3/8], [1/8, 1/2], [1/8, 3/8]}, {[1/4, 3/8], [3/8, 1/4], [3/8, 3/8]}, {[1/4, 5/8], [1/8, 3/4], [1/8, 5/8]}, {[1/4, 5/8], [3/8, 1/2], [3/8, 5/8]}, {[1/4, 7/8], [3/8, 3/4], [3/8, 7/8]}, {[3/4, 0], [3/4, -1/8], [5/8, -1/8]}, {[3/4, 0], [3/4, -1/8], [7/8, 0]}, {[3/4, 0], [3/4, 1/8], [5/8, 1/8]}, {[3/4, 0], [3/4, 1/8], [7/8, 0]}, {[3/4, 0], [5/8, 0], [5/8, -1/8]}, {[3/4, 0], [5/8, 0], [5/8, 1/8]}, {[3/4, -5/8], [3/4, -1/2], [5/8, -5/8]}, {[3/4, -5/8], [5/8, -5/8], [5/8, -3/4]}, {[3/4, -3/8], [3/4, -1/2], [5/8, -1/2]}, {[3/4, -3/8], [3/4, -1/2], [7/8, -3/8]}, {[3/4, -3/8], [3/4, -1/4], [5/8, -3/8]}, {[3/4, -3/8], [3/4, -1/4], [7/8, -1/4]}, {[3/4, -3/8], [5/8, -3/8], [5/8, -1/2]}, {[3/4, -3/8], [7/8, -3/8], [7/8, -1/4]}, {[3/4, -1/2], [5/8, -5/8], [5/8, -1/2]}, {[3/4, -1/4], [3/4, -1/8], [5/8, -1/4]}, {[3/4, -1/4], [3/4, -1/8], [7/8, -1/8]}, {[3/4, -1/4], [5/8, -3/8], [5/8, -1/4]}, {[3/4, -1/4], [7/8, -1/4], [7/8, -1/8]}, {[3/4, -1/8], [5/8, -1/4], [5/8, -1/8]}, {[3/4, -1/8], [7/8, 0], [7/8, -1/8]}, {[3/4, 1/2], [3/4, 3/8], [5/8, 1/2]}, {[3/4, 1/2], [3/4, 3/8], [7/8, 3/8]}, {[3/4, 1/2], [3/4, 5/8], [5/8, 5/8]}, {[3/4, 1/2], [5/8, 1/2], [5/8, 5/8]}, {[3/4, 1/4], [3/4, 1/8], [5/8, 1/4]}, {[3/4, 1/4], [3/4, 1/8], [7/8, 1/8]}, {[3/4, 1/4], [3/4, 3/8], [5/8, 3/8]}, {[3/4, 1/4], [3/4, 3/8], [7/8, 1/4]}, {[3/4, 1/4], [5/8, 1/4], [5/8, 3/8]}, {[3/4, 1/4], [7/8, 1/4], [7/8, 1/8]}, {[3/4, 1/8], [5/8, 1/4], [5/8, 1/8]}, {[3/4, 1/8], [7/8, 0], [7/8, 1/8]}, {[3/4, 3/8], [5/8, 1/2], [5/8, 3/8]}, {[3/4, 3/8], [7/8, 1/4], [7/8, 3/8]}, {[3/4, 5/8], [5/8, 3/4], [5/8, 5/8]}}