milieu

Construis le solide proposé en utilisant
les points qui sont déjà placés sur les 
arêtes du cube.

Afficher/Cacher le cube

A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B = Point(c)
n = 4 (slider from 3 to 100, step 1)
a: 360 / n
l: (2 * sin(π / n))
d = Circle(B, l)
C = Intersect(c, d, 1)
b, D, E, F, G, H, I, faceBCDE, faceBEIF, faceBCGF, faceCDHG, faceDEIH, faceFGHI, arêteBE, arêteBC, arêteCD, arêteDE, arêteBF, arêteEI, arêteFI, arêteFG, arêteCG, arêteGH, arêteDH, arêteHI = Cube(B, C, xOyPlane)
J = Midpoint(arêteFI)
K = Midpoint(arêteFG)
L = Midpoint(arêteGH)
M = Midpoint(arêteHI)
N = Midpoint(arêteDH)
O = Midpoint(arêteEI)
P = Midpoint(arêteBE)
Q = Midpoint(arêteBF)
R = Midpoint(arêteBC)
S = Midpoint(arêteCG)
T = Midpoint(arêteDE)
U = Midpoint(arêteCD)
e = true
V, W = partage_en(G, L)
Z, A_1 = partage_en(L, H)
B_1, C_1 = partage_en(H, M)
D_1, E_1 = partage_en(M, I)
F_1, G_1 = partage_en(I, J)
H_1, I_1 = partage_en(J, F)
J_1, K_1 = partage_en(F, K)
L_1, M_1 = partage_en(K, G)
N_1, O_1 = partage_en(G, S)
P_1, Q_1 = partage_en(S, C)
R_1, S_1 = partage_en(C, R)
T_1, U_1 = partage_en(R, B)
V_1, W_1 = partage_en(B, Q)
Z_1, A_2 = partage_en(Q, F)
B_2, C_2 = partage_en(B, P)
D_2, E_2 = partage_en(P, E)
F_2, G_2 = partage_en(E, T)
H_2, I_2 = partage_en(T, D)
J_2, K_2 = partage_en(D, U)
L_2, M_2 = partage_en(U, C)
N_2, O_2 = partage_en(O, E)
P_2, Q_2 = partage_en(N, D)
R_2, S_2 = partage_en(H, N)
T_2, U_2 = partage_en(O, I)
V_2 = (-3, -1)
W_2 = (3, -1)
f = Segment(V_2, W_2)
Z_2 = (-3, 5)
g = Segment(V_2, Z_2)
A_3 = (3, 5)
h = Segment(Z_2, A_3)
i = Segment(A_3, W_2)
B_3 = (6, 1)
j = Segment(W_2, B_3)
C_3 = (6, 7)
k = Segment(A_3, C_3)
D_3 = (0, 7)
m = Segment(Z_2, D_3)
p = Segment(D_3, C_3)
q = Segment(C_3, B_3)
E_3 = Midpoint(h)
F_3 = Midpoint(f)
G_3 = Midpoint(j)
H_3 = Midpoint(k)
I_3 = Midpoint(q)
J_3 = Midpoint(p)
K_3 = Midpoint(m)
L_3 = Midpoint(g)
M_3, N_3 = partage_en(H_3, A_3)
O_3, P_3 = partage_en(H_3, C_3)
Q_3, R_3 = partage_en(C_3, I_3)
S_3, T_3 = partage_en(I_3, B_3)
U_3, V_3 = partage_en(B_3, G_3)
W_3, Z_3 = partage_en(G_3, W_2)
A_4, B_4 = partage_en(W_2, F_3)
C_4, D_4 = partage_en(F_3, V_2)
E_4, F_4 = partage_en(V_2, L_3)
G_4, H_4 = partage_en(L_3, Z_2)
I_4, J_4 = partage_en(Z_2, E_3)
K_4, L_4 = partage_en(E_3, A_3)
M_4, N_4 = partage_en(Z_2, K_3)
O_4, P_4 = partage_en(K_3, D_3)
Q_4, R_4 = partage_en(D_3, J_3)
S_4, T_4 = partage_en(J_3, C_3)
U_4 = (0, 1)
r = Segment(D_3, U_4)
s = Segment(U_4, V_2)
t = Segment(U_4, B_3)
V_4 = Midpoint(r)
W_4 = Midpoint(s)
Z_4 = Midpoint(t)
A_5, B_5 = partage_en(D_3, V_4)
C_5, D_5 = partage_en(U_4, W_4)
E_5, F_5 = partage_en(W_4, V_2)
G_5, H_5 = partage_en(U_4, Z_4)
I_5, J_5 = partage_en(Z_4, B_3)
K_5, L_5 = partage_en(V_4, U_4)
M_5 = Midpoint(i)
N_5, O_5 = partage_en(A_3, M_5)
P_5, Q_5 = partage_en(M_5, W_2)
R_5 = Intersect(m, p)
T_5 = Intersect(f, g)
V_5 = Intersect(j, q)
o = true
a_1 = Segment(E_3, F_3)
b_1 = Segment(H_4, N_5)
c_1 = Segment(E_4, Q_5)
d_1 = Segment(L_4, A_4)
e_1 = Segment(L_3, M_5)
f_1 = Segment(I_4, D_4)
h_1 = Segment(P_4, P_3)
i_1 = Segment(T_4, L_4)
g_1 = Segment(M_4, N_3)
j_1 = Segment(Q_4, I_4)
k_1 = Segment(K_3, H_3)
l_1 = Segment(J_3, E_3)
m_1 = Segment(N_3, Z_3)
n_1 = Segment(Q_5, T_3)
p_1 = Segment(M_5, I_3)
q_1 = Segment(N_5, Q_3)
r_1 = Segment(H_3, G_3)
s_1 = Segment(P_3, U_3)
S_5 = Intersect(e_1, f_1)
U_5 = Intersect(a_1, c_1)
W_5 = Intersect(d_1, e_1)
Z_5 = Intersect(m_1, p_1)
A_6 = Intersect(n_1, r_1)
B_6 = Intersect(p_1, s_1)
C_6 = Intersect(q_1, r_1)
D_6 = Intersect(i_1, k_1)
E_6 = Intersect(h_1, l_1)
F_6 = Intersect(g_1, l_1)
G_6 = Intersect(j_1, k_1)
poly1, e_6, g_6, f_6, d_6 = Polygon(E_6, G_6, F_6, D_6)
poly2, v_4, w_5, u_5, s_5 = Polygon(V_4, W_5, U_5, S_5)
poly3, z_5, c_6, b_6, a_6 = Polygon(Z_5, C_6, B_6, A_6)
poly4, f_2, v_1, w_1, z_1, c_2, d_2 = Polygon(F_6, V_4, W_5, Z_5, C_6, D_6)
t_1 = Segment(J_5, A_4)
a_2 = Segment(F_3, Z_4)
b_2 = Segment(W_4, G_3)
e_2 = Segment(F_5, Z_3)
g_2 = Segment(D_4, G_5)
H_6 = Intersect(c_1, b_2)
I_6 = Intersect(c_1, b_2)
J_6 = Intersect(c_1, b_2)
K_6 = Intersect(g_2, c_1)
L_6 = Intersect(g_2, a_2)
M_6 = Intersect(a_2, e_2)
N_6 = Intersect(m_1, t_1)
h_2 = Segment(C_5, U_3)
O_6 = Intersect(a_2, h_2)
poly5, w_2, z_2, a_3, n_6, m_6, u_1 = Polygon(W_5, Z_5, A_6, N_6, M_6, U_5)
i_2 = Segment(H_4, A_5)
j_2 = Segment(L_3, V_4)
k_2 = Segment(M_4, F_5)
P_6 = Intersect(j_2, k_2)
l_2 = Segment(K_3, W_4)
Q_6 = Intersect(h, i_2)
poly6, f_3, g_3, q_6, p_6, s_2, v_2 = Polygon(F_6, G_6, Q_6, P_6, S_5, V_4)
m_2 = Segment(E_4, L_5)
R_6 = Intersect(l_2, m_2)
poly7, p_2, s_3, u_2, m_3, k_6, r_6 = Polygon(P_6, S_5, U_5, M_6, K_6, R_6)
n_2 = Segment(B_3, A_6)
S_6 = Intersect(f, g)
T_6 = Point(k_6)
q_2 = Segment(S_6, T_6)
U_6 = Intersect(m, p)
V_6 = Point(e_6)
r_2 = Segment(U_6, V_6)

Tool: partage_en_3_3d (command partage_en)
partage_en[ <Point>, <Point> ]
Input: A, B
Output: C, D

C: (x(B) / 3 + (2 * x(A) / 3), y(B) / 3 + (2 * y(A) / 3), z(B) / 3 + (2 * z(A) / 3))
D: ((2 * x(B) / 3) + x(A) / 3, (2 * y(B) / 3) + y(A) / 3, (2 * z(B) / 3) + z(A) / 3)