Aff. sec_u

Aff. plan_u

Aff. sec_v

Aff. plan_v

Aff. sec_w

Aff. plan_w

aff. sommets

Aff. som. sec_u

Aff. som. sec_v

Aff. som. sec_w

Aff. d_{v,w} et M_u et N_u

Aff. d_{w,u} et M_v et N_v

Aff. d_{u,v} et M_w et N_w

Aff. plan_{v,w}

Aff. plan_{w,u}

Aff. plan_{u,v}

dec_u = 2.9 (slider from -5 to 5, step 0.1)
l_v = 10 (slider from 0 to 10, step 0.5)
dep = 3
A = (8, 1)
l_u = 6 (slider from 0 to 10, step 0.5)
θ = 2.356194490192345 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
k_3: {0, 0, 1}
j_3: {0, 1, 0}
i_3: {1, 0, 0}
O_3: {0, 0, 0}
O: (Element[O_3, 1], Element[O_3, 2])
φ_m = 1.8151424220741026 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
φ: φ_m - 90°
P: {(-sin(θ)), cos(θ), 0, ((-cos(θ)) * sin(φ)), ((-sin(θ)) * sin(φ)), cos(φ), (cos(θ) * cos(φ)), (sin(θ) * cos(φ)), sin(φ)}
w = Vector(O, ((Element[P, 1] * Element[k_3, 1]) + (Element[P, 2] * Element[k_3, 2]) + (Element[P, 3] * Element[j_3, 3]), (Element[P, 4] * Element[k_3, 1]) + (Element[P, 5] * Element[k_3, 2]) + (Element[P, 6] * Element[k_3, 3])))
u = Vector(O, ((Element[P, 1] * Element[i_3, 1]) + (Element[P, 2] * Element[i_3, 2]) + (Element[P, 3] * Element[i_3, 3]), (Element[P, 4] * Element[i_3, 1]) + (Element[P, 5] * Element[i_3, 2]) + (Element[P, 6] * Element[i_3, 3])))
B: A + (l_u * u)
B_u: B + (dec_u * u)
v = Vector(O, ((Element[P, 1] * Element[j_3, 1]) + (Element[P, 2] * Element[j_3, 2]) + (Element[P, 3] * Element[j_3, 3]), (Element[P, 4] * Element[j_3, 1]) + (Element[P, 5] * Element[j_3, 2]) + (Element[P, 6] * Element[j_3, 3])))
C: B + (l_v * v)
l_w = 8.5 (slider from 0 to 10, step 0.5)
H: C + (l_w * w)
H_u: H + (dec_u * u)
dec_v = 2
G: B + (l_w * w)
i = Vector(O, (Element[i_3, 1], Element[i_3, 2]))
j = Vector(O, (Element[j_3, 1], Element[j_3, 2]))
coefEq: {1, 0, 1 / sin(φ)^(2)}
Eq: (Element[coefEq, 1] * x^(2)) + ((Element[coefEq, 2] * x) * y) + (Element[coefEq, 3] * y^(2)) = 1
coefMer_0: {(Element[P, 6]^(2) + Element[P, 4]^(2)) / ((Element[P, 1] * Element[P, 6]) - (Element[P, 4] * Element[P, 3]))^(2), (-2 * ((Element[P, 3] * Element[P, 6]) + (Element[P, 4] * Element[P, 1])) / ((Element[P, 1] * Element[P, 6]) - (Element[P, 4] * Element[P, 3]))^(2)), (Element[P, 3]^(2) + Element[P, 1]^(2)) / ((Element[P, 1] * Element[P, 6]) - (Element[P, 4] * Element[P, 3]))^(2)}
Mer_0: (Element[coefMer_0, 1] * x^(2)) + ((Element[coefMer_0, 2] * x) * y) + (Element[coefMer_0, 3] * y^(2)) = 1
coefMer_{90}: {(Element[P, 6]^(2) + Element[P, 5]^(2)) / ((Element[P, 2] * Element[P, 6]) - (Element[P, 5] * Element[P, 3]))^(2), (-2 * ((Element[P, 3] * Element[P, 6]) + (Element[P, 5] * Element[P, 2])) / ((Element[P, 2] * Element[P, 6]) - (Element[P, 5] * Element[P, 3]))^(2)), (Element[P, 3]^(2) + Element[P, 2]^(2)) / ((Element[P, 2] * Element[P, 6]) - (Element[P, 5] * Element[P, 3]))^(2)}
Mer_{90}: (Element[coefMer_{90}, 1] * x^(2)) + ((Element[coefMer_{90}, 2] * x) * y) + (Element[coefMer_{90}, 3] * y^(2)) = 1
D: A + (l_v * v)
E: D + (l_w * w)
F: A + (l_w * w)
svis_{AB} = Segment(A, B)
scac_{BC} = Segment(B, C)
scac_{CD} = Segment(C, D)
scac_{DA} = Segment(D, A)
scac_{EF} = Segment(E, F)
scac_{FG} = Segment(F, G)
scac_{GH} = Segment(G, H)
scac_{HE} = Segment(H, E)
scac_{AF} = Segment(A, F)
scac_{BG} = Segment(B, G)
scac_{CH} = Segment(C, H)
scac_{DE} = Segment(D, E)
scac_{AB} = Segment(A, B)
svis_{DA} = Segment(D, A)
svis_{BC} = Segment(B, C)
svis_{CD} = Segment(C, D)
svis_{AF} = Segment(A, F)
svis_{BG} = Segment(B, G)
svis_{CH} = Segment(C, H)
svis_{DE} = Segment(D, E)
svis_{FG} = Segment(F, G)
svis_{GH} = Segment(G, H)
svis_{HE} = Segment(H, E)
svis_{EF} = Segment(E, F)
dec_w = 2
affsec_u = false
affplan_u = true
affsec_v = false
affplan_v = true
affsec_w = false
affplan_w = true
affsom = false
affsomsec_u = false
affsomsec_v = false
affsomsec_w = false
affdroite_{v,w} = false
affdroite_{w,u} = false
affdroite_{u,v} = false
C_u: C + (dec_u * u)
G_u: G + (dec_u * u)
P_{0,1}: B_u - (dep * v) - (dep * w)
P_{0,2}: C_u + (dep * v) - (dep * w)
P_{0,4}: G_u - (dep * v) + (dep * w)
P_{0,3}: H_u + (dep * v) + (dep * w)
Plan_{v,w}, p_{0,1}, p_{0,2}, p_{0,3}, p_{0,4} = Polygon(P_{0,1}, P_{0,2}, P_{0,3}, P_{0,4})
N_u = Point(Plan_{v,w})
M_u = Point(Plan_{v,w})
d_{v,w} = Segment(M_u, N_u)
s_{BuCu} = Segment(B_u, C_u)
s_{CuHu} = Segment(C_u, H_u)
s_{HuGu} = Segment(H_u, G_u)
s_{GuBu} = Segment(G_u, B_u)
P_u = Intersect(d_{v,w}, s_{BuCu})
Q_u = Intersect(d_{v,w}, s_{CuHu})
R_u = Intersect(d_{v,w}, s_{HuGu})
S_u = Intersect(d_{v,w}, s_{GuBu})
P_1: P_u - (dec_u * u)
Q_1: Q_u - (dec_u * u)
R_1: R_u - (dec_u * u)
S_1: S_u - (dec_u * u)
P_2: P_u - ((dec_u + l_u) * u)
Q_2: Q_u - ((dec_u + l_u) * u)
R_2: R_u - ((dec_u + l_u) * u)
S_2: S_u - ((dec_u + l_u) * u)
section_{u,1}, α_{u,1,1}, α_{u,1,2}, α_{u,1,3}, α_{u,1,4} = Polygon(P_1, Q_1, Q_2, P_2)
section_{u,2}, α_{u,2,1}, α_{u,2,2}, α_{u,2,3}, α_{u,2,4} = Polygon(P_1, R_1, R_2, P_2)
section_{u,3}, α_{u,3,1}, α_{u,3,2}, α_{u,3,3}, α_{u,3,4} = Polygon(P_1, S_1, S_2, P_2)
section_{u,4}, α_{u,4,1}, α_{u,4,2}, α_{u,4,3}, α_{u,4,4} = Polygon(Q_1, R_1, R_2, Q_2)
section_{u,5}, α_{u,5,1}, α_{u,5,2}, α_{u,5,3}, α_{u,5,4} = Polygon(Q_1, S_1, S_2, Q_2)
section_{u,6}, α_{u,6,1}, α_{u,6,2}, α_{u,6,3}, α_{u,6,4} = Polygon(R_1, S_1, S_2, R_2)
scac_{P1Q1} = Segment(P_1, Q_1)
svis_{P1Q1} = Segment(P_1, Q_1)
scac_{Q1Q2} = Segment(Q_1, Q_2)
svis_{Q1Q2} = Segment(Q_1, Q_2)
scac_{Q2P2} = Segment(Q_2, P_2)
svis_{Q2P2} = Segment(Q_2, P_2)
scac_{P2P1} = Segment(P_2, P_1)
svis_{P2P1} = Segment(P_2, P_1)
scac_{P1R1} = Segment(P_1, R_1)
svis_{P1R1} = Segment(P_1, R_1)
scac_{R1R2} = Segment(R_1, R_2)
svis_{R1R2} = Segment(R_1, R_2)
scac_{R2P2} = Segment(R_2, P_2)
svis_{R2P2} = Segment(R_2, P_2)
scac_{P1S1} = Segment(P_1, S_1)
svis_{P1S1} = Segment(P_1, S_1)
scac_{S1S2} = Segment(S_1, S_2)
svis_{S1S2} = Segment(S_1, S_2)
scac_{S2P2} = Segment(S_2, P_2)
svis_{S2P2} = Segment(S_2, P_2)
scac_{Q1R1} = Segment(Q_1, R_1)
svis_{Q1R1} = Segment(Q_1, R_1)
scac_{R2Q2} = Segment(R_2, Q_2)
svis_{R2Q2} = Segment(R_2, Q_2)
scac_{Q1S1} = Segment(Q_1, S_1)
svis_{Q1S1} = Segment(Q_1, S_1)
scac_{S2Q2} = Segment(S_2, Q_2)
svis_{S2Q2} = Segment(S_2, Q_2)
scac_{R1S1} = Segment(R_1, S_1)
svis_{R1S1} = Segment(R_1, S_1)
scac_{S2R2} = Segment(S_2, R_2)
svis_{S2R2} = Segment(S_2, R_2)
condcac_{ABCD}: φ_m > 90°
affplan_{v,w} = false
affplan_{w,u} = false
affplan_{u,v} = false
condcac_{EFGH}: ¬condcac_{ABCD}
condcac_{BCHG}: (θ > 90°) ∧ (θ  <  270°)
condcac_{ADEF}: ¬condcac_{BCHG}
condcac_{CDEH}: θ > 180°
condcac_{ABGF}: ¬condcac_{CDEH}
M'_u: M_u - (((2 * dec_u) + l_u) * u)
N'_u: N_u - (((2 * dec_u) + l_u) * u)
Plan_u, m_u, n_u, n'_u, m'_u = Polygon(M_u, N_u, N'_u, M'_u)
E_w: E + (dec_w * w)
F_w: F + (dec_w * w)
G_w: G + (dec_w * w)
H_w: H + (dec_w * w)
s_{EwFw} = Segment(E_w, F_w)
s_{FwGw} = Segment(F_w, G_w)
s_{GwHw} = Segment(G_w, H_w)
s_{HwEw} = Segment(H_w, E_w)
P_{2,1}: E_w - (dep * u) + (dep * v)
P_{2,2}: F_w - (dep * u) - (dep * v)
P_{2,3}: G_w + (dep * u) - (dep * v)
P_{2,4}: H_w + (dep * u) + (dep * v)
Plan_{u,v}, p_{2,1}, p_{2,2}, p_{2,3}, p_{2,4} = Polygon(P_{2,1}, P_{2,2}, P_{2,3}, P_{2,4})
M_w = Point(Plan_{u,v})
N_w = Point(Plan_{u,v})
d_{u,v} = Segment(M_w, N_w)
M'_w: M_w - (((2 * dec_w) + l_w) * w)
N'_w: N_w - (((2 * dec_w) + l_w) * w)
Plan_w, m_w, n_w, n'_w, m'_w = Polygon(M_w, N_w, N'_w, M'_w)
P_w = Intersect(d_{u,v}, s_{EwFw})
Q_w = Intersect(d_{u,v}, s_{FwGw})
R_w = Intersect(d_{u,v}, s_{GwHw})
S_w = Intersect(d_{u,v}, s_{HwEw})
P_5: P_w - (dec_w * w)
Q_5: Q_w - (dec_w * w)
R_5: R_w - (dec_w * w)
S_5: S_w - (dec_w * w)
P_6: P_w - ((dec_w + l_w) * w)
Q_6: Q_w - ((dec_w + l_w) * w)
R_6: R_w - ((dec_w + l_w) * w)
S_6: S_w - ((dec_w + l_w) * w)
section_{w,1}, α_{w,1,1}, α_{w,1,2}, α_{w,1,3}, α_{w,1,4} = Polygon(P_5, Q_5, Q_6, P_6)
section_{w,2}, α_{w,2,1}, α_{w,2,2}, α_{w,2,3}, α_{w,2,4} = Polygon(P_5, R_5, R_6, P_6)
section_{w,3}, α_{w,3,1}, α_{w,3,2}, α_{w,3,3}, α_{w,3,4} = Polygon(P_5, S_5, S_6, P_6)
section_{w,4}, α_{w,4,1}, α_{w,4,2}, α_{w,4,3}, α_{w,4,4} = Polygon(Q_5, R_5, R_6, Q_6)
section_{w,5}, α_{w,5,1}, α_{w,5,2}, α_{w,5,3}, α_{w,5,4} = Polygon(Q_5, S_5, S_6, Q_6)
section_{w,6}, α_{w,6,1}, α_{w,6,2}, α_{w,6,3}, α_{w,6,4} = Polygon(R_5, S_5, S_6, R_6)
scac_{P5Q5} = Segment(P_5, Q_5)
svis_{P5Q5} = Segment(P_5, Q_5)
scac_{Q5Q6} = Segment(Q_5, Q_6)
svis_{Q5Q6} = Segment(Q_5, Q_6)
scac_{Q6P6} = Segment(Q_6, P_6)
svis_{Q6P6} = Segment(Q_6, P_6)
scac_{P6P5} = Segment(P_6, P_5)
svis_{P6P5} = Segment(P_6, P_5)
scac_{P5R5} = Segment(P_5, R_5)
svis_{P5R5} = Segment(P_5, R_5)
scac_{R5R6} = Segment(R_5, R_6)
svis_{R5R6} = Segment(R_5, R_6)
scac_{R6P6} = Segment(R_6, P_6)
svis_{R6P6} = Segment(R_6, P_6)
scac_{P5S5} = Segment(P_5, S_5)
svis_{P5S5} = Segment(P_5, S_5)
scac_{S5S6} = Segment(S_5, S_6)
svis_{S5S6} = Segment(S_5, S_6)
scac_{S6P6} = Segment(S_6, P_6)
svis_{S6P6} = Segment(S_6, P_6)
scac_{Q5R5} = Segment(Q_5, R_5)
svis_{Q5R5} = Segment(Q_5, R_5)
scac_{R6Q6} = Segment(R_6, Q_6)
svis_{R6Q6} = Segment(R_6, Q_6)
scac_{Q5S5} = Segment(Q_5, S_5)
svis_{Q5S5} = Segment(Q_5, S_5)
scac_{S6Q6} = Segment(S_6, Q_6)
svis_{S6Q6} = Segment(S_6, Q_6)
scac_{R5S5} = Segment(R_5, S_5)
svis_{R5S5} = Segment(R_5, S_5)
scac_{S6R6} = Segment(S_6, R_6)
svis_{S6R6} = Segment(S_6, R_6)
C_v: C + (dec_v * v)
D_v: D + (dec_v * v)
E_v: E + (dec_v * v)
H_v: H + (dec_v * v)
s_{CvDv} = Segment(C_v, D_v)
s_{DvEv} = Segment(D_v, E_v)
s_{EvHv} = Segment(E_v, H_v)
s_{HvCv} = Segment(H_v, C_v)
P_{1,1}: C_v + (dep * u) - (dep * w)
P_{1,2}: D_v - (dep * u) - (dep * w)
P_{1,3}: E_v - (dep * u) + (dep * w)
P_{1,4}: H_v + (dep * u) + (dep * w)
Plan_{w,u}, p_{1,1}, p_{1,2}, p_{1,3}, p_{1,4} = Polygon(P_{1,1}, P_{1,2}, P_{1,3}, P_{1,4})
M_v = Point(Plan_{w,u})
N_v = Point(Plan_{w,u})
d_{w,u} = Segment(M_v, N_v)
P_v = Intersect(d_{w,u}, s_{CvDv})
Q_v = Intersect(d_{w,u}, s_{DvEv})
R_v = Intersect(d_{w,u}, s_{EvHv})
S_v = Intersect(d_{w,u}, s_{HvCv})
P_3: P_v - (dec_v * v)
Q_3: Q_v - (dec_v * v)
R_3: R_v - (dec_v * v)
S_3: S_v - (dec_v * v)
P_4: P_v - ((dec_v + l_v) * v)
Q_4: Q_v - ((dec_v + l_v) * v)
R_4: R_v - ((dec_v + l_v) * v)
S_4: S_v - ((dec_v + l_v) * v)
section_{v,1}, α_{v,1,1}, α_{v,1,2}, α_{v,1,3}, α_{v,1,4} = Polygon(P_3, Q_3, Q_4, P_4)
section_{v,2}, α_{v,2,1}, α_{v,2,2}, α_{v,2,3}, α_{v,2,4} = Polygon(P_3, R_3, R_4, P_4)
section_{v,3}, α_{v,3,1}, α_{v,3,2}, α_{v,3,3}, α_{v,3,4} = Polygon(P_3, S_3, S_4, P_4)
section_{v,4}, α_{v,4,1}, α_{v,4,2}, α_{v,4,3}, α_{v,4,4} = Polygon(Q_3, R_3, R_4, Q_4)
section_{v,5}, α_{v,5,1}, α_{v,5,2}, α_{v,5,3}, α_{v,5,4} = Polygon(Q_3, S_3, S_4, Q_4)
section_{v,6}, α_{v,6,1}, α_{v,6,2}, α_{v,6,3}, α_{v,6,4} = Polygon(R_3, S_3, S_4, R_4)
M'_v: M_v - (((2 * dec_v) + l_v) * v)
N'_v: N_v - (((2 * dec_v) + l_v) * v)
Plan_v, m_v, n_v, n'_v, m'_v = Polygon(M_v, N_v, N'_v, M'_v)
scac_{P3Q3} = Segment(P_3, Q_3)
svis_{P3Q3} = Segment(P_3, Q_3)
scac_{Q3Q4} = Segment(Q_3, Q_4)
svis_{Q3Q4} = Segment(Q_3, Q_4)
scac_{Q4P4} = Segment(Q_4, P_4)
svis_{Q4P4} = Segment(Q_4, P_4)
scac_{P4P3} = Segment(P_4, P_3)
svis_{P4P3} = Segment(P_4, P_3)
scac_{P3R3} = Segment(P_3, R_3)
svis_{P3R3} = Segment(P_3, R_3)
scac_{R3R4} = Segment(R_3, R_4)
svis_{R3R4} = Segment(R_3, R_4)
scac_{R4P4} = Segment(R_4, P_4)
svis_{R4P4} = Segment(R_4, P_4)
scac_{P3S3} = Segment(P_3, S_3)
svis_{P3S3} = Segment(P_3, S_3)
scac_{S3S4} = Segment(S_3, S_4)
svis_{S3S4} = Segment(S_3, S_4)
scac_{S4P4} = Segment(S_4, P_4)
svis_{S4P4} = Segment(S_4, P_4)
scac_{R3Q3} = Segment(R_3, Q_3)
svis_{R3Q3} = Segment(R_3, Q_3)
scac_{Q4R4} = Segment(Q_4, R_4)
svis_{Q4R4} = Segment(Q_4, R_4)
scac_{Q3S3} = Segment(Q_3, S_3)
svis_{Q3S3} = Segment(Q_3, S_3)
scac_{S4Q4} = Segment(S_4, Q_4)
svis_{S4Q4} = Segment(S_4, Q_4)
scac_{R3S3} = Segment(R_3, S_3)
svis_{R3S3} = Segment(R_3, S_3)
scac_{S4R4} = Segment(S_4, R_4)
svis_{S4R4} = Segment(S_4, R_4)