Aff. sec_{u,v}

Aff. plan_{u,v}

Aff. sec_{v,w}

Aff. plan_{v,w}

Aff. sec_{w,u}

Aff. plan_{w,u}

Aff. sommets

Aff. som. sec_{u,v}

Aff. som. sec_{v,w}

Aff. som. sec_{w,u}

Aff. d_w et P_0

Aff. d_u et Q_0

Aff. d_v et R_0

Aff. O_b

l_v = 6 (slider from 0 to 10, step 0.5)
l_u = 4 (slider from 0 to 10, step 0.5)
θ = 0.6108652381980153 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
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 = 2.007128639793479 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)}
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]))
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]))
l_w = 2.5 (slider from 0 to 10, step 0.5)
dec_v = 2
k_3: {0, 0, 1}
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]))
O_b = (11, 0)
A: O_b - l_u / 2 u - l_v / 2 v
B: A + l_u u
G: B + l_w w
dep = 3
dec_u = 2
G_w: G + dec_u u - dec_v v
B_w: B + dec_u u - dec_v v
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
C: B + l_v v
D: A + l_v v
E: D + l_w w
F: A + l_w w
H: C + 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)
P_m: B_w - dep w
P_M: G_w + dep w
d_w = Segment(P_m, P_M)
P_0 = Point(d_w)
dec_w = 2
P_{0,1}: P_0 + (l_v + 2 dec_v) v
P_{0,3}: P_0 - (l_u + 2 dec_u) u
P_{0,2}: P_0 + Vector[P_0, P_{0,1}] + Vector[P_0, P_{0,3}]
Plan_{u,v}, p_0, p_{0,1}, p_{0,2}, p_{0,3} = Polygon(P_0, P_{0,1}, P_{0,2}, P_{0,3})
vect_{w,u} = Vector(B, B + dec_u u)
vect_{w,v} = Vector(B + dec_u u, B + dec_u u - dec_v v)
test_w: Length[Vector[B_w, P_0]] + Length[Vector[P_0, G_w]] - Length[Vector[B_w, G_w]]
exissec_{u,v}: test_w ≟ 0
P_1: P_0 - dec_u u + dec_v v
P_2: P_1 + l_v v
P_4: P_1 - l_u u
P_3: P_1 - l_u u + l_v v
sec_{u,v}, pcac_1, pcac_2, pcac_3, pcac_4 = Polygon(P_1, P_2, P_3, P_4)
vect_{u,v} = Vector(B, B - dec_v v)
vect_{u,w} = Vector(B - dec_v v, B - dec_v v - dec_w w)
B_u: B - dec_v v - dec_w w
A_u: A - dec_v v - dec_w w
Q_m: B_u + dep u
Q_M: A_u - dep u
d_u = Segment(Q_m, Q_M)
Q_0 = Point(d_u)
Q_{0,1}: Q_0 + (l_v + 2 dec_v) v
Q_{0,3}: Q_0 + (l_w + 2 dec_w) w
Q_{0,2}: Q_0 + Vector[Q_0, Q_{0,1}] + Vector[Q_0, Q_{0,3}]
Plan_{v,w}, q_0, q_{0,1}, q_{0,2}, q_{0,3} = Polygon(Q_0, Q_{0,1}, Q_{0,2}, Q_{0,3})
test_u: Length[Vector[B_u, Q_0]] + Length[Vector[Q_0, A_u]] - Length[Vector[B_u, A_u]]
exissec_{v,w}: test_u ≟ 0
Q_1: Q_0 + dec_v v + dec_w w
Q_2: Q_1 + l_v v
Q_4: Q_1 + l_w w
Q_3: Q_1 + l_v v + l_w w
sec_{v,w}, qcac_1, qcac_2, qcac_3, qcac_4 = Polygon(Q_1, Q_2, Q_3, Q_4)
vect_{v,w} = Vector(B, B - dec_w w)
vect_{v,u} = Vector(B - dec_w w, B - dec_w w + dec_u u)
B_v: B - dec_w w + dec_u u
C_v: C - dec_w w + dec_u u
R_m: B_v - dep v
R_M: C_v + dep v
d_v = Segment(R_m, R_M)
R_0 = Point(d_v)
test_v: Length[Vector[B_v, R_0]] + Length[Vector[R_0, C_v]] - Length[Vector[B_v, C_v]]
exissec_{w,u}: test_v ≟ 0
R_{0,1}: R_0 + (l_w + 2 dec_w) w
R_{0,3}: R_0 - (l_u + 2 dec_u) u
R_{0,2}: R_0 + Vector[R_0, R_{0,1}] + Vector[R_0, R_{0,3}]
Plan_{w,u}, r_0, r_{0,1}, r_{0,2}, r_{0,3} = Polygon(R_0, R_{0,1}, R_{0,2}, R_{0,3})
R_1: R_0 + dec_w w - dec_u u
R_2: R_1 + l_w w
R_4: R_1 - l_u u
R_3: R_1 + l_w w - l_u u
sec_{w,u}, rcac_1, rcac_2, rcac_3, rcac_4 = Polygon(R_1, R_2, R_3, R_4)
affsec_{u,v} = true
affplan_{u,v} = true
affsec_{v,w} = false
affplan_{v,w} = true
affsec_{w,u} = false
affplan_{w,u} = true
affsom = false
affsomsec_{u,v} = false
affsomsec_{v,w} = false
affsomsec_{w,u} = false
pvis_4 = Segment(P_4, P_1)
pvis_1 = Segment(P_1, P_2)
pvis_2 = Segment(P_2, P_3)
pvis_3 = Segment(P_3, P_4)
qvis_1 = Segment(Q_1, Q_2)
qvis_3 = Segment(Q_3, Q_4)
qvis_2 = Segment(Q_2, Q_3)
qvis_4 = Segment(Q_4, Q_1)
rvis_1 = Segment(R_1, R_2)
rvis_3 = Segment(R_3, R_4)
rvis_2 = Segment(R_2, R_3)
rvis_4 = Segment(R_4, R_1)
affdroite_w = true
affdroite_u = true
affdroite_v = true
condcac_{ABCD}: φ_m ≥ 90 °
condcac_{BCHG}: 90 ° ≤ θ ∧ θ ≤ 270 °
condcac_{CDEH}: θ ≟ 0 ° ∨ θ ≥ 180 °
condcac_{ABGF}: θ ≤ 180 °
condcac_{ADEF}: θ ≤ 90 ° ∨ 270 ° ≤ θ
condcac_{EFGH}: φ_m ≤ 90 °
affO_b = false