Aff. sec_{w,u}

Aff. plan_{w,u}

Aff. d_v et P

Aff. sec_v

Aff. plan_v

Aff. plan_{w,u} sup.

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

Aff. som. sec_v

Aff. bases

Aff. som. bases

Aff. axe

dec_w = 2
dec_u = 2
k_3: {0, 0, 1}
dec_v = 4
j_3: {0, 1, 0}
O_b = (7, 2)
O_3: {0, 0, 0}
O: (Element[O_3, 1], Element[O_3, 2])
l = 4 (slider from 0 to 10, step 0.5)
φ_m = 1.8325957145940461 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
φ: φ_m - 90 °
θ = 0.6108652381980154 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
P_1: {-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, 1] Element[k_3, 1] + Element[P_1, 2] Element[k_3, 2] + Element[P_1, 3] Element[j_3, 3], Element[P_1, 4] Element[k_3, 1] + Element[P_1, 5] Element[k_3, 2] + Element[P_1, 6] Element[k_3, 3]))
v = Vector(O, (Element[P_1, 1] Element[j_3, 1] + Element[P_1, 2] Element[j_3, 2] + Element[P_1, 3] Element[j_3, 3], Element[P_1, 4] Element[j_3, 1] + Element[P_1, 5] Element[j_3, 2] + Element[P_1, 6] Element[j_3, 3]))
i_3: {1, 0, 0}
u = Vector(O, (Element[P_1, 1] Element[i_3, 1] + Element[P_1, 2] Element[i_3, 2] + Element[P_1, 3] Element[i_3, 3], Element[P_1, 4] Element[i_3, 1] + Element[P_1, 5] Element[i_3, 2] + Element[P_1, 6] Element[i_3, 3]))
h = 6 (slider from 0 to 10, step 0.5)
O_s: O_b + h v
O_{w,u}: O_s + dec_v v
P_{1,0}: O_{w,u} + l / 2 * (w + u) + dec_w w + dec_u u
P_{1,1}: P_{1,0} - (l + 2 dec_w) w
P_{1,2}: P_{1,0} - (l + 2 dec_w) w - (l + 2 dec_u) u
P_{1,3}: P_{1,0} - (l + 2 dec_u) u
Plansup_{w,u}, p_{1,0}, p_{1,1}, p_{1,2}, p_{1,3} = Polygon(P_{1,0}, P_{1,1}, P_{1,2}, P_{1,3})
M_v = Point(Plansup_{w,u})
M_{v,1}: P_{1,2} - Vector[P_{1,1}, M_v]
testMv1_1 = If(Length[Vector[P_{1,1}, M_{v,1}]] + Length[Vector[M_{v,1}, P_{1,2}]] ≟ Length[Vector[P_{1,1}, P_{1,2}]], 1, 0)
M_{v,0}: P_{1,1} - Vector[P_{1,0}, M_v]
testMv0_0 = If(Length[Vector[P_{1,0}, M_{v,0}]] + Length[Vector[M_{v,0}, P_{1,1}]] ≟ Length[Vector[P_{1,0}, P_{1,1}]], 1, 0)
M_{v,2}: P_{1,3} - Vector[P_{1,2}, M_v]
testMv2_0 = If(Length[Vector[P_{1,0}, M_{v,2}]] + Length[Vector[M_{v,2}, P_{1,1}]] ≟ Length[Vector[P_{1,0}, P_{1,1}]], 1, 0)
testMv2_1 = If(Length[Vector[P_{1,1}, M_{v,2}]] + Length[Vector[M_{v,2}, P_{1,2}]] ≟ Length[Vector[P_{1,1}, P_{1,2}]], 1, 0)
testMv2_2 = If(Length[Vector[P_{1,2}, M_{v,2}]] + Length[Vector[M_{v,2}, P_{1,3}]] ≟ Length[Vector[P_{1,2}, P_{1,3}]], 1, 0)
M_{v,3}: P_{1,3} - Vector[P_{1,0}, M_v]
testMv3_3 = If(Length[Vector[P_{1,3}, M_{v,3}]] + Length[Vector[M_{v,3}, P_{1,0}]] ≟ Length[Vector[P_{1,3}, P_{1,0}]], 1, 0)
testMv0_2 = If(Length[Vector[P_{1,2}, M_{v,0}]] + Length[Vector[M_{v,0}, P_{1,3}]] ≟ Length[Vector[P_{1,2}, P_{1,3}]], 1, 0)
testMv0_1 = If(Length[Vector[P_{1,1}, M_{v,0}]] + Length[Vector[M_{v,0}, P_{1,2}]] ≟ Length[Vector[P_{1,1}, P_{1,2}]], 1, 0)
testMv0_3 = If(Length[Vector[P_{1,3}, M_{v,0}]] + Length[Vector[M_{v,0}, P_{1,0}]] ≟ Length[Vector[P_{1,3}, P_{1,0}]], 1, 0)
testMv2_3 = If(Length[Vector[P_{1,3}, M_{v,2}]] + Length[Vector[M_{v,2}, P_{1,0}]] ≟ Length[Vector[P_{1,3}, P_{1,0}]], 1, 0)
i = Vector(O, (Element[i_3, 1], Element[i_3, 2]))
j = Vector(O, (Element[j_3, 1], Element[j_3, 2]))
longMv_3: Length[Vector[P_{1,3}, M_v]] / Length[Vector[P_{1,3}, P_{1,0}]]
longMv_1: Length[Vector[P_{1,1}, M_v]] / Length[Vector[P_{1,1}, P_{1,2}]]
longMv_0: Length[Vector[P_{1,0}, M_v]] / Length[Vector[P_{1,0}, P_{1,1}]]
longMv_2: Length[Vector[P_{1,2}, M_v]] / Length[Vector[P_{1,2}, P_{1,3}]]
δMv_1 = If(testMv1_1 ≟ 1 ∧ (testMv2_2 ≟ 0 ∨ testMv0_0 ≟ 0), 1, 0)
P_{2,0}: O_b + l / 2 * (j - i) + dec_w j - dec_u i
P_{2,2}: P_{2,0} - (l + 2 dec_w) j + (l + 2 dec_u) i
P_{2,1}: P_{2,0} - (l + 2 dec_w) j
vectMv_1: Vector[P_{2,0}, P_{2,1}] + longMv_1 Vector[P_{2,1}, P_{2,2}]
vectMv_0: longMv_0 Vector[P_{2,0}, P_{2,1}]
P_{2,3}: P_{2,0} + (l + 2 dec_u) i
vectMv_3: Vector[P_{2,0}, P_{2,3}] + longMv_3 Vector[P_{2,3}, P_{2,0}]
vectMv_2: Vector[P_{2,0}, P_{2,2}] + longMv_2 Vector[P_{2,2}, P_{2,3}]
testMv_3 = If(Length[Vector[P_{1,3}, M_v]] + Length[Vector[M_v, P_{1,0}]] ≟ Length[Vector[P_{1,3}, P_{1,0}]], 1, 0)
testMv_2 = If(Length[Vector[P_{1,2}, M_v]] + Length[Vector[M_v, P_{1,3}]] ≟ Length[Vector[P_{1,2}, P_{1,3}]], 1, 0)
testMv_1 = If(Length[Vector[P_{1,1}, M_v]] + Length[Vector[M_v, P_{1,2}]] ≟ Length[Vector[P_{1,1}, P_{1,2}]], 1, 0)
testMv_0 = If(Length[Vector[P_{1,0}, M_v]] + Length[Vector[M_v, P_{1,1}]] ≟ Length[Vector[P_{1,0}, P_{1,1}]], 1, 0)
valrem_θ: θ ≟ 0 ° ∨ θ ≟ 180 ° ∨ θ ≟ 360 °
valrem_{φm}: φ_m ≟ 0 ° ∨ φ_m ≟ 180 °
coefMer_0: {(Element[P_1, 6]^(2) + Element[P_1, 4]^(2)) / (Element[P_1, 1] Element[P_1, 6] - Element[P_1, 4] Element[P_1, 3])^(2), -2 * (Element[P_1, 3] Element[P_1, 6] + Element[P_1, 4] Element[P_1, 1]) / (Element[P_1, 1] Element[P_1, 6] - Element[P_1, 4] Element[P_1, 3])^(2), (Element[P_1, 3]^(2) + Element[P_1, 1]^(2)) / (Element[P_1, 1] Element[P_1, 6] - Element[P_1, 4] Element[P_1, 3])^(2)}
Mer_0: Element[coefMer_0, 1] x^(2) + Element[coefMer_0, 2] x y + Element[coefMer_0, 3] y^(2) = 1
T_1, T_2, T_3, T_4 = Intersect(Mer_0, Σ)
Σsup_{w,u}: Element[coefMer_0, 1] (2 * (x - x(O_{w,u})) / l)^(2) + Element[coefMer_0, 2] 4 * (x - x(O_{w,u})) * (y - y(O_{w,u})) / l^(2) + Element[coefMer_0, 3] (2 * (y - y(O_{w,u})) / l)^(2) = 1
T_{b,3} = If((¬valrem_{φm}) ∧ (¬valrem_θ), O_b + l / 2 Vector[O, T_3], If[valrem_{φm} ∧ (¬valrem_θ), O_b + l / 2 u, O_b + l / 2 j])
T_{w,u,3}: T_{b,3} + Vector[O_b, O_{w,u}]
T_{b,1} = If((¬valrem_{φm}) ∧ (¬valrem_θ), O_b + l / 2 Vector[O, T_1], If[valrem_{φm} ∧ (¬valrem_θ), O_b - l / 2 u, O_b - l / 2 j])
T_{w,u,1}: T_{b,1} + Vector[O_b, O_{w,u}]
N_v = Point(Plansup_{w,u})
d_{w,u} = Segment(M_v, N_v)
Q_{w,u,1}, Q_{w,u,2} = Intersect(Σsup_{w,u}, d_{w,u})
A_b: O_b + l / 2 * (-u + w)
B_b: A_b + l u
T_{s,3}: T_{b,3} + h v
T_{s,1}: T_{b,1} + h v
Σ_s: Element[coefMer_0, 1] (2 * (x - x(O_s)) / l)^(2) + Element[coefMer_0, 2] 4 * (x - x(O_s)) * (y - y(O_s)) / l^(2) + Element[coefMer_0, 3] (2 * (y - y(O_s)) / l)^(2) = 1
Y_{Mer0}(x) = Element[P_1, 4] l / 2 cos(x) + Element[P_1, 6] l / 2 sin(x)
X_{Mer0}(x) = Element[P_1, 1] l / 2 cos(x) + Element[P_1, 3] l / 2 sin(x)
dep_{axe} = 3
coefEq: {1, 0, 1 / sin(φ)^(2)}
O_{v,b}: B_b + dec_w w + dec_u u
O_{v,s}: O_{v,b} + h v
dep = 3
V_M: O_{v,s} + dep v
V_m: O_{v,b} - dep v
d_v = Segment(V_m, V_M)
P_{0,0} = Point(d_v)
O_i: O_b + Vector[O_{v,b}, P_{0,0}]
Σ_i: Element[coefMer_0, 1] (2 * (x - x(O_i)) / l)^(2) + Element[coefMer_0, 2] 4 * (x - x(O_i)) * (y - y(O_i)) / l^(2) + Element[coefMer_0, 3] (2 * (y - y(O_i)) / l)^(2) = 1
Eq: Element[coefEq, 1] x^(2) + Element[coefEq, 2] x y + Element[coefEq, 3] y^(2) = 1
coefMer_{90}: {(Element[P_1, 6]^(2) + Element[P_1, 5]^(2)) / (Element[P_1, 2] Element[P_1, 6] - Element[P_1, 5] Element[P_1, 3])^(2), -2 * (Element[P_1, 3] Element[P_1, 6] + Element[P_1, 5] Element[P_1, 2]) / (Element[P_1, 2] Element[P_1, 6] - Element[P_1, 5] Element[P_1, 3])^(2), (Element[P_1, 3]^(2) + Element[P_1, 2]^(2)) / (Element[P_1, 2] Element[P_1, 6] - Element[P_1, 5] Element[P_1, 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: A_b + l * (u - w)
D_b: A_b - l w
s_{AbBb} = Segment(A_b, B_b)
X_{eq}(x) = Element[P_1, 1] l / 2 cos(x) + Element[P_1, 2] l / 2 sin(x)
Y_{eq}(x) = Element[P_1, 4] l / 2 cos(x) + Element[P_1, 5] l / 2 sin(x)
s_{BbCb} = Segment(B_b, C_b)
s_{CbDb} = Segment(C_b, D_b)
s_{DbAb} = Segment(D_b, A_b)
s_{Tb1Ts1} = Segment(T_{b,1}, T_{s,1})
s_{Tb3Ts3} = Segment(T_{b,3}, T_{s,3})
A_s: A_b + h v
B_s: B_b + h v
C_s: C_b + h v
D_s: D_b + h v
s_{AsBs} = Segment(A_s, B_s)
s_{BsCs} = Segment(B_s, C_s)
s_{CsDs} = Segment(C_s, D_s)
s_{DsAs} = Segment(D_s, A_s)
vectdec_w = Vector(B_b, B_b + dec_w w)
vectdec_u = Vector(B_b + dec_w w, B_b + dec_w w + dec_u u)
affsec_{w,u} = true
affplan_{w,u} = true
affdroite_v = true
test_v: Length[Vector[O_{v,b}, P_{0,0}]] + Length[Vector[P_{0,0}, O_{v,s}]] - Length[Vector[O_{v,b}, O_{v,s}]]
exissec_{w,u}: test_v ≟ 0
P_{0,3}: P_{0,0} - (l + 2 dec_u) u
P_{0,2}: P_{0,0} - (l + 2 dec_w) w - (l + 2 dec_u) u
P_{0,1}: P_{0,0} - (l + 2 dec_w) w
Plan_{w,u}, p_{0,0}, p_{0,1}, p_{0,2}, p_{0,3} = Polygon(P_{0,0}, P_{0,1}, P_{0,2}, P_{0,3})
affsec_v = true
affplan_v = true
affplansup_{w,u} = true
affdroite_{w,u} = true
M'_w: M_v - (l + 2 dec_v) v
N'_w: N_v - (l + 2 dec_v) v
Plan_v, m_w, n_w, n'_w, m'_w = Polygon(M_v, N_v, N'_w, M'_w)
Q_{s,1}: Q_{w,u,1} - dec_v v
Q_{s,2}: Q_{w,u,2} - dec_v v
Q_{b,1}: Q_{w,u,1} - (h + dec_v) v
Q_{b,2}: Q_{w,u,2} - (h + dec_v) v
affsomsec_v = false
section_w, q_{s,1}, q_{b,1}, q_{b,2}, q_{s,2} = Polygon(Q_{s,1}, Q_{b,1}, Q_{b,2}, Q_{s,2})
scac_{Qs1Qb1} = Segment(Q_{s,1}, Q_{b,1})
svis_{Qs1Qb1} = Segment(Q_{s,1}, Q_{b,1})
scac_{Qb1Qb2} = Segment(Q_{b,1}, Q_{b,2})
svis_{Qb1Qb2} = Segment(Q_{b,1}, Q_{b,2})
scac_{Qb2Qs2} = Segment(Q_{b,2}, Q_{s,2})
svis_{Qb2Qs2} = Segment(Q_{b,2}, Q_{s,2})
scac_{Qs2Qs1} = Segment(Q_{s,2}, Q_{s,1})
svis_{Qs2Qs1} = Segment(Q_{s,2}, Q_{s,1})
section_{w,u} = Sector(Σ_i, -θ - 3 / 4 * 3.14159, -θ + 13 / 4 * 3.14159)
affbase = false
affsombase = false
O_m: O_b - dep_{axe} v
O_M: O_b + (h + dep_{axe}) v
axe = Segment(O_m, O_M)
affaxe = false
Σ_b: Element[coefMer_0, 1] (2 * (x - x(O_b)) / l)^(2) + Element[coefMer_0, 2] 4 * (x - x(O_b)) * (y - y(O_b)) / l^(2) + Element[coefMer_0, 3] (2 * (y - y(O_b)) / l)^(2) = 1
ΣvisT1T3_b = Arc(Σ_b, T_{b,1}, T_{b,3})
ΣcacT1T3_b = Arc(Σ_b, T_{b,1}, T_{b,3})
ΣvisT3T1_b = Arc(Σ_b, T_{b,3}, T_{b,1})
ΣcacT3T1_b = Arc(Σ_b, T_{b,3}, T_{b,1})
s_{Tb3Tb1} = Segment(T_{b,3}, T_{b,1})
s_{Ts1Ts3} = Segment(T_{s,1}, T_{s,3})
condarr_b: θ < 180 °
ΣcacT1T3_s = Arc(Σ_s, T_{s,1}, T_{s,3})
ΣvisT1T3_s = Arc(Σ_s, T_{s,1}, T_{s,3})
ΣcacT3T1_s = Arc(Σ_s, T_{s,3}, T_{s,1})
ΣvisT3T1_s = Arc(Σ_s, T_{s,3}, T_{s,1})
T_{i,1}: T_{b,1} + Vector[O_b, O_i]
T_{i,3}: T_{b,3} + Vector[O_b, O_i]
ΣcacT1T3_i = Arc(Σ_i, T_{i,1}, T_{i,3})
ΣvisT3T1_i = Arc(Σ_i, T_{i,3}, T_{i,1})
ΣcacT3T1_i = Arc(Σ_i, T_{i,3}, T_{i,1})
ΣvisT1T3_i = Arc(Σ_i, T_{i,1}, T_{i,3})
s_{Ti3Ti1} = Segment(T_{i,3}, T_{i,1})
Γ_i = Circle(O_i, l / 2 Length[u])
Γ_{b,s} = Circle(O_b, l / 2 Length[u])
a_{w,u}: (y(T_{w,u,3}) - y(T_{w,u,1})) / (x(T_{w,u,3}) - x(T_{w,u,1}))
b_{w,u}: y(T_{w,u,1}) - a_{w,u} x(T_{w,u,1})
f_{w,u}(x) = a_{w,u} x + b_{w,u}
condQ1surd: y(Q_{w,u,1}) > f_{w,u}(x(Q_{w,u,1}))
condcac_1: condQ1surd ∧ φ_m < 90 ° ∨ (¬condQ1surd) ∧ φ_m > 90 °
condQ2surd: y(Q_{w,u,2}) > f_{w,u}(x(Q_{w,u,2}))
condcac_2: condQ2surd ∧ φ_m < 90 ° ∨ (¬condQ2surd) ∧ φ_m > 90 °
longNv_0: Length[Vector[P_{1,0}, N_v]] / Length[Vector[P_{1,0}, P_{1,1}]]
longNv_1: Length[Vector[P_{1,1}, N_v]] / Length[Vector[P_{1,1}, P_{1,2}]]
longNv_2: Length[Vector[P_{1,2}, N_v]] / Length[Vector[P_{1,2}, P_{1,3}]]
longNv_3: Length[Vector[P_{1,3}, N_v]] / Length[Vector[P_{1,3}, P_{1,0}]]
vectNv_0: longNv_0 Vector[P_{2,0}, P_{2,1}]
vectNv_1: Vector[P_{2,0}, P_{2,1}] + longNv_1 Vector[P_{2,1}, P_{2,2}]
vectNv_2: Vector[P_{2,0}, P_{2,2}] + longNv_2 Vector[P_{2,2}, P_{2,3}]
vectNv_3: Vector[P_{2,0}, P_{2,3}] + longNv_3 Vector[P_{2,3}, P_{2,0}]
Γ_{v,2} = Circle(O_b, l / 2)
δMv_2 = If(testMv2_2 ≟ 1 ∧ (testMv3_3 ≟ 0 ∨ testMv1_1 ≟ 0) ∧ (testMv0_0 ≟ 0 ∨ testMv0_0 ≟ 1 ∧ (testMv2_0 ≟ 1 ∨ testMv2_3 ≟ 1)), 1, 0)
δMv_3 = If(testMv3_3 ≟ 1 ∧ (testMv0_0 ≟ 0 ∨ testMv2_2 ≟ 0), 1, 0)
δMv_0 = If(testMv0_0 ≟ 1 ∧ (testMv1_1 ≟ 0 ∨ testMv3_3 ≟ 0), 1, 0)
M'_v: P_{2,0} + δMv_0 vectMv_0 + δMv_1 vectMv_1 + δMv_2 vectMv_2 + δMv_3 vectMv_3
testMv1_0 = If(Length[Vector[P_{1,0}, M_{v,1}]] + Length[Vector[M_{v,1}, P_{1,1}]] ≟ Length[Vector[P_{1,0}, P_{1,1}]], 1, 0)
testMv1_2 = If(Length[Vector[P_{1,2}, M_{v,1}]] + Length[Vector[M_{v,1}, P_{1,3}]] ≟ Length[Vector[P_{1,2}, P_{1,3}]], 1, 0)
testMv1_3 = If(Length[Vector[P_{1,3}, M_{v,1}]] + Length[Vector[M_{v,1}, P_{1,0}]] ≟ Length[Vector[P_{1,3}, P_{1,0}]], 1, 0)
testMv3_0 = If(Length[Vector[P_{1,0}, M_{v,3}]] + Length[Vector[M_{v,3}, P_{1,1}]] ≟ Length[Vector[P_{1,0}, P_{1,1}]], 1, 0)
testMv3_1 = If(Length[Vector[P_{1,1}, M_{v,3}]] + Length[Vector[M_{v,3}, P_{1,2}]] ≟ Length[Vector[P_{1,1}, P_{1,2}]], 1, 0)
testMv3_2 = If(Length[Vector[P_{1,2}, M_{v,3}]] + Length[Vector[M_{v,3}, P_{1,3}]] ≟ Length[Vector[P_{1,2}, P_{1,3}]], 1, 0)