Aff. sec_{u,v}

Aff. plan_{u,v}

Aff. d_w et P

Aff. sec_w

Aff. plan_w

Aff. plan_{u,v} sup.

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

Aff. som. sec_w

Aff. bases

Aff. som. bases

Aff. axe

dep_{axe} = 3
h = 5 (slider from 0 to 10, step 0.5)
O_b = (8, 1)
θ = 0.5235987755982988 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
k_3: {0, 0, 1}
j_3: {0, 1, 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_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]))
coefEq: {1, 0, 1 / sin(φ)^(2)}
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]))
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]))
l = 4 (slider from 0 to 10, step 0.5)
A_b: O_b - l / 2 * (u + v)
B_b: A_b + l u
dec_u = 2
dec_v = 2
O_{w,b}: B_b + dec_u u - dec_v v
O_{w,s}: O_{w,b} + h w
dep = 3
W_M: O_{w,s} + dep w
W_m: O_{w,b} - dep w
d_w = Segment(W_m, W_M)
P_{0,0} = Point(d_w)
O_i: O_b + Vector[O_{w,b}, P_{0,0}]
Σ_i: Element[coefEq, 1] (2 * (x - x(O_i)) / l)^(2) + Element[coefEq, 2] 4 * (x - x(O_i)) / l * (y - y(O_i)) / l + Element[coefEq, 3] (2 * (y - y(O_i)) / l)^(2) = 1
i = Vector(O, (Element[i_3, 1], Element[i_3, 2]))
j = Vector(O, (Element[j_3, 1], Element[j_3, 2]))
Eq: Element[coefEq, 1] x^(2) + Element[coefEq, 2] x y + Element[coefEq, 3] y^(2) = 1
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
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 + v)
D_b: A_b + l v
s_{AbBb} = Segment(A_b, B_b)
Coordsph_{Tb2}: {cos(θ + 90 °), sin(θ + 90 °), 0}
T_{b,2}: O_b + Element[Coordsph_{Tb2}, 1] l / 2 u + Element[Coordsph_{Tb2}, 2] l / 2 v + Element[Coordsph_{Tb2}, 3] w
Coordsph_{Tb1}: {cos(θ - 90 °), sin(θ - 90 °), 0}
T_{b,1}: O_b + Element[Coordsph_{Tb1}, 1] l / 2 u + Element[Coordsph_{Tb1}, 2] l / 2 v + Element[Coordsph_{Tb1}, 3] w
O_s: O_b + h w
T_{s,1}: T_{b,1} + h w
T_{s,2}: T_{b,2} + h w
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)
Σdevvis_b = CurveCartesian(x(O_b) + X_{eq}(t), y(O_b) + Y_{eq}(t), t, θ - 3.141592653589793 / 2, 3.141592653589793 + θ - 3.141592653589793 / 2)
Σdercac_b = CurveCartesian(x(O_b) + X_{eq}(t), y(O_b) + Y_{eq}(t), t, 3.141592653589793 + θ - 3.141592653589793 / 2, 2 * 3.141592653589793 + θ - 3.141592653589793 / 2)
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_{Tb2Ts2} = Segment(T_{b,2}, T_{s,2})
condcac_{Σderb}: φ_m > 90 ° ∧ φ_m < 180 °
Σdervis_b = CurveCartesian(x(O_b) + X_{eq}(t), y(O_b) + Y_{eq}(t), t, 3.14159 + θ - 3.14159 / 2, 2 * 3.14159 + θ - 3.14159 / 2)
Σdevvis_s = CurveCartesian(x(O_s) + X_{eq}(t), y(O_s) + Y_{eq}(t), t, θ - 3.14159 / 2, 3.14159 + θ - 3.14159 / 2)
Σdercac_s = CurveCartesian(x(O_s) + X_{eq}(t), y(O_s) + Y_{eq}(t), t, 3.14159 + θ - 3.14159 / 2, 2 * 3.14159 + θ - 3.14159 / 2)
Σdervis_s = CurveCartesian(x(O_s) + X_{eq}(t), y(O_s) + Y_{eq}(t), t, 3.14159 + θ - 3.14159 / 2, 2 * 3.14159 + θ - 3.14159 / 2)
A_s: A_b + h w
B_s: B_b + h w
C_s: C_b + h w
D_s: D_b + h w
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)
dec_w = 2
vectdec_u = Vector(B_b, B_b + dec_u u)
vectdec_v = Vector(B_b + dec_u u, B_b + dec_u u - dec_v v)
affsec_{u,v} = false
affplan_{u,v} = true
affdroite_w = true
test_w: Length[Vector[O_{w,b}, P_{0,0}]] + Length[Vector[P_{0,0}, O_{w,s}]] - Length[Vector[O_{w,b}, O_{w,s}]]
exissec_{u,v}: test_w ≟ 0
P_{0,3}: P_{0,0} - (l + 2 dec_u) u
P_{0,2}: P_{0,0} + (l + 2 dec_v) v - (l + 2 dec_u) u
P_{0,1}: P_{0,0} + (l + 2 dec_v) v
Plan_{u,v}, 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})
Σdevvis_i = CurveCartesian(x(O_i) + X_{eq}(t), y(O_i) + Y_{eq}(t), t, θ - 3.14159 / 2, 3.14159 + θ - 3.14159 / 2)
Σdercac_i = CurveCartesian(x(O_i) + X_{eq}(t), y(O_i) + Y_{eq}(t), t, 3.14159 + θ - 3.14159 / 2, 2 * 3.14159 + θ - 3.14159 / 2)
affsec_w = true
O_{u,v}: O_s + dec_w w
P_{1,0}: O_{u,v} + l / 2 * (u - v) + dec_u u - dec_v v
P_{1,1}: P_{1,0} + (l + 2 dec_v) v
P_{1,2}: P_{1,0} + (l + 2 dec_v) v - (l + 2 dec_u) u
P_{1,3}: P_{1,0} - (l + 2 dec_u) u
affplan_w = true
affplansup_{u,v} = true
affdroite_{u,v} = true
Plansup_{u,v}, 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_w = Point(Plansup_{u,v})
N_w = Point(Plansup_{u,v})
d_{u,v} = Segment(M_w, N_w)
M'_w: M_w - (l + 2 dec_w) w
N'_w: N_w - (l + 2 dec_w) w
Plan_w, m_w, n_w, n'_w, m'_w = Polygon(M_w, N_w, N'_w, M'_w)
Σsup_{u,v}: Element[coefEq, 1] (2 * (x - x(O_{u,v})) / l)^(2) + Element[coefEq, 2] 4 * (x - x(O_{u,v})) / l * (y - y(O_{u,v})) / l + Element[coefEq, 3] (2 * (y - y(O_{u,v})) / l)^(2) = 1
Q_{u,v,1}, Q_{u,v,2} = Intersect(Σsup_{u,v}, d_{u,v})
Q_{s,1}: Q_{u,v,1} - dec_w w
Q_{s,2}: Q_{u,v,2} - dec_w w
Q_{b,1}: Q_{u,v,1} - (h + dec_w) w
Q_{b,2}: Q_{u,v,2} - (h + dec_w) w
affsomsec_w = 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})
test_{Q1Ouv}: y(Q_{u,v,1}) - y(O_{u,v})
test_{Q2Ouv}: y(Q_{u,v,2}) - y(O_{u,v})
condcac_1: test_{Q1Ouv} > 0 ∧ φ_m > 90 ° ∨ test_{Q1Ouv} < 0 ∧ φ_m < 90 °
condcac_2: test_{Q2Ouv} > 0 ∧ φ_m > 90 ° ∨ test_{Q2Ouv} < 0 ∧ φ_m < 90 °
section_{u,v} = Sector(Σ_i, -θ - 3 / 4 * 3.14159, -θ + 13 / 4 * 3.14159)
affbase = true
affsombase = false
O_m: O_b - dep_{axe} w
O_M: O_b + (h + dep_{axe}) w
axe = Segment(O_m, O_M)
affaxe = true