Aff. sommets

Aff. H

Aff. [SH]

Aff. O_b

Aff. sec_{u,v}

Aff. plan_{u,v}

Aff. d_w et P_0

Aff. som. sec_{u,v}

k_{mem} = 0.78 (slider from 0 to 1, step 0.01)
dep = 3
dec_v = 2
dec_u = 2
h = 6 (slider from 0 to 10, step 0.5)
k_3: {0, 0, 1}
O_b = (10, -2)
l_v = 4.5 (slider from 0 to 10, step 0.5)
l_u = 4 (slider from 0 to 10, step 0.5)
θ = 0.5235987755982988 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)}
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]))
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]))
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: O_b + l_u / 2 u - l_v / 2 v
B_w: B + dec_u u - dec_v v
W_M: B_w + (h + dep) w
W_m: B_w - dep w
d_w = Segment(W_m, W_M)
P_0 = Point(d_w)
S_w: B_w + h w
k = If((φ_m ≠ 0 °) ∧ (φ_m ≠ 180 °), Length[Vector[S_w, P_0]] / Length[Vector[S_w, B_w]], k_{mem})
Z_0 = (-1, 5)
i = Vector(O, (Element[i_3, 1], Element[i_3, 2]))
Z_2: Z_0 + 4 i
s_{Z0Z2} = Segment(Z_0, Z_2)
H_0 = Point(s_{Z0Z2})
j = Vector(O, (Element[j_3, 1], Element[j_3, 2]))
Z_1: Z_0 - 1 / 2 j
Z_3: Z_1 + 4 i
s_{Z1Z3} = Segment(Z_1, Z_3)
H_1 = Point(s_{Z1Z3})
l_{H,u}: Length[Vector[Z_0, H_0]] / Length[Vector[Z_0, Z_2]] l_u
l_{H,v}: Length[Vector[Z_1, H_1]] / Length[Vector[Z_1, Z_3]] l_v
A: O_b - l_u / 2 u - l_v / 2 v
H: A + l_{H,u} u + l_{H,v} v
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: O_b + l_u / 2 u + l_v / 2 v
D: O_b - l_u / 2 u + l_v / 2 v
svis_{AB} = Segment(A, B)
scac_{BC} = Segment(B, C)
scac_{CD} = Segment(C, D)
scac_{DA} = Segment(D, A)
scac_{AB} = Segment(A, B)
svis_{DA} = Segment(D, A)
svis_{BC} = Segment(B, C)
svis_{CD} = Segment(C, D)
affsom = false
textl_{H,u}: Name[l_{H,u}] + "\,=\, " + l_{H,u}
textl_{H,v}: Name[l_{H,v}] + "\,=\," + l_{H,v}
S: H + h w
scac_{SA} = Segment(S, A)
svis_{SA} = Segment(S, A)
scac_{SB} = Segment(S, B)
svis_{SB} = Segment(S, B)
scac_{SC} = Segment(S, C)
svis_{SC} = Segment(S, C)
scac_{SD} = Segment(S, D)
svis_{SD} = Segment(S, D)
condcac_{ABCD}: φ_m > 90 °
a_{DA}: (y(A) - y(D)) / (x(A) - x(D))
b_{DA}: y(D) - a_{DA} x(D)
f_{DA}(x) = a_{DA} x + b_{DA}
condSsurDA: y(S) > f_{DA}(x(S))
a_{AB}: (y(B) - y(A)) / (x(B) - x(A))
b_{AB}: y(A) - a_{AB} x(A)
f_{AB}(x) = a_{AB} x + b_{AB}
condSsurAB: y(S) > f_{AB}(x(S))
condcac_{SAB}: θ < 180 ° ∧ condSsurAB ∨ θ > 180 ° ∧ (θ ≠ 360 °) ∧ (¬condSsurAB) ∨ (θ ≟ 0 ° ∨ θ ≟ 360 °) ∧ y(B) > y(A) ∨ θ ≟ 180 ° ∧ y(B) < y(A)
condcac_{SDA}: (θ < 90 ° ∨ θ > 270 °) ∧ condSsurDA ∨ 90 ° < θ ∧ θ < 270 ° ∧ (¬condSsurDA) ∨ θ ≟ 90 ° ∧ y(D) > y(A) ∨ θ ≟ 270 ° ∧ y(D) < y(A)
a_{BC}: (y(C) - y(B)) / (x(C) - x(B))
b_{BC}: y(B) - a_{BC} x(B)
f_{BC}(x) = a_{BC} x + b_{BC}
condSsurBC: y(S) > f_{BC}(x(S))
condcac_{SBC}: (θ < 90 ° ∨ θ > 270 °) ∧ (¬condSsurBC) ∨ 90 ° < θ ∧ θ < 270 ° ∧ condSsurBC ∨ θ ≟ 90 ° ∧ y(C) > y(B) ∨ θ ≟ 270 ° ∧ y(B) > y(C)
a_{CD}: (y(D) - y(C)) / (x(D) - x(C))
b_{CD}: y(C) - a_{CD} x(C)
f_{CD}(x) = a_{CD} x + b_{CD}
condSsurCD: y(S) > f_{CD}(x(S))
condcac_{SCD}: (θ ≠ 0 °) ∧ θ < 180 ° ∧ (¬condSsurCD) ∨ 180 ° < θ ∧ (θ ≠ 360 °) ∧ condSsurCD ∨ (θ ≟ 0 ° ∨ θ ≟ 360 °) ∧ y(C) > y(D) ∨ θ ≟ 180 ° ∧ y(C) < y(D)
affH = true
affSH = true
scac_{SH} = Segment(S, H)
l_{croix} = 0.1
H_{0,1}: H + l_{croix} * (u - v)
H_{0,2}: H + l_{croix} * (u + v)
H_{0,3}: H + l_{croix} * (-u + v)
H_{0,0}: H + l_{croix} * (-u - v)
s_{H00H02} = Segment(H_{0,0}, H_{0,2})
s_{H01H03} = Segment(H_{0,1}, H_{0,3})
textH: Name[H] + ""
vectdec_u = Vector(B, B + dec_u u)
vectdec_v = Vector(B + dec_u u, B + dec_u u - dec_v v)
affO_b = false
affsec_{u,v} = true
affplan_{u,v} = true
affdroite_w = true
P_{0,1}: P_0 + (l_v + 2 dec_v) v
P_{0,2}: P_0 + (l_v + 2 dec_v) v - (l_u + 2 dec_u) u
P_{0,3}: P_0 - (l_u + 2 dec_u) u
Plan_{u,v}, p_{0,0}, p_{0,1}, p_{0,2}, p_{0,3} = Polygon(P_0, P_{0,1}, P_{0,2}, P_{0,3})
test_w: Length[Vector[S_w, P_0]] + Length[Vector[P_0, B_w]] - Length[Vector[S_w, B_w]]
exissec_{u,v}: test_w ≟ 0
affsomsec_{u,v} = false
H_i: S - k h w
H_{i,0}: H_i + k l_{croix} * (-u - v)
H_{i,1}: H_i + k l_{croix} * (u - v)
H_{i,2}: H_i + k l_{croix} * (u + v)
H_{i,3}: H_i + k l_{croix} * (-u + v)
s_{Hi0Hi2} = Segment(H_{i,0}, H_{i,2})
s_{Hi1Hi3} = Segment(H_{i,1}, H_{i,3})
A_i: S + k Vector[S, A]
B_i: S + k Vector[S, B]
C_i: S + k Vector[S, C]
D_i: S + k Vector[S, D]
text1: Name[H_i] + ""
scac_{AiBi} = Segment(A_i, B_i)
svis_{AiBi} = Segment(A_i, B_i)
scac_{BiCi} = Segment(B_i, C_i)
svis_{BiCi} = Segment(B_i, C_i)
scac_{CiDi} = Segment(C_i, D_i)
svis_{CiDi} = Segment(C_i, D_i)
scac_{DiAi} = Segment(D_i, A_i)
svis_{DiAi} = Segment(D_i, A_i)
section_{u,v}, a_i, b_i, c_i, d_i = Polygon(A_i, B_i, C_i, D_i)
textmem: "MÉMOIRE" + " 
 Ajustez la valeur de " + (Name[k_{mem}]) + " 
 " + (Name[k]) + " = " + k
intφ_m = 0.08726646259971647 rad