Vue du dessus

Aff. param. persp.

Aff. ellipses

Aff. découpage

Aff. faces cachées

Aff. intérieur

Aff. faces

Aff. pavé base

ε(x) = x - floor(x)
α = 0.6981317007977318 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
λ = 0.65 (slider from 0.5 to 1, step 0.05)
v = Vector((0, 0), (λ cos(α), λ sin(α)))
u = Vector((0, 0), (1, 0))
l_u = 1.5 (slider from 0 to 5, step 0.5)
l_v = 1 (slider from 0 to 5, step 0.5)
k = 4 (slider from 0 to 8, step 1)
δ_0(x) = 1 - floor(x / (k - 1))
δ_1(x) = floor(x / (k - 1))
B_0 = (7, 1)
f_{u,v,+}(x) = λ^(2) cos(α) sin(α) / (1 + λ^(2) cos(α)^(2)) x + λ sin(α) / (1 + λ^(2) cos(α)^(2)) sqrt(-x^(2) + 1 + λ^(2) cos(α)^(2))
coefEl_{u,v}: {1, -2 cos(α) / sin(α), (1 + λ^(2) cos(α)^(2)) / (λ^(2) sin(α)^(2))}
w = Vector((0, 0), (0, 1))
k_0 = 2 (slider from 0 to 4, step 0.5)
C_{0,0}: (0, 0) + k_0 / 2 * (-u - w - v)
C_{0,1}: (0, 0) + k_0 / 2 * (u - w - v)
C_{0,2}: (0, 0) + k_0 / 2 * (u - w + v)
C_{0,3}: (0, 0) + k_0 / 2 * (-u - w + v)
C_{0,4}: (0, 0) + k_0 / 2 * (-u + w - v)
C_{0,5}: (0, 0) + k_0 / 2 * (u + w - v)
C_{0,6}: (0, 0) + k_0 / 2 * (u + w + v)
C_{0,7}: (0, 0) + k_0 / 2 * (-u + w + v)
svis_{C00C01} = Segment(C_{0,0}, C_{0,1})
svis_{C01C02} = Segment(C_{0,1}, C_{0,2})
svis_{C02C03} = Segment(C_{0,2}, C_{0,3})
svis_{C03C00} = Segment(C_{0,3}, C_{0,0})
svis_{C04C05} = Segment(C_{0,4}, C_{0,5})
svis_{C05C06} = Segment(C_{0,5}, C_{0,6})
svis_{C06C07} = Segment(C_{0,6}, C_{0,7})
svis_{C07C04} = Segment(C_{0,7}, C_{0,4})
svis_{C00C04} = Segment(C_{0,0}, C_{0,4})
svis_{C01C05} = Segment(C_{0,1}, C_{0,5})
svis_{C02C06} = Segment(C_{0,2}, C_{0,6})
svis_{C03C07} = Segment(C_{0,3}, C_{0,7})
vue_{dessus} = true
scac_{C04C05} = Segment(C_{0,4}, C_{0,5})
scac_{C01C05} = Segment(C_{0,1}, C_{0,5})
scac_{C05C06} = Segment(C_{0,5}, C_{0,6})
scac_{C02C03} = Segment(C_{0,2}, C_{0,3})
scac_{C03C07} = Segment(C_{0,3}, C_{0,7})
scac_{C03C00} = Segment(C_{0,3}, C_{0,0})
condcac_{w,u,1}: ¬vue_{dessus}
condcac_{v,w,2}: vue_{dessus} ∧ 90 ° ≤ α ∨ (¬vue_{dessus}) ∧ α ≤ 90 °
scac_{C01C02} = Segment(C_{0,1}, C_{0,2})
scac_{C00C04} = Segment(C_{0,0}, C_{0,4})
scac_{C02C06} = Segment(C_{0,2}, C_{0,6})
scac_{C07C04} = Segment(C_{0,7}, C_{0,4})
condcac_{w,u,2}: ¬condcac_{w,u,1}
condcac_{v,w,1}: ¬condcac_{v,w,2}
condcac_{u,v,2}: ¬vue_{dessus}
condcac_{u,v,1}: ¬condcac_{u,v,2}
El_{u,v}: Element[coefEl_{u,v}, 1] x^(2) + Element[coefEl_{u,v}, 2] x y + Element[coefEl_{u,v}, 3] y^(2) = 1
T_{u,v,0}: (sqrt(1 + λ^(2) cos(α)^(2)), λ^(2) cos(α) sin(α) / (1 + λ^(2) cos(α)^(2)) sqrt(1 + λ^(2) cos(α)^(2)))
T_{u,v,1}: (-sqrt(1 + λ^(2) cos(α)^(2)), -λ^(2) cos(α) sin(α) / (1 + λ^(2) cos(α)^(2)) sqrt(1 + λ^(2) cos(α)^(2)))
f_{u,v,-}(x) = -f_{u,v,+}(-x)
s_{Tuv0Tuv1} = Segment(T_{u,v,0}, T_{u,v,1})
affper = false
affell = false
l_w = 1 (slider from 0 to 5, step 0.5)
A_0 = (3, 1)
A_1: A_0 + l_u u
A_2: A_0 + l_u u + l_v v
A_3: A_0 + l_v v
A_4: A_0 + l_w w
A_5: A_0 + l_u u + l_w w
A_6: A_0 + l_u u + l_v v + l_w w
A_7: A_0 + l_v v + l_w w
svis_{A0A1} = Segment(A_0, A_1)
scac_{A1A2} = Segment(A_1, A_2)
svis_{A1A2} = Segment(A_1, A_2)
scac_{A2A3} = Segment(A_2, A_3)
svis_{A2A3} = Segment(A_2, A_3)
scac_{A3A0} = Segment(A_3, A_0)
svis_{A3A0} = Segment(A_3, A_0)
scac_{A0A4} = Segment(A_0, A_4)
svis_{A0A4} = Segment(A_0, A_4)
scac_{A1A5} = Segment(A_1, A_5)
svis_{A1A5} = Segment(A_1, A_5)
scac_{A2A6} = Segment(A_2, A_6)
svis_{A2A6} = Segment(A_2, A_6)
scac_{A3A7} = Segment(A_3, A_7)
svis_{A3A7} = Segment(A_3, A_7)
scac_{A4A5} = Segment(A_4, A_5)
svis_{A4A5} = Segment(A_4, A_5)
scac_{A5A6} = Segment(A_5, A_6)
svis_{A5A6} = Segment(A_5, A_6)
svis_{A6A7} = Segment(A_6, A_7)
scac_{A7A4} = Segment(A_7, A_4)
svis_{A7A4} = Segment(A_7, A_4)
B_1: B_0 + k l_u u
B_2: B_0 + k * (l_u u + l_v v)
B_3: B_0 + k l_v v
B_4: B_0 + k l_w w
B_5: B_0 + k * (l_u u + l_w w)
B_6: B_0 + k * (l_u u + l_v v + l_w w)
B_7: B_0 + k * (l_v v + l_w w)
svis_{B0B1} = Segment(B_0, B_1)
scac_{B1B2} = Segment(B_1, B_2)
svis_{B1B2} = Segment(B_1, B_2)
scac_{B2B3} = Segment(B_2, B_3)
svis_{B2B3} = Segment(B_2, B_3)
scac_{B3B0} = Segment(B_3, B_0)
svis_{B3B0} = Segment(B_3, B_0)
scac_{B0B4} = Segment(B_0, B_4)
svis_{B0B4} = Segment(B_0, B_4)
scac_{B1B5} = Segment(B_1, B_5)
svis_{B1B5} = Segment(B_1, B_5)
scac_{B2B6} = Segment(B_2, B_6)
svis_{B2B6} = Segment(B_2, B_6)
scac_{B3B7} = Segment(B_3, B_7)
svis_{B3B7} = Segment(B_3, B_7)
scac_{B4B5} = Segment(B_4, B_5)
svis_{B4B5} = Segment(B_4, B_5)
scac_{B5B6} = Segment(B_5, B_6)
svis_{B5B6} = Segment(B_5, B_6)
svis_{B6B7} = Segment(B_6, B_7)
X_1(x) = δ_0(x) * (x(B_0) + (floor(x) + 1) l_v x(v) + k ε(x) l_u x(u)) + δ_1(x) * (x(B_0) + (floor(x - (k - 1)) + 1) l_u x(u) + k ε(x) l_v x(v))
scac_{B7B4} = Segment(B_7, B_4)
svis_{B7B4} = Segment(B_7, B_4)
Y_1(x) = δ_0(x) * (y(B_0) + (floor(x) + 1) l_v y(v)) + δ_1(x) * (y(B_0) + k ε(x) l_v y(v))
dec_1 = CurveCartesian(X_1(t), Y_1(t), t, 0, 2 * (k - 1))
affdec = true
afffacecac = false
Y_2(x) = δ_0(x) * (y(B_0) + k l_w y(w) + (floor(x) + 1) l_v y(v)) + δ_1(x) * (y(B_0) + k l_w y(w) + k ε(x) l_v y(v))
dec_2 = CurveCartesian(X_1(t), Y_2(t), t, 0, 2 * (k - 1))
X_3(x) = δ_0(x) * (x(B_0) + (floor(x) + 1) l_v x(v)) + δ_1(x) * (x(B_0) + k ε(x) l_v x(v))
Y_3(x) = δ_0(x) * (y(B_0) + (floor(x) + 1) l_v y(v) + k ε(x) l_w y(w)) + δ_1(x) * (y(B_0) + (floor(x - (k - 1)) + 1) l_w y(w) + k ε(x) l_v y(v))
dec_3 = CurveCartesian(X_3(t), Y_3(t), t, 0, 2 * (k - 1))
X_4(x) = δ_0(x) * (x(B_0) + k l_u x(u) + (floor(x) + 1) l_v x(v)) + δ_1(x) * (x(B_0) + k l_u x(u) + k ε(x) l_v x(v))
dec_4 = CurveCartesian(X_4(t), Y_3(t), t, 0, 2 * (k - 1))
X_5(x) = δ_0(x) * (x(B_0) + (floor(x) + 1) l_u x(u)) + δ_1(x) * (x(B_0) + k ε(x) l_u x(u))
Y_5(x) = δ_0(x) * (y(B_0) + k ε(x) l_w y(w)) + δ_1(x) * (y(B_0) + (floor(x - (k - 1)) + 1) l_w y(w))
dec_5 = CurveCartesian(X_5(t), Y_5(t), t, 0, 2 * (k - 1))
X_6(x) = δ_0(x) * (x(B_0) + k l_v x(v) + (floor(x) + 1) l_u x(u)) + δ_1(x) * (x(B_0) + k l_v x(v) + k ε(x) l_u x(u))
Y_6(x) = δ_0(x) * (y(B_0) + k l_v y(v) + k ε(x) l_w y(w)) + δ_1(x) * (y(B_0) + k l_v y(v) + (floor(x - (k - 1)) + 1) l_w y(w))
dec_6 = CurveCartesian(X_6(t), Y_6(t), t, 0, 2 * (k - 1))
X_u(x) = x(B_0) + (δ_1(x) + 1) l_w x(w) + (floor(x - δ_1(x) * (k - 1)) + 1) l_v x(v) + k ε(x) l_u x(u)
Y_u(x) = y(B_0) + (δ_1(x) + 1) l_w y(w) + (floor(x - δ_1(x) * (k - 1)) + 1) l_v y(v)
dec_u = CurveCartesian(X_u(t), Y_u(t), t, 0, (k - 1)^(2))
affint = false
affface = true
X_v(x) = x(B_0) + (δ_1(x) + 1) l_w x(w) + (floor(x - δ_1(x) * (k - 1)) + 1) l_u x(u) + k ε(x) l_v x(v)
Y_v(x) = y(B_0) + (δ_1(x) + 1) l_w y(w) + (floor(x - δ_1(x) * (k - 1)) + 1) l_u y(u) + k ε(x) l_v y(v)
dec_v = CurveCartesian(X_v(t), Y_v(t), t, 0, (k - 1)^(2))
X_w(x) = x(B_0) + (δ_1(x) + 1) l_u x(u) + (floor(x - δ_1(x) * (k - 1)) + 1) l_v x(v)
Y_w(x) = y(B_0) + (δ_1(x) + 1) l_u y(u) + (floor(x - δ_1(x) * (k - 1)) + 1) l_v y(v) + k ε(x) l_w y(w)
dec_w = CurveCartesian(X_w(t), Y_w(t), t, 0, (k - 1)^(2))
affpav = false
γ_0 = If(0 ≤ x ∧ x < 1, 1, 0)
γ_1 = If(1 ≤ x ∧ x < 2, 1, 0)
γ_2 = If(2 ≤ x ∧ x < 3, 1, 0)
X_{p,1}(x) = γ_0(x) * (x(B_0) + (k - 1) l_u x(u) + ε(x) l_v x(v)) + γ_1(x) * (x(B_0) + (k - 1) l_u x(u) + l_v x(v) + ε(x) l_u x(u)) + γ_2(x) * (x(B_0) + (k - 1) l_u x(u) + l_v x(v))
Y_{p,1}(x) = γ_0(x) * (y(B_0) + (k - 1) l_w y(w) + ε(x) l_v y(v)) + γ_1(x) * (y(B_0) + (k - 1) l_w y(w) + l_v y(v)) + γ_2(x) * (y(B_0) + (k - 1) l_w y(w) + l_v y(v) + ε(x) l_w y(w))
dec_{p,1} = CurveCartesian(X_{p,1}(t), Y_{p,1}(t), t, 0, 3)
X_{p,2}(x) = γ_0(x) * (x(B_0) + l_v x(v) + ε(x) l_u x(u)) + γ_1(x) * (x(B_0) + l_v x(v) + l_u x(u) - ε(x) l_v x(v)) + γ_2(x) * (x(B_0) + l_v x(v) + l_u x(u))
Y_{p,2}(x) = γ_0(x) * (y(B_0) + (k - 1) l_w y(w) + l_v y(v)) + γ_1(x) * (y(B_0) + (k - 1) l_w y(w) + l_v y(v) - ε(x) l_v y(v)) + γ_2(x) * (y(B_0) + (k - 1) l_w y(w) + l_v y(v) + ε(x) l_w y(w))
dec_{p,2} = CurveCartesian(X_{p,2}(t), Y_{p,2}(t), t, 0, 3)
X_{p,3}(x) = γ_0(x) * (x(B_0) + (k - 1) l_v x(v) + ε(x) l_u x(u)) + γ_1(x) * (x(B_0) + (k - 1) l_v x(v) + l_u x(u)) + γ_2(x) * (x(B_0) + (k - 1) l_v x(v) + l_u x(u) + ε(x) l_v x(v))
Y_{p,3}(x) = γ_0(x) * (y(B_0) + (k - 1) l_v y(v) + l_w y(w)) + γ_1(x) * (y(B_0) + (k - 1) l_v y(v) + l_w y(w) - ε(x) l_w y(w)) + γ_2(x) * (y(B_0) + (k - 1) l_v y(v) + l_w y(w) + ε(x) l_v y(v))
dec_{p,3} = CurveCartesian(X_{p,3}(t), Y_{p,3}(t), t, 0, 3)
X_{p,4}(x) = γ_0(x) * (x(B_0) + (k - 1) l_v x(v) + (k - 1) l_u x(u)) + γ_1(x) * (x(B_0) + (k - 1) l_v x(v) + (k - 1) l_u x(u) + ε(x) l_u x(u)) + γ_2(x) * (x(B_0) + (k - 1) l_v x(v) + (k - 1) l_u x(u) + ε(x) l_v x(v))
Y_{p,4}(x) = γ_0(x) * (y(B_0) + (k - 1) l_v y(v) + ε(x) l_w y(w)) + γ_1(x) * (y(B_0) + (k - 1) l_v y(v) + l_w y(w)) + γ_2(x) * (y(B_0) + (k - 1) l_v y(v) + l_w y(w) + ε(x) l_v y(v))
dec_{p,4} = CurveCartesian(X_{p,4}(t), Y_{p,4}(t), t, 0, 3)