Aff. génératrice

Aff. génératrice_i

Aff. séquence génératrices

Aff. cercle

Aff. cercle_i

Aff. séquence cercles

%n = %v × 2 π

C_1 = Corner(1.0)
C_2 = Corner(2.0)
C_4 = Corner(4.0)
v_x = Vector(C_1, C_2)
v_y = Vector(C_1, C_4)
D_{Cyl,Con,Sph}: C_1 + 1.0 / 20.0 * v_x + 38.0 / 40.0 * v_y
chx = 2 (slider from 1 to 4, step 1)
TxtChx: {"Cylindre", "Cône", "Sphère", "Tous"}
txtChx: Element[TxtChx, chx] + ""
affgen = true
affgeni = true
affgenseq = true
affcer = true
affceri = true
affcerseq = true
D_θ: C_1 + 12.0 / 40.0 * v_x + 38.0 / 40.0 * v_y
θ = 0.767944870877505 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
D_φ: C_1 + 12.0 / 40.0 * v_x + 36.0 / 40.0 * v_y
φ = 0.5235987755982988 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
D_α: C_1 + 12.0 / 40.0 * v_x + 34.0 / 40.0 * v_y
α = 0 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
D_Θ: C_1 + 21.0 / 40.0 * v_x + 38.0 / 40.0 * v_y
n_Θ = 14 (slider from 0 to 40, step 1)
D_{Θ,i}: C_1 + 15.0 / 20.0 * v_x + 38.0 / 40.0 * v_y
F_{Θ,i}: D_{Θ,i} + 1.0 / 5.0 * v_x
D_ρ: C_1 + 21.0 / 40.0 * v_x + 36.0 / 40.0 * v_y
ρ = 4 (slider from 0 to 20, step 1)
D_h: C_1 + 21.0 / 40.0 * v_x + 34.0 / 40.0 * v_y
h = 4 (slider from 0 to 10, step 1)
n_Σ = 2 (slider from 0 to 12, step 1)
D_{h,i}: C_1 + 21.0 / 40.0 * v_x + 32.0 / 40.0 * v_y
F_{h,i}: D_{h,i} + 17.0 / 40.0 * v_x
s_{h,i} = Segment(D_{h,i}, F_{h,i})
D_Σ: C_1 + 15.0 / 20.0 * v_x + 34.0 / 40.0 * v_y
U: (sin(θ), -cos(θ) * sin(φ))
V: (cos(α) * cos(θ), cos(α) * sin(θ) * sin(φ) + sin(α) * cos(φ))
W: (-sin(α) * cos(θ), -sin(α) * sin(θ) * sin(φ) + cos(α) * cos(φ))
u = Vector((0.0, 0.0), U)
v = Vector((0.0, 0.0), V)
w = Vector((0.0, 0.0), W)
D_{m1}: C_1 + 21.0 / 40.0 * v_x + 30.0 / 40.0 * v_y
m_Θ = 0.77 (slider from 0 to 1, step 0.01)
D_{m2}: C_1 + 30.0 / 40.0 * v_x + 30.0 / 40.0 * v_y
m_2 = 0.27 (slider from 0 to 1, step 0.01)
Cyl_{gen,h,ρ,mΘ} = CurveCartesian(x(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + x(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + x(W) * t, y(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + y(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + y(W) * t, t, -(h), h)
Cyl_{gen,h,ρ} = Sequence(CurveCartesian[x(U) * ρ * cos(k * 2.0 * 3.141592653589793 / n_Θ) + x(V) * ρ * sin(k * 2.0 * 3.141592653589793 / n_Θ) + x(W) * t, y(U) * ρ * cos(k * 2.0 * 3.141592653589793 / n_Θ) + y(V) * ρ * sin(k * 2.0 * 3.141592653589793 / n_Θ) + y(W) * t, t, -(h), h], k, 0.0, n_Θ - 1.0)
Cyl_{cer,h,ρ,m2} = CurveCartesian(x(U) * ρ * cos(a) + x(V) * ρ * sin(a) + x(W) * (2.0 * m_2 - 1.0) * h, y(U) * ρ * cos(a) + y(V) * ρ * sin(a) + y(W) * (2.0 * m_2 - 1.0) * h, a, 0.0, 6.28319)
Cyl_{cer,h,ρ} = Sequence(CurveCartesian[x(U) * ρ * cos(a) + x(V) * ρ * sin(a) + x(W) * k, y(U) * ρ * cos(a) + y(V) * ρ * sin(a) + y(W) * k, a, 0.0, 6.28319], k, -(h), h, 1.0 / n_Σ)
Sph_{gen,ρ,mΘ} = CurveCartesian(x(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) * cos(Φ) + x(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) * cos(Φ) + x(W) * ρ * sin(Φ), y(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) * cos(Φ) + y(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) * cos(Φ) + y(W) * ρ * sin(Φ), Φ, -1.5708, 1.5708)
Sph_{gen,ρ} = Sequence(CurveCartesian[x(U) * ρ * cos(k * 2.0 * 3.141592653589793 / n_Θ) * cos(Φ) + x(V) * ρ * sin(k * 2.0 * 3.141592653589793 / n_Θ) * cos(Φ) + x(W) * ρ * sin(Φ), y(U) * ρ * cos(k * 2.0 * 3.141592653589793 / n_Θ) * cos(Φ) + y(V) * ρ * sin(k * 2.0 * 3.141592653589793 / n_Θ) * cos(Φ) + y(W) * ρ * sin(Φ), Φ, -1.5708, 1.5708], k, 0.0, n_Θ - 1.0)
Sph_{cer,ρ,m2} = If(m_2 ≠ floor(m_2), CurveCartesian[x(U) * ρ * cos(a) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + x(V) * ρ * sin(a) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + x(W) * ρ * sin(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0), y(U) * ρ * cos(a) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + y(V) * ρ * sin(a) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + y(W) * ρ * sin(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0), a, 0.0, 6.28319])
f = If(x ≥ 0.0, -2.0 * h / ρ * x + h)
Con_{gen,h,ρ,mΘ} = CurveCartesian(x(U) * r * cos(m_Θ * 2.0 * 3.141592653589793) + x(V) * r * sin(m_Θ * 2.0 * 3.141592653589793) + x(W) * f(r), y(U) * r * cos(m_Θ * 2.0 * 3.141592653589793) + y(V) * r * sin(m_Θ * 2.0 * 3.141592653589793) + y(W) * f(r), r, 0.0, ρ)
Con_{gen,h,ρ} = Sequence(CurveCartesian[x(U) * r * cos(k * 2.0 * 3.141592653589793 / n_Θ) + x(V) * r * sin(k * 2.0 * 3.141592653589793 / n_Θ) + x(W) * f(r), y(U) * r * cos(k * 2.0 * 3.141592653589793 / n_Θ) + y(V) * r * sin(k * 2.0 * 3.141592653589793 / n_Θ) + y(W) * f(r), r, 0.0, ρ], k, 0.0, n_Θ - 1.0)
Con_{cer,h,ρ,m_2} = If(m_2 ≠ 1.0, CurveCartesian[x(U) * (1.0 - m_2) * ρ * cos(a) + x(V) * (1.0 - m_2) * ρ * sin(a) + x(W) * f((1.0 - m_2) * ρ), y(U) * (1.0 - m_2) * ρ * cos(a) + y(V) * (1.0 - m_2) * ρ * sin(a) + y(W) * f((1.0 - m_2) * ρ), a, 0.0, 6.28319])
Con_{cer,h,ρ} = Sequence(CurveCartesian[x(U) * (1.0 / 2.0 - k / (2.0 * h)) * ρ * cos(a) + x(V) * (1.0 / 2.0 - k / (2.0 * h)) * ρ * sin(a) + x(W) * f((1.0 / 2.0 - k / (2.0 * h)) * ρ), y(U) * (1.0 / 2.0 - k / (2.0 * h)) * ρ * cos(a) + y(V) * (1.0 / 2.0 - k / (2.0 * h)) * ρ * sin(a) + y(W) * f((1.0 / 2.0 - k / (2.0 * h)) * ρ), a, 0.0, 6.28319], k, -(h), h - 1.0 / n_Σ, 1.0 / n_Σ)
Sph_{cer,ρ} = Sequence(CurveCartesian[x(U) * ρ * cos(a) * cos(k / ρ * 3.141592653589793 / 2.0) + x(V) * ρ * sin(a) * cos(k / ρ * 3.141592653589793 / 2.0) + x(W) * ρ * sin(k / ρ * 3.141592653589793 / 2.0), y(U) * ρ * cos(a) * cos(k / ρ * 3.141592653589793 / 2.0) + y(V) * ρ * sin(a) * cos(k / ρ * 3.141592653589793 / 2.0) + y(W) * ρ * sin(k / ρ * 3.141592653589793 / 2.0), a, 0.0, 6.28319], k, -(ρ) + 1.0 / n_Σ, ρ - 1.0 / n_Σ, 1.0 / n_Σ)
M_{Cyl}: (x(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + x(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + x(W) * (2.0 * m_2 - 1.0) * h, y(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + y(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + y(W) * (2.0 * m_2 - 1.0) * h)
M_{Con}: (x(U) * (1.0 - m_2) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + x(V) * (1.0 - m_2) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + x(W) * f((1.0 - m_2) * ρ), y(U) * (1.0 - m_2) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + y(V) * (1.0 - m_2) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + y(W) * f((1.0 - m_2) * ρ))
M_{Sph}: (x(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + x(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + x(W) * ρ * sin(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0), y(U) * ρ * cos(m_Θ * 2.0 * 3.141592653589793) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + y(V) * ρ * sin(m_Θ * 2.0 * 3.141592653589793) * cos(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0) + y(W) * ρ * sin(m_2 * 3.141592653589793 - 3.141592653589793 / 2.0))