Aff. génératrice

Aff. génératrice_i

Aff. séquence génératrices

Aff. cercle

Aff. cercle_i

Aff. séquence cercles

Aff. f

θ = 1.186823891356144 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
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_θ: C_1 + 12.0 / 40.0 * v_x + 38.0 / 40.0 * v_y
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_2: 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)
A_φ: {{1.0, 0.0}, {0.0, sin(φ)}}
R_θ: {{cos(θ), -sin(θ)}, {sin(θ), cos(θ)}}
A'_φ: {{1.0, 0.0}, {0.0, cos(φ)}}
R_α: {{1.0, 0.0, 0.0}, {0.0, cos(α), -sin(α)}, {0.0, sin(α), cos(α)}}
U: A_φ * R_θ * (0.0, -1.0)
V_0: A_φ * R_θ * (1.0, 0.0)
W_0: A'_φ * (0.0, 1.0)
A: {{x(U), x(V_0), x(W_0)}, {y(U), y(V_0), y(W_0)}}
V: (Element[Element[A * R_α * {{0.0}, {1.0}, {0.0}}, 1.0], 1.0], Element[Element[A * R_α * {{0.0}, {1.0}, {0.0}}, 2.0], 1.0])
W: (Element[Element[A * R_α * {{0.0}, {0.0}, {1.0}}, 1.0], 1.0], Element[Element[A * R_α * {{0.0}, {0.0}, {1.0}}, 2.0], 1.0])
u = Vector((0.0, 0.0), U)
v = Vector((0.0, 0.0), V)
w = Vector((0.0, 0.0), W)
Σ_0 = CurveCartesian(x(U) * cos(a) + x(V) * sin(a) + x(W) * 0.0, y(U) * cos(a) + y(V) * sin(a) + y(W) * 0.0, a, 0.0, 6.283185307179586)
ε_0 = CurveCartesian(x(U) * sin(a) + x(V) * 0.0 + x(W) * cos(a), y(U) * sin(a) + y(V) * 0.0 + y(W) * cos(a), a, 0.0, 6.283185307179586)
ε_{90} = CurveCartesian(x(U) * 0.0 + x(V) * cos(a) + x(W) * sin(a), y(U) * 0.0 + y(V) * cos(a) + y(W) * sin(a), a, 0.0, 6.283185307179586)
affgen = true
affgeni = false
affgenseq = true
affcer = true
affceri = false
affcerseq = true
afff = false
D_Θ: C_1 + 21.0 / 40.0 * v_x + 38.0 / 40.0 * v_y
n_Θ = 24 (slider from 0 to 40, step 1)
Fonctions: {If[x > 0.0, -2.0 / x * cos(2.0 * x)], If[x ≥ 0.0, 1.0 / 4.0 * x * sin(x)], If[x ≥ 0.0, (-(x) / 3.0 + 4.0) * cos(x)], If[x ≥ 0.0, 3.0 * exp(-(x) / 10.0) * cos(x)], If[x ≥ 0.0, 16.0 * x * exp(-(x)) * sin(x)], If[x > 0.0, 1.0 / x], If[x ≥ 0.0, 1.0 / 2.0 * (x - 2.0) * sin(3.141592653589793 / 2.0 * x)]}
D_ρ: C_1 + 21.0 / 40.0 * v_x + 36.0 / 40.0 * v_y
ρ = 8 (slider from 1 to 25, step 1)
TxtF: {"-\frac{2}{x}\;cos(2x)", "\frac{1}{4}\;x\;sin(x)", "(-\frac{1}{3}\;x\;+4)\;cos(x)", "3\;exp(-\frac{x}{10})\;cos(x)", "16\;x\;exp(-x)\;sin(x)", "\frac{1}{x}", "\frac{1}{2}\;(x-2)\;sin(\frac{π}{2}x)"}
D_{fi}: C_1 + 1.0 / 20.0 * v_x + 38.0 / 40.0 * v_y
F_{fi}: D_{fi} + 1.0 / 5.0 * v_x
s_{fi} = Segment(D_{fi}, F_{fi})
C_{fi} = Point(s_{fi})
l_{fi}: floor((Length[Fonctions] - 1.0) * Distance[D_{fi}, C_{fi}] / s_{fi}) + 1.0
Grad_{fi} = Sequence(Segment[D_{fi} + k / (Length[Fonctions] - 1.0) * Vector[D_{fi}, F_{fi}], D_{fi} + k / (Length[Fonctions] - 1.0) * Vector[D_{fi}, F_{fi}] + 1.0 / 300.0 * v_y], k, 0.0, Length[Fonctions] - 1.0)
txtC_{fi}: "f_i = " + l_{fi}
Txtvalfonc: Element[TxtF, l_{fi}] + ""
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_Σ: C_1 + 15.0 / 20.0 * v_x + 36.0 / 40.0 * v_y
n_Σ = 4 (slider from 1 to 8, step 1)
D_{ρ,i}: C_1 + 21.0 / 40.0 * v_x + 34.0 / 40.0 * v_y
F_{ρ,i}: D_{ρ,i} + 17.0 / 40.0 * v_x
D_{mvt,1}: C_1 + 21.0 / 40.0 * v_x + 32.0 / 40.0 * v_y
m_Θ = 0.05 (slider from 0 to 1, step 0.01)
D_{mvt,2}: C_1 + 30.0 / 40.0 * v_x + 32.0 / 40.0 * v_y
m_2 = 0.33 (slider from 0.01 to 1, step 0.01)
f = Element(Fonctions, l_{fi})
Γ_{Θ,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)
Σ_{ρ,m_2} = CurveCartesian(x(U) * m_2 * ρ * cos(a) + x(V) * m_2 * ρ * sin(a) + x(W) * f(m_2 * ρ), y(U) * m_2 * ρ * cos(a) + y(V) * m_2 * ρ * sin(a) + y(W) * f(m_2 * ρ), a, 0.0, 6.28319)
Γ_Θ = 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, 1.0)
Σ_ρ = Sequence(CurveCartesian[x(U) * r * cos(a) + x(V) * r * sin(a) + x(W) * f(r), y(U) * r * cos(a) + y(V) * r * sin(a) + y(W) * f(r), a, 0.0, 6.28319], r, 1.0 / n_Σ, ρ, 1.0 / n_Σ)
M_{Γ,Σ}: (x(U) * m_2 * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + x(V) * m_2 * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + x(W) * f(m_2 * ρ), y(U) * m_2 * ρ * cos(m_Θ * 2.0 * 3.141592653589793) + y(V) * m_2 * ρ * sin(m_Θ * 2.0 * 3.141592653589793) + y(W) * f(m_2 * ρ))
f_{test} = If(x ≥ 0.0, 1.0 / 2.0 * (x - 2.0) * sin(3.141592653589793 / 2.0 * x))