Author: Créach Pierre-Yves

Nombre de points

Cacher les points

B3 = (5, 1)
B2 = (7, 2)
B1 = (-5, 1)
A10 = (2, -1)
A9 = (-2, 1)
A8 = (0, 4)
A7 = (3, 2)
A6 = (-1, 0)
A5 = (-4, -2)
A4 = (1, 3)
A3 = (4, 2)
A2 = (6, 2)
A1 = (-6, 2)
n = 3 (slider from 2 to 10, step 1)
B4 = (2, 1)
B5 = (-3, -2)
B6 = (0, 1)
B7 = (2.768493317643974, 0.32462151845565557)
B8 = (-1, 4)
B9 = (-3, 1)
B10 = (3, -4)
L_1: {A1, A2, A3, A4, A5, A6, A7, A8, A9, A10}
L_2: {B1, B2, B3, B4, B5, B6, B7, B8, B9, B10}
liste1 = Sequence(Segment[Element[L_2, i], Mirror[Element[L_2, i], Element[L_1, i]]], i, 1, n)
liste2: {{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}, {A9, B9}, {A10, B10}}
L_3 = Sort(Sequence[(Element[x(L_1), i], i), i, 1, n])
f_1 = Spline(Element[L_1, Element[y(L_3), 1]], Element[L_2, Element[y(L_3), 1]], Element[L_1, Element[y(L_3), 2]], Element[L_2, Element[y(L_3), 2]])
f_2 = Spline(Element[L_1, Element[y(L_3), 2]], Element[L_2, Element[y(L_3), 2]], Element[L_1, Element[y(L_3), 3]], Element[L_2, Element[y(L_3), 3]])
f_3 = Spline(Element[L_1, Element[y(L_3), 3]], Element[L_2, Element[y(L_3), 3]], Element[L_1, Element[y(L_3), 4]], Element[L_2, Element[y(L_3), 4]])
f_4 = Spline(Element[L_1, Element[y(L_3), 4]], Element[L_2, Element[y(L_3), 4]], Element[L_1, Element[y(L_3), 5]], Element[L_2, Element[y(L_3), 5]])
f_5 = Spline(Element[L_1, Element[y(L_3), 5]], Element[L_2, Element[y(L_3), 5]], Element[L_1, Element[y(L_3), 6]], Element[L_2, Element[y(L_3), 6]])
f_6 = Spline(Element[L_1, Element[y(L_3), 6]], Element[L_2, Element[y(L_3), 6]], Element[L_1, Element[y(L_3), 7]], Element[L_2, Element[y(L_3), 7]])
f_7 = Spline(Element[L_1, Element[y(L_3), 7]], Element[L_2, Element[y(L_3), 7]], Element[L_1, Element[y(L_3), 8]], Element[L_2, Element[y(L_3), 8]])
f_8 = Spline(Element[L_1, Element[y(L_3), 8]], Element[L_2, Element[y(L_3), 8]], Element[L_1, Element[y(L_3), 9]], Element[L_2, Element[y(L_3), 9]])
f_9 = Spline(Element[L_1, Element[y(L_3), 9]], Element[L_2, Element[y(L_3), 9]], Element[L_1, Element[y(L_3), 10]], Element[L_2, Element[y(L_3), 10]])
a = true

Tool: Spline
pointt, condition1, point2, condition2
Input: N_1, C_1, N_2, C_2
Output: f

d_1 = Line(C_1, N_1)
d_2 = Line(C_2, N_2)
a: (((Slope[d_1] + Slope[d_2]) * (x(N_1) - x(N_2))) - (2 * (y(N_1) - y(N_2)))) / (x(N_1) - x(N_2))^(3)
b: (Slope[d_1] - Slope[d_2]) / ((2 * (x(N_1) - x(N_2)))) - ((3 * a) * (x(N_1) + x(N_2)) / 2)
c: Slope[d_1] - ((3 * a) * x(N_1)^(2)) - ((2 * b) * x(N_1))
d: y(N_1) - (a * x(N_1)^(3)) - (b * x(N_1)^(2)) - (c * x(N_1))
f(x) = If[Min[x(N_1), x(N_2)] ≤ x ∧ x ≤ Max[x(N_1), x(N_2)], (a * x^(3)) + (b * x^(2)) + (c * x) + d]

Tool: Spline (command Spline1)
pointt, condition1, point2, condition2
Input: N_1, C_1, N_2, C_2
Output: f

d_1 = Line(C_1, N_1)
d_2 = Line(C_2, N_2)
a: (((Slope[d_1] + Slope[d_2]) * (x(N_1) - x(N_2))) - (2 * (y(N_1) - y(N_2)))) / (x(N_1) - x(N_2))^(3)
b: (Slope[d_1] - Slope[d_2]) / ((2 * (x(N_1) - x(N_2)))) - ((3 * a) * (x(N_1) + x(N_2)) / 2)
c: Slope[d_1] - ((3 * a) * x(N_1)^(2)) - ((2 * b) * x(N_1))
d: y(N_1) - (a * x(N_1)^(3)) - (b * x(N_1)^(2)) - (c * x(N_1))
f(x) = If[Min[x(N_1), x(N_2)] ≤ x ∧ x ≤ Max[x(N_1), x(N_2)], (a * x^(3)) + (b * x^(2)) + (c * x) + d]