Pyramide

Prisme

rotation2 = 0.4363323129985824 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
rotation1 = 0.6981317007977318 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O_3: {0.0, 0.0, 0.0}
O_0: (Element[O_3, 1.0], Element[O_3, 2.0])
i_3: {1.0, 0.0, 0.0}
i = Vector(O_0, (Element[i_3, 1.0], Element[i_3, 2.0]))
j_3: {0.0, 1.0, 0.0}
j = Vector(O_0, (Element[j_3, 1.0], Element[j_3, 2.0]))
k_3: {0.0, 0.0, 1.0}
P: {-sin(rotation1), cos(rotation1), 0.0, -cos(rotation1) * sin(rotation2), -sin(rotation1) * sin(rotation2), cos(rotation2), cos(rotation1) * cos(rotation2), sin(rotation1) * cos(rotation2), sin(rotation2)}
u = Vector(O_0, (Element[P, 1.0] * Element[i_3, 1.0] + Element[P, 2.0] * Element[i_3, 2.0] + Element[P, 3.0] * Element[i_3, 3.0], Element[P, 4.0] * Element[i_3, 1.0] + Element[P, 5.0] * Element[i_3, 2.0] + Element[P, 6.0] * Element[i_3, 3.0]))
v = Vector(O_0, (Element[P, 1.0] * Element[j_3, 1.0] + Element[P, 2.0] * Element[j_3, 2.0] + Element[P, 3.0] * Element[j_3, 3.0], Element[P, 4.0] * Element[j_3, 1.0] + Element[P, 5.0] * Element[j_3, 2.0] + Element[P, 6.0] * Element[j_3, 3.0]))
w = Vector(O_0, (Element[P, 1.0] * Element[k_3, 1.0] + Element[P, 2.0] * Element[k_3, 2.0] + Element[P, 3.0] * Element[j_3, 3.0], Element[P, 4.0] * Element[k_3, 1.0] + Element[P, 5.0] * Element[k_3, 2.0] + Element[P, 6.0] * Element[k_3, 3.0]))
CoordA: {1.0, 0.0, 1.0}
A: Element[CoordA, 1.0] * u + Element[CoordA, 2.0] * v + Element[CoordA, 3.0] * w
CoordB: {0.0, 1.0, 2.0}
B: Element[CoordB, 1.0] * u + Element[CoordB, 2.0] * v + Element[CoordB, 3.0] * w
U_{A,B}(x) = Element[CoordA, 1.0] + (1.0 - x) * (Element[CoordB, 1.0] - Element[CoordA, 1.0])
V_{A,B}(x) = Element[CoordA, 2.0] + (1.0 - x) * (Element[CoordB, 2.0] - Element[CoordA, 2.0])
W_{A,B}(x) = Element[CoordA, 3.0] + (1.0 - x) * (Element[CoordB, 3.0] - Element[CoordA, 3.0])
X_{A,B}(x) = Element[P, 1.0] * U_{A,B}(x) + Element[P, 2.0] * V_{A,B}(x) + Element[P, 3.0] * W_{A,B}(x)
Y_{A,B}(x) = Element[P, 4.0] * U_{A,B}(x) + Element[P, 5.0] * V_{A,B}(x) + Element[P, 6.0] * W_{A,B}(x)
Se_{A,B} = CurveCartesian(X_{A,B}(t), Y_{A,B}(t), t, 0.0, 1.0)
rayon = 2 (slider from 0.5 to 5, step 0.5)
X_Σ(x) = Element[P, 1.0] * cos(x) + Element[P, 2.0] * sin(x)
Y_Σ(x) = Element[P, 4.0] * cos(x) + Element[P, 5.0] * sin(x)
O = (4, -3.84)
Σ_O = CurveCartesian(x(O) + rayon * X_Σ(t), y(O) + rayon * Y_Σ(t), t, 0.0, 6.28)
nbcôtésbase = 5 (slider from 3 to 24, step 1)
hauteur = 5 (slider from 0 to 6, step 0.5)
CoordS: {0.0, 0.0, hauteur}
S: O + Element[CoordS, 1.0] * u + Element[CoordS, 2.0] * v + Element[CoordS, 3.0] * w
k(x) = floor(nbcôtésbase * x / (2.0 * 3.14))
U_{Po}(x) = cos(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * (cos((k(x) + 1.0) * 2.0 * 3.14 / nbcôtésbase) - cos(k(x) * 2.0 * 3.14 / nbcôtésbase))
V_{Po}(x) = sin(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * (sin((k(x) + 1.0) * 2.0 * 3.14 / nbcôtésbase) - sin(k(x) * 2.0 * 3.14 / nbcôtésbase))
W_{po}(x) = 0.0
X_{Po}(x) = Element[P, 1.0] * U_{Po}(x) + Element[P, 2.0] * V_{Po}(x) + Element[P, 3.0] * W_{po}(x)
Y_{Po}(x) = Element[P, 4.0] * U_{Po}(x) + Element[P, 5.0] * V_{Po}(x) + Element[P, 6.0] * W_{po}(x)
Po_b = CurveCartesian(x(O) + rayon * X_{Po}(t), y(O) + rayon * Y_{Po}(t), t, 0.0, 6.28)
AffPyr = true
U_{Ar,Py}(x) = rayon * cos(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * (Element[CoordS, 1.0] - rayon * cos(k(x) * 2.0 * 3.14 / nbcôtésbase))
V_{Ar,Py}(x) = rayon * sin(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * (Element[CoordS, 2.0] - rayon * sin(k(x) * 2.0 * 3.14 / nbcôtésbase))
W_{Ar,Py}(x) = (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * Element[CoordS, 3.0]
X_{Ar,Py}(x) = Element[P, 1.0] * U_{Ar,Py}(x) + Element[P, 2.0] * V_{Ar,Py}(x) + Element[P, 3.0] * W_{Ar,Py}(x)
Y_{Ar,Py}(x) = Element[P, 4.0] * U_{Ar,Py}(x) + Element[P, 5.0] * V_{Ar,Py}(x) + Element[P, 6.0] * W_{Ar,Py}(x)
Ar_{Py} = CurveCartesian(x(O) + X_{Ar,Py}(t), y(O) + Y_{Ar,Py}(t), t, 0.0, 6.28)
AffPri = false
Po_h = CurveCartesian(x(S) + rayon * X_{Po}(t), y(S) + rayon * Y_{Po}(t), t, 0.0, 6.28)
U_{Ar,Pr}(x) = rayon * cos(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * Element[CoordS, 1.0]
V_{Ar,Pr}(x) = rayon * sin(k(x) * 2.0 * 3.14 / nbcôtésbase) + (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * Element[CoordS, 2.0]
W_{Ar,Pr}(x) = (nbcôtésbase * x / (2.0 * 3.14) - k(x)) * Element[CoordS, 3.0]
X_{Ar,Pr}(x) = Element[P, 1.0] * U_{Ar,Pr}(x) + Element[P, 2.0] * V_{Ar,Pr}(x) + Element[P, 3.0] * W_{Ar,Pr}(x)
Y_{Ar,Pr}(x) = Element[P, 4.0] * U_{Ar,Pr}(x) + Element[P, 5.0] * V_{Ar,Pr}(x) + Element[P, 6.0] * W_{Ar,Pr}(x)
Ar_{Pr} = CurveCartesian(x(O) + X_{Ar,Pr}(t), y(O) + Y_{Ar,Pr}(t), t, 0.0, 6.28)