Pyramide

Prisme

θ = 0.4363323129985824 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
φ_m = 0.6981317007977318 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O_3: {0, 0, 0}
O_0: (Element[O_3, 1], Element[O_3, 2])
i_3: {1, 0, 0}
i = Vector(O_0, (Element[i_3, 1], Element[i_3, 2]))
j_3: {0, 1, 0}
j = Vector(O_0, (Element[j_3, 1], Element[j_3, 2]))
k_3: {0, 0, 1}
P: {-sin(φ_m), cos(φ_m), 0, -cos(φ_m) sin(θ), -sin(φ_m) sin(θ), cos(θ), cos(φ_m) cos(θ), sin(φ_m) cos(θ), sin(θ)}
u = Vector(O_0, (Element[P, 1] Element[i_3, 1] + Element[P, 2] Element[i_3, 2] + Element[P, 3] Element[i_3, 3], Element[P, 4] Element[i_3, 1] + Element[P, 5] Element[i_3, 2] + Element[P, 6] Element[i_3, 3]))
v = Vector(O_0, (Element[P, 1] Element[j_3, 1] + Element[P, 2] Element[j_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[j_3, 1] + Element[P, 5] Element[j_3, 2] + Element[P, 6] Element[j_3, 3]))
w = Vector(O_0, (Element[P, 1] Element[k_3, 1] + Element[P, 2] Element[k_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[k_3, 1] + Element[P, 5] Element[k_3, 2] + Element[P, 6] Element[k_3, 3]))
CoordA: {1, 0, 1}
A: Element[CoordA, 1] u + Element[CoordA, 2] v + Element[CoordA, 3] w
CoordB: {0, 1, 2}
B: Element[CoordB, 1] u + Element[CoordB, 2] v + Element[CoordB, 3] w
U_{A,B}(x) = Element[CoordA, 1] + (1 - x) * (Element[CoordB, 1] - Element[CoordA, 1])
V_{A,B}(x) = Element[CoordA, 2] + (1 - x) * (Element[CoordB, 2] - Element[CoordA, 2])
W_{A,B}(x) = Element[CoordA, 3] + (1 - x) * (Element[CoordB, 3] - Element[CoordA, 3])
X_{A,B}(x) = Element[P, 1] U_{A,B}(x) + Element[P, 2] V_{A,B}(x) + Element[P, 3] W_{A,B}(x)
Y_{A,B}(x) = Element[P, 4] U_{A,B}(x) + Element[P, 5] V_{A,B}(x) + Element[P, 6] W_{A,B}(x)
Se_{A,B} = CurveCartesian(X_{A,B}(t), Y_{A,B}(t), t, 0, 1)
r = 2 (slider from 0.5 to 5, step 0.5)
X_Σ(x) = Element[P, 1] cos(x) + Element[P, 2] sin(x)
Y_Σ(x) = Element[P, 4] cos(x) + Element[P, 5] sin(x)
O = (4, -3.84)
Σ_O = CurveCartesian(x(O) + r X_Σ(t), y(O) + r Y_Σ(t), t, 0, 6.28)
n = 5 (slider from 3 to 12, step 1)
h = 4 (slider from 0 to 5, step 0.5)
CoordS: {0, 0, h}
S: O + Element[CoordS, 1] u + Element[CoordS, 2] v + Element[CoordS, 3] w
k(x) = floor(n x / (2 * 3.14))
U_{Po}(x) = cos(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) * (cos((k(x) + 1) 2 * 3.14 / n) - cos(k(x) 2 * 3.14 / n))
V_{Po}(x) = sin(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) * (sin((k(x) + 1) 2 * 3.14 / n) - sin(k(x) 2 * 3.14 / n))
W_{po}(x) = 0
X_{Po}(x) = Element[P, 1] U_{Po}(x) + Element[P, 2] V_{Po}(x) + Element[P, 3] W_{po}(x)
Y_{Po}(x) = Element[P, 4] U_{Po}(x) + Element[P, 5] V_{Po}(x) + Element[P, 6] W_{po}(x)
Po_b = CurveCartesian(x(O) + r X_{Po}(t), y(O) + r Y_{Po}(t), t, 0, 6.28)
AffPyr = true
U_{Ar,Py}(x) = r cos(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) * (Element[CoordS, 1] - r cos(k(x) 2 * 3.14 / n))
V_{Ar,Py}(x) = r sin(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) * (Element[CoordS, 2] - r sin(k(x) 2 * 3.14 / n))
W_{Ar,Py}(x) = 0 + (n x / (2 * 3.14) - k(x)) Element[CoordS, 3]
X_{Ar,Py}(x) = Element[P, 1] U_{Ar,Py}(x) + Element[P, 2] V_{Ar,Py}(x) + Element[P, 3] W_{Ar,Py}(x)
Y_{Ar,Py}(x) = Element[P, 4] U_{Ar,Py}(x) + Element[P, 5] V_{Ar,Py}(x) + Element[P, 6] W_{Ar,Py}(x)
Ar_{Py} = CurveCartesian(x(O) + X_{Ar,Py}(t), y(O) + Y_{Ar,Py}(t), t, 0, 6.28)
AffPri = true
Po_h = CurveCartesian(x(S) + r X_{Po}(t), y(S) + r Y_{Po}(t), t, 0, 6.28)
U_{Ar,Pr}(x) = r cos(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) Element[CoordS, 1]
V_{Ar,Pr}(x) = r sin(k(x) 2 * 3.14 / n) + (n x / (2 * 3.14) - k(x)) Element[CoordS, 2]
W_{Ar,Pr}(x) = 0 + (n x / (2 * 3.14) - k(x)) Element[CoordS, 3]
X_{Ar,Pr}(x) = Element[P, 1] U_{Ar,Pr}(x) + Element[P, 2] V_{Ar,Pr}(x) + Element[P, 3] W_{Ar,Pr}(x)
Y_{Ar,Pr}(x) = Element[P, 4] U_{Ar,Pr}(x) + Element[P, 5] V_{Ar,Pr}(x) + Element[P, 6] W_{Ar,Pr}(x)
Ar_{Pr} = CurveCartesian(x(O) + X_{Ar,Pr}(t), y(O) + Y_{Ar,Pr}(t), t, 0, 6.28)