57580492-440a-49ce-9b1e-edb0c2540abc 28 4 5 decimal

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Dome of Viviani Windows

A Viviani curve (or Viviani window) is generated by the intersection of a sphere and a cylinder that passes through the center of and is also tangent to sphere. This Animation shows a dome made out of of Viviani curves as the cylinder is rotated.

A real-life application of this can be seen at the Osaka Maritime Museum.

Поворот на угол α вокруг оси OX α Ω1 1000 α cos α sin - 0 α sin α cos 33 mat :

Поворот на угол φ вокруг оси OY φ Ω2 φ cos 0 φ sin 010 φ sin - 0 φ cos 33 mat :

Поворот на угол ψ вокруг оси OZ ψ Ω3 ψ cos ψ sin - 0 ψ sin ψ cos 000133 mat :

α π - 5 / :

φ π 8 / :

ψ 0.85 π * :

Матрица поворота  вокруг  трех осей γ α Ω1 φ Ω2 * ψ Ω3 * eval :

n 60 :

N 30 :

Δt 2 π n / * :

Δφ 2 π N / * :

Parametric equations i 1 n range x i el 1 Δt i 1 - (* cos + : y i el Δt i 1 - (* sin : z i el 212 / Δt * i 1 - (* sin * : s i el . : ras i el 10 : c i el blue : 61 line for t Vγ x y z augment Δφ t 1 - (* Ω3 * γ * : 21 line

u v Fs 2 u cos * v cos * 2 u cos * v sin * 2 u sin * 31 mat :

u v Fc v cos 1 + v sin u 31 mat :

S u v Fs 01 π * 02 π * 2020 CreateMesh γ * :

t C u v Fc 0202 π * 1020 CreateMesh Δφ t 1 - (* Ω3 * γ * :

τ 1 N range :

t Vγ 1 col t Vγ 2 col s ras c augment augment t C 1 col t C 2 col augment S 1 col S 2 col augment 5 1 sys

τ 3 N 16 + (range :

Dome of Viviani Windows

t N 3 + > ( t N 3 + : t t : if S 1 col S 2 col augment t 3 ≡ L t Vγ 1 col t Vγ 2 col augment : L L t Vγ 1 col t Vγ 2 col augment stack : if 7 1 sys