Custom Solid with Elliptical Cross Sections Parallel to yAxis

GeoGebra Commands & Parameters

1. Segment(H, I) → s_1
2. Midpoint(s_1) → A_1
3. Segment(J, K) → q_1
4. Midpoint(q_1) → Z
5. Midpoint(s_1) → E
6. Midpoint(q_1) → F
7. Intersect(upper, h, (0, 6)) → B
8. Intersect(lower, h, (0, -7)) → C
9. Segment(C, B) → q
10. Intersect(upper, q, (0, 6)) → G
11. Midpoint(C, G) → T
12. Line(B, D) → i
13. Segment(C, B) → p
14. Textfield(upper) → InputBox1
15. Textfield(lower) → InputBox2
16. Textfield(a) → InputBox3
17. Textfield(b) → InputBox4
18. Segment(C, G) → k_1
19. Line(C, G) → j
20. Line(T, T + (1, 0, 0)) → m
21. Line(F_1, F_1 + (1, 0, 0)) → n
22. Line(Z, Z + (1, 0, 0)) → f
23. Line(D_1, D_1 + (1, 0, 0)) → g
24. Line(T, T + (0, 0, 1)) → l
25. Sphere(T, Distance[G, T] / sqrt(1 - ecc^(2))) → c
26. Intersect(l, c) → V, W
27. CurveCartesian(x(C), y(T) + ((y(G) - y(T)) * cos(t)), ((z(W) - z(T)) * sin(t)), t, 0, (2 * pi)) → e
28. Point(e) → E_1
29. Line(E, E + (0, 0, 1)) → r
30. Point(e) → G_1
31. Conic(W, G_1, C, V, G) → s
32. Eccentricity(s) → k
33. Sphere(A_1, Distance[H, A_1] / sqrt(1 - ecc^(2))) → o
34. Intersect(r, o) → J_1, K_1
35. CurveCartesian(x(A_1), y(A_1) + ((y(H) - y(A_1)) * cos(t)), ((z(K_1) - z(A_1)) * sin(t)), t, 0, (2 * pi)) → t
36. Point(t) → L_1
37. Conic(K_1, L_1, I, J_1, H) → c_1
38. Line(F, F + (0, 0, 1)) → f_1
39. Sphere(F, Distance[J, F] / sqrt(1 - ecc^(2))) → u
40. Intersect(f_1, u) → M_1, N_1
41. CurveCartesian(x(F), y(F) + ((y(J) - y(F)) * cos(t)), ((z(N_1) - z(F)) * sin(t)), t, 0, (2 * pi)) → v
42. Point(v) → O_1
43. Conic(O_1, N_1, K, M_1, J) → d_1
44. Surface(u, (0.5 * (upper(u) + lower(u))) + ((0.5 * (upper(u) - lower(u))) * cos(v)), ((0.5 * sin(v)) * (upper(u) - lower(u)) / sqrt(1 - ecc^(2))), u, a, b, v, 0, (2 * pi)) → w