水战演示：GeoGebra表面处理

GeoGebra 命令及参数

1. CurveCartesian(t, (-t^(2)) + 1, 0, t, -1, 1) → a
2. CurveCartesian(t, 0, (-2 * t^(2)) + 2, t, -1, 1) → b
3. Surface(t, ((1 - u) * ((-t^(2)) + 1)), (u * ((-2 * t^(2)) + 2)), t, -1, 1, u, 0, 1) → d
4. Point(yAxis) → C
5. CircumcircleArc(A, C, B) → c
6. Center(c) → D
7. Radius(c) → e
8. Angle(B, D, (0, 0)) → α
9. CurveCartesian(x(D) + (e * cos(t)), y(D) + (e * sin(t)), 0, t, π / 2 + α, (2 * π) + π / 2 - α) → f
10. Point(zAxis) → E
11. Surface(t, ((1 - f_1(u)) * ((-t^(2)) + 1)), (f_2(u) * ((-2 * t^(2)) + 2)), t, -1, 1, u, π / 2 - α, π / 2 + α) → i
12. Mirror(F, z = 0) → F'
13. Circle(F', e, zAxis) → p
14. Surface(x(D) + (e * cos(t)), y(D) + (e * sin(t)), ((-u) * z(F)), t, π / 2 + α, (2 * π) + π / 2 - α, u, 0, 1) → h
15. Surface(f_1(t), (((1 - u) * (1 - f_3(t))) * ((-f_1(t)^(2)) + 1)) + (u * f_2(t)), (((-(1 - u)) * f_3(t)) * ((-2 * f_1(t)^(2)) + 2)) + (u * z(F')), u, 0, 1, t, π / 2 - α, π / 2 + α) → m
16. Surface(((1 - u) * cos(t)) + (u * f_1(t)), ((u * (1 - f_3(t))) * ((-f_1(t)^(2)) + 1)) + ((1 - u) * ((-cos(t)^(2)) + 1)), (((-u) * f_3(t)) * ((-2 * f_1(t)^(2)) + 2)), u, 0, 1, t, π / 2 - α, π / 2 + α) → o
17. CurveCartesian(f_1(t), ((1 - f_3(t)) * ((-f_1(t)^(2)) + 1)), ((-f_3(t)) * ((-2 * f_1(t)^(2)) + 2)), t, π / 2 - α, π / 2 + α) → j
18. CurveCartesian(x(F) + (e * cos(t)), y(F) + (e * sin(t)), z(F'), t, π / 2 + α, (2 * π) + π / 2 - α) → g
19. CurveCartesian(x(F') + (e * cos(t)), y(F') + (e * sin(t)), z(F'), t, π / 2 - α, π / 2 + α) → l
20. Mirror(b, z = 0) → b'
21. Surface(t, ((1 - u) * ((-t^(2)) + 1)), ((-u) * ((-2 * t^(2)) + 2)), t, -1, 1, u, 0, 1) → n
22. Segment(D, B) → q
23. CurveCartesian(x(F) + (e * cos(t)), y(F) + (e * sin(t)), 0, t, π / 2 - α, π / 2 + α) → r