圆锥曲面与侧面积的几何可视化

GeoGebra 命令及参数

1. Intersect(yAxis, xAxis) → C
2. OrthogonalLine((1, 0, 0), xOyPlane) → a
3. Intersect(xAxis, a) → B
4. Distance(B, C) → r
5. Point(a) → A
6. Angle(A, C, B) → α
7. Rotate(A, (t * α), yAxis) → A'
8. OrthogonalLine(A', xOyPlane) → f
9. Intersect(f, xOyPlane) → B'
10. Distance(A', B') → h
11. Rotate(C, β / 2, f) → C'
12. Distance(B', C') → r'
13. Circle(a, (0, 0, 0)) → c
14. Surface(((k - ((v * r') * cos((u * β / 2)))) * cos(ϕ)) - (((1 - v) * h) * sin(ϕ)), ((v * r') * sin((u * β / 2))), (((1 - v) * h) * cos(ϕ)) + ((k - ((v * r') * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1, v, 0, 1) → i
15. Cone(B, A, 1) → e, d, b
16. Rotate(C, (-(β / 2)), f) → C'_{1}
17. CircumcircleArc(C', C, C'_{1}) → g
18. CurveCartesian(((k - (r' * cos((u * β / 2)))) * cos(ϕ)), (r' * sin((u * β / 2))), ((k - ((v * r') * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1) → j
19. Segment(D, F) → l
20. Segment(E, F) → m