有规曲面：用分段直线生成与几何变换构造

GeoGebra 命令及参数

1. Midpoint(A, B) → C
2. Midpoint(C, B) → E
3. Mirror(D, E) → D'
4. Sequence(Translate[A, Vector[(i * Vector[A, D'])]], i, 0, 1, 1 / n) → l1
5. Sequence(Translate[A, Vector[(i * Vector[A, D])]], i, 0, 1, 1 / n) → l2
6. Sequence(Translate[D, Vector[(i * Vector[D, B])]], i, 0, 1, 1 / n) → l3
7. Sequence(Translate[B, Vector[(i * Vector[B, D'])]], i, 0, 1, 1 / n) → l4
8. Sequence(Segment[Element[l1, i], Element[l2, Length[l2] - i]], i, 1, Length[l1]) → l5
9. Sequence(Segment[Element[l1, i], Element[l3, Length[l3] - i]], i, 1, Length[l1]) → l6
10. Sequence(Segment[Element[l2, i], Element[l4, i]], i, 1, Length[l1]) → l7
11. Translate(Dilate[l8, b, A], Vector[A, B]) → l8'
12. Dilate(B, b, A) → B'
13. Rotate(Dilate[l8, b / 1.5, A], (-(45°)), B + (2, -1)) → l8'_{1}
14. Sequence(Translate[D, Vector[(i * Vector[D, D + (3, 0.15)])]], i, 0, 1, 1 / n) → l3b
15. Sequence(Segment[Element[l3, i], Element[l3b, Length[l3] - i]], i, 1, Length[l3]) → l11
16. Sequence(Translate[D', Vector[(i * Vector[D', D' + (3, -0.15)])]], i, 0, 1, 1 / n) → l4b
17. Sequence(Segment[Element[l4, i], Element[l4b, i]], i, 1, Length[l3]) → l12
18. Mirror(B - (((-b)) / 2, 0), B') → B'_{1}
19. Mirror(l8', B'_{1} - (b / 2, 0)) → l8''
20. Translate(Dilate[l3, b, A], Vector[A, B]) → l3c
21. Translate(Dilate[l4, b, A], Vector[A, B]) → l4c
22. Translate(Dilate[l1, b, A], Vector[A, B]) → l1c
23. Translate(Dilate[l2, b, A], Vector[A, B]) → l2c
24. Mirror(l1c, B'_{1} - (1, 0)) → l1c'
25. Midpoint(B', B'_{1}) → F
26. Line(A, zAxis) → f
27. Sequence(Rotate[l8, i, f], i, 0, (2 * π), (2 * π / m)) → l9
28. Sequence(Rotate[l8', i, f], i, 0, (2 * π), π / m) → l10
29. Sequence(Rotate[l11, i, f], i, 0, (2 * π), (2 * π / m)) → l13
30. Sequence(Rotate[l12, i, f], i, 0, (2 * π), (2 * π / m)) → l14
31. Sequence(Rotate[l8'', i, f], i, 0, (2 * π), π / m) → l15
32. Sequence(Rotate[F, i, f], i, 0, (2 * π), (2 * π / m)) → l16
33. Point(l15) → G
34. Point(l15) → H
35. Point(l15) → I