两条参数曲线的交点：隐式曲线与数值CAS求解

GeoGebra 命令及参数

1. ImplicitCurve(f1(x, y)) → a
2. Intersect(Circle[D, r_a], OrthogonalLine[D, Segment[D, ClosestPoint[a, D]]], 2) → Hzz2
3. ImplicitCurve(f2(x, y)) → b
4. Intersect(Circle[D, r_b], OrthogonalLine[D, Segment[D, ClosestPoint[b, D]]], 1) → Z1_b
5. Intersect(Circle[D, r_b], OrthogonalLine[D, Segment[D, ClosestPoint[b, D]]], 2) → Z2_b
6. Intersect(Circle[D, r_a], OrthogonalLine[D, Segment[D, ClosestPoint[a, D]]], 1) → Z1_a
7. PolyLine(Zip[ClosestPoint[b, B], B, Z1_b + ((Z2_b - Z1_b) / n_b * Sequence[i, i, 0, n_b])]) → polZb
8. PolyLine(Zip[ClosestPoint[a, B], B, Z1_a + ((Z2_a - Z1_a) / n_a * Sequence[i, i, 0, n_a])]) → polZa
9. Element({Intersect[polZa, polZb]}, 1) → PZ
10. Point(a) → B_a
11. PathParameter(B_a) → Pf1B
12. Textfield(Nn) → InputBox4
13. Textfield(e) → InputBox5
14. Textfield(x_{min}) → InputBox6
15. Textfield(x_{max}) → InputBox7
16. Textfield(y_{min}) → InputBox8
17. Textfield(y_{max}) → InputBox9
18. Polygon((x_{min}, y_{min}), (x_{max}, y_{min}), (x_{max}, y_{max}), (x_{min}, y_{max})) → poly1, g1_s, g2_s, g3_s, s4_s
19. Textfield(α) → InputBox2
20. Length(lr1) → llr1
21. Length(lf2) → llf2
22. Textfield(r) → InputBox16
23. CurveCartesian(fa_x(u), fa_y(u), u, x_{min}, x_{max}) → a_c
24. CurveCartesian(fb_x(v), fb_y(v), v, y_{min}, y_{max}) → b_c
25. Element(lr1, i_{manual}) → C_t
26. Element(lgr2_bscan, f) → B_{xy}
27. Length(lf1) → llf1
28. Textfield(fa_x) → InputBox17
29. Textfield(fa_y) → InputBox18
30. Textfield(fb_x) → InputBox19
31. Textfield(fb_y) → InputBox20
32. Textfield(n_a) → InputBox21
33. Textfield(n_b) → InputBox22
34. Textfield(r_a) → InputBox23
35. Textfield(q) → InputBox24
36. PolyLine(Z1_a + ((Z2_a - Z1_a) / n_a * Sequence[i, i, 0, n_a])) → poly2_aa
37. PolyLine(Z1_b + ((Z2_b - Z1_b) / n_b * Sequence[i, i, 0, n_b])) → poly2_bb
38. Point(poly2_aa, e1) → R_a
39. Point(poly2_bb, e2) → R_b
40. ClosestPoint(a, R_a) → R'_a
41. ClosestPoint(b, R_b) → R'_b
42. Length(R'_a - R'_b) → dmaxmins2
43. If(Defined[PZ], If[fza2 < fzb2, (f1za2, f2za2), (f1zb2, f2zb2)], (NaN, NaN)) → errorz2
44. If(Defined[PZ], If[fza2 < fzb2, R'_a, R'_b], (NaN, NaN)) → Pz2
45. If(ca, PZ, Pz2) → PZ0
46. If(ca, f11, x(errorz2)) → f110
47. If(ca, f22, y(errorz2)) → f220
48. Textfield(r_b) → InputBox13
49. Textfield(α) → InputBox11
50. Element(roots0, f) → A
51. Sequence((fa_x(x(Element[lr1, i])), fa_y(x(Element[lr1, i]))), i, 1, llr1) → lgr2_a
52. Sequence((fb_x(y(Element[lr1, i])), fb_y(y(Element[lr1, i]))), i, 1, llr1) → lr2_b
53. Zip((((abs(x(a - b) / x(a)) * 100), (abs(y(a - b) / y(a)) * 100)) * 1000000000), a, lgr2_a, b, lr2_b) → lgr2
54. Element(lgr2_a, i_{manual}) → Cxy_t
55. Textfield(t) → InputBox1
56. Textfield(f) → InputBox3
57. Textfield(i_{manual}) → Eingabefeld1
58. Textfield(q2) → Eingabefeld2
59. ImplicitCurve(f01(x, y)) → c
60. If(Length[listxyres1] ≟ 0 ∨ (i > m1), F, Element[listxyres1, i]) → B
61. Length(lr2) → llr2
62. TableText({Join[{{"N"}, Sequence[i, i, 1, Length[roots0]]}], Join[{{""}, Sequence["→", i, 1, f]}], Join[{{" u:"}, x(roots0)}], Join[{{" v:"}, y(roots0)}], Join[{{"f1*10^-9"}, lf1_{Pr}2}], Join[{{"f2* 10^-9"}, lf2_{Pr}2}]}, "vr") → Text2
63. TableText({Join[{{"N"}, Sequence[i, i, 1, Length[roots0]]}], Join[{{""}, Sequence["→", i, 1, f]}], Join[{{"(x,y)_a"}, lgr2_ascan}], Join[{{"(x,y)_b"}, lgr2_bscan}], Join[{{"(δx,δy) %*10^-9"}, lgr2scan}]}, "vr") → text12a
64. TableText({Join[{{"N"}, Sequence[i, i, 1, llr1]}], Join[{{""}, Sequence["→", i, 1, i_{manual}]}], Join[{{"u:"}, x(lr1)}], Join[{{"v:"}, y(lr1)}], Join[{{"f1* 10^-9"}, lf1}], Join[{{"f2* 10^-9"}, lf2}]}, "vr") → text8
65. Intersect(Circle[D, r_a], OrthogonalLine[D, Segment[D, ClosestPoint[a, D]]], 1) → Hzz1
66. TableText({Join[{{"N"}, Sequence[i, i, 1, llr1]}], Join[{{""}, Sequence["→", i, 1, i_{manual}]}], Join[{{"(x,y)_a"}, lgr2_a}], Join[{{"(x,y)_b"}, lr2_b}], Join[{{"(δx,δy) %*10-9"}, lgr2}]}, "vr") → text12r
67. Textfield(v_i) → InputBox10