克莱福特环面的立体投影

GeoGebra 命令及参数

1. If(χStereoPrj, StereoPrj(x, y), If[χParallelPrj, (x * 6), 0]) → Prj
2. If(χPunctured, (R * π / 8), 0) → punc
3. Text("x^2+z^2=y^2+w^2=1 ↔ x^2+w^2=y^2+z^2=1; Rotate: ϕ=arg(z,w); Stereo-projected from w=R", (0, 0), false, true) → txtExplain
4. Vector(OW - (1, 0), OW + (1.8, 0)) → vW
5. Polygon(OW + (sZW * (Wzxy(0, 0), Zw(0, 0))), OW + (sZW * (Wzxy(0, π), Zw(0, π))), 4) → TZW
6. Vector(OW - (0, 1), OW + (0, 1.5)) → vZ
7. Angle(PR + (-1, 1), PR, PR + (-1, -1)) → αWR
8. Sequence(Vector[PR + (0, z), PR + (-0.1, z)], z, -1, 1, 0.1) → ParallelPrjRays, {(-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0), (-0.1, 0)}
9. Vector(OW + (sZW * (Wzxy(0, 0), Zw(0, 0))), OW + (sZW * (Wzxy(π, 0), Zw(π, 0)))) → vZWU
10. Vector(OW + (sZW * (Wzxy(0, π), Zw(0, π))), OW + (sZW * (Wzxy(π, π), Zw(π, π)))) → vZWUπ
11. Vector(OW + (sZW * (Wzxy(0, 0), Zw(0, 0))), OW + (sZW * (Wzxy(0, π), Zw(0, π)))) → vZWV
12. Vector(OW + (sZW * (Wzxy(π, 0), Zw(π, 0))), OW + (sZW * (Wzxy(π, π), Zw(π, π)))) → vZWVπ
13. Angle(OW + (sZW * (Wzxy(0, π), Zw(0, π))), OW + (sZW * (Wzxy(0, 0), Zw(0, 0))), OW + (sZW * (Wzxy(π, 0), Zw(π, 0)))) → αPuncture
14. Vector(PUV00, PUV00 + (0, 2, 0)) → vV00
15. Vector(PUV0π, PUV0π + (0, -2, 0)) → vV0π
16. Vector(PUVπ0, PUVπ0 + (0, 2, 0)) → vVπ0
17. Vector(PUVππ, PUVππ + (0, -2, 0)) → vVππ
18. Vector(PUV0π, PUV0π + (2, 0, 0)) → vU0π
19. Vector(PUVπ0, PUVπ0 + (-2, 0, 0)) → vUπ0
20. Vector(PUV00, PUV00 + (2, 0, 0)) → vU00
21. Vector(PUVππ, PUVππ + (-2, 0, 0)) → vUππ
22. Surface(PrjX(u, v), PrjY(u, v), PrjZ(u, v), u, punc, (2 * π) - punc, v, punc, (2 * π) - punc) → Torus
23. Surface(PrjX(u, v), PrjY(u, v), PrjZ(u, v), u, 0, (2 * π), v, (-0.005 * π), (0.005 * π)) → TorusU
24. CurveCartesian(PrjX(u, π), PrjY(u, π), PrjZ(u, π), u, 0, (2 * π)) → TorusUπ
25. CurveCartesian(PrjX(π, v), PrjY(π, v), PrjZ(π, v), v, 0, (2 * π)) → TorusVπ
26. Surface(PrjX(u, v), PrjY(u, v), PrjZ(u, v), u, (-0.005 * π), (0.005 * π), v, 0, (2 * π)) → TorusV
27. CurveCartesian(PrjX(u, punc), PrjY(u, punc), PrjZ(u, punc), u, (-punc), punc) → TorusPuncU
28. CurveCartesian(PrjX(u, (-punc)), PrjY(u, (-punc)), PrjZ(u, (-punc)), u, (-punc), punc) → TorusPuncUn
29. CurveCartesian(PrjX(punc, v), PrjY(punc, v), PrjZ(punc, v), v, (-punc), punc) → TorusPuncV
30. CurveCartesian(PrjX((-punc), v), PrjY((-punc), v), PrjZ((-punc), v), v, (-punc), punc) → TorusPuncVn
31. Surface(PrjX(u, v), PrjY(u, v), PrjZ(u, v), u, punc, (2 * π) - punc, v, (-punc), punc) → TorusPatchU
32. Surface(PrjX(u, v), PrjY(u, v), PrjZ(u, v), u, (-punc), punc, v, punc, (2 * π) - punc) → TorusPatchV