将正方形变形为双曲抛物面

GeoGebra 命令及参数

1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
3. Point(edgeBF) → I
4. Intersect(yAxis, xAxis) → J
5. Intersect(yAxis, faceABFE) → K
6. Intersect(xAxis, faceBCGF) → L
7. Intersect(yAxis, faceCDHG) → M
8. Intersect(xAxis, faceADHE) → N
9. Intersect(zAxis, faceEFGH) → O
10. Point(zAxis) → P
11. Mirror(I, K) → I'
12. Mirror(I', N) → I''
13. Mirror(I, L) → Q
14. CurveCartesian((t * x(I')) + ((1 - t) * x(I)), (t * y(I')) + ((1 - t) * y(I)), (t * z(I')) + ((1 - t) * z(I)), t, 0, 1) → b
15. CurveCartesian((t * x(I')) + ((1 - t) * x(I'')), (t * y(I')) + ((1 - t) * y(I'')), (t * z(I')) + ((1 - t) * z(I'')), t, 0, 1) → c
16. CurveCartesian((t * x(Q)) + ((1 - t) * x(I)), (t * y(Q)) + ((1 - t) * y(I)), (t * z(Q)) + ((1 - t) * z(I)), t, 0, 1) → d
17. CurveCartesian((t * x(I'')) + ((1 - t) * x(Q)), (t * y(I'')) + ((1 - t) * y(Q)), (t * z(I'')) + ((1 - t) * z(Q)), t, 0, 1) → e
18. Surface((u * x(b(t))) + ((1 - u) * x(e(t))), (u * y(b(t))) + ((1 - u) * y(e(t))), (u * z(b(t))) + ((1 - u) * z(e(t))), u, 0, 1, t, 0, 1) → f