表面积入门：长方体展开图与三维表面积计算

GeoGebra 命令及参数

1. Ray((0, 0, 0), (1, 0, 0)) → f
2. Ray((0, 0, 0), (0, 1, 0)) → g
3. Ray((0, 0, 0), (0, 0, 1)) → h
4. Prism(E, A, D, B, C) → d, F, edgeAE, edgeAD, edgeBD, edgeBE, edgeCE, edgeAF, edgeDG, edgeBH, edgeCF, edgeFG, G, edgeGH, edgeCH, H, faceADBE, faceAECF, faceADGF, faceBDGH, faceBECH, faceCFGH
5. Net(d, openclose) → i, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
6. Sequence(Segment[(i, 0, 0), (i, WIDTH, 0)], i, 1, LENGTH - 1, 1) → L_1
7. Translate(L_1, Vector[A, F]) → L_2
8. Sequence(Segment[(0, i + 1, 0), (LENGTH, i + 1, 0)], i, 0, WIDTH - 2) → L_3
9. Translate(L_3, Vector[A, F]) → L_4
10. Vector(M, V) → u
11. Sequence((x(M) + i, y(M), z(M)), i, 1, LENGTH - 1, 1) → L_5
12. Translate(L_5, u) → L_6
13. Sequence(Segment[Element[L_5, i], Element[L_6, i]], i, 1, LENGTH - 1) → L_7
14. Sequence((x(M), y(M) + (i * y(u) / WIDTH), z(M) + (i * z(u) / WIDTH)), i, 1, WIDTH - 1, 1) → L_8
15. Vector(V, U) → v
16. Translate(L_8, v) → L_9
17. Sequence(Segment[Element[L_8, i], Element[L_9, i]], i, 1, WIDTH - 1) → L_{10}
18. Vector(A, O) → w
19. Sequence((x(A) + (i * x(w) / HEIGHT), y(A), z(A) + (i * z(w) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{11}
20. Vector(O, P) → l
21. Translate(L_{11}, l) → L_{12}
22. Sequence(Segment[Element[L_{11}, i], Element[L_{12}, i]], i, 1, HEIGHT - 1) → L_{13}
23. Sequence((x(O), y(O) + (i * y(l) / WIDTH), z(O) + (i * z(l) / WIDTH)), i, 1, WIDTH - 1, 1) → L_{14}
24. Translate(L_{14}, Vector[(-w)]) → L_{15}
25. Sequence(Segment[Element[L_{14}, i], Element[L_{15}, i]], i, 1, WIDTH - 1) → L_{16}
26. Mirror(L_{13}, k) → L_{17}
27. Mirror(L_{16}, k) → L_{18}
28. Vector(D, Q) → m
29. Sequence((x(B) + (i * x(v) / LENGTH), y(B), z(B)), i, 1, LENGTH - 1, 1) → L_{19}
30. Translate(L_{19}, m) → L_{20}
31. Sequence(Segment[Element[L_{19}, i], Element[L_{20}, i]], i, 1, LENGTH - 1) → L_{21}
32. Sequence((x(B), y(B) + (i * y(m) / HEIGHT), z(B) + (i * z(M) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{22}
33. Translate(L_{22}, v) → L_{23}
34. Sequence(Segment[Element[L_{22}, i], Element[L_{23}, i]], i, 1, HEIGHT - 1) → L_{24}
35. Mirror(L_{21}, n) → L_{25}
36. Mirror(L_{24}, n) → L_{26}