向量坐标系与法向量几何演示

GeoGebra 命令及参数

1. Line(A, B) → a
2. OrthogonalLine(C, a) → b
3. OrthogonalLine(C, b) → c
4. Circle(C, l) → d
5. Circle(C, br) → e
6. Intersect(d, c) → D, E
7. Intersect(e, b) → F, G
8. OrthogonalLine(G, b) → f
9. OrthogonalLine(D, c) → g
10. OrthogonalLine(F, b) → h
11. OrthogonalLine(E, c) → i
12. Intersect(f, i) → H
13. Intersect(g, f) → I
14. Intersect(g, h) → J
15. Intersect(h, i) → K
16. Polygon(H, I, J, K) → mangekant1, h_1, i_1, j, k
17. OrthogonalLine(Rotate, h_1) → m
18. OrthogonalLine(Rotate, k) → n
19. Intersect(h_1, m) → M
20. Intersect(k, n) → N
21. Distance(Rotate, M) → avstandLM
22. Distance(Rotate, N) → avstandLN
23. OrthogonalLine(O, a) → p
24. OrthogonalLine(O, p) → q
25. Circle(O, size) → r
26. Intersect(r, q) → P, Q
27. Intersect(r, p) → R, S
28. OrthogonalLine(S, p) → s
29. OrthogonalLine(P, q) → t
30. OrthogonalLine(R, p) → a_1
31. OrthogonalLine(Q, q) → b_1
32. Intersect(s, b_1) → T
33. Intersect(s, t) → U
34. Intersect(a_1, t) → V
35. Intersect(a_1, b_1) → W
36. Polygon(U, T, W, V) → mangekant2, u, t_1, w, v
37. Rotate(U, ho, O) → U'
38. Rotate(T, ho, O) → T'
39. Rotate(W, ho, O) → W'
40. Rotate(V, ho, O) → V'
41. Polygon(U', T', W', V') → mangekant2', u', t', w', v'
42. OrthogonalLine(T', q) → c_1
43. OrthogonalLine(W', q) → d_1
44. OrthogonalLine(V', q) → e_1
45. OrthogonalLine(U', q) → f_1
46. OrthogonalLine(T', q) → g_1
47. OrthogonalLine(V', q) → j_1
48. OrthogonalLine(U', q) → k_1
49. OrthogonalLine(W', q) → l_1
50. Intersect(g_1, q) → Z
51. Intersect(l_1, q) → A_1
52. Intersect(q, k_1) → B_1
53. Intersect(q, j_1) → C_1
54. Distance(Z, T') → avstandZT'
55. Distance(B_1, U') → avstandB1U'
56. Dilate(T', l1, Z) → T''
57. Dilate(W', l1, A_1) → W''
58. Dilate(U', l1, B_1) → U''
59. Dilate(V', l1, C_1) → V''
60. Polygon(T'', W'', V'', U'') → mangekant3, t'', w'', v'', u''
61. Midpoint(W'', V'') → D_1
62. Midpoint(V'', U'') → E_1
63. Distance(O, D_1) → avstandOD1
64. Distance(O, E_1) → avstandOE1
65. If(((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)) ∧ ((-π) / 2 < ho) ∧ (ho < π / 2) ∨ ((-π) / 2 < ve) ∧ (ve < π / 2) ∧ ((-π < ho) ∧ (ho < (-π) / 2) ∨ (π / 2 < ho) ∧ (ho < π)), van / (size - xp) + 3, (-van) / (size - xp) - 3) → ix
66. Dilate(D_1, ix, O) → F_1
67. If((0 < ho) ∧ (ho < π) ∧ ((-π) / 2 < ve) ∧ (ve < π / 2) ∨ (-π < ho) ∧ (ho < 0) ∧ ((-π < ve) ∧ (ve < (-π) / 2) ∨ (π / 2 < ve) ∧ (ve < π)), van / (size - yp) + 3, (-van) / (size - yp) - 3) → iy
68. Dilate(E_1, iy, O) → G_1
69. If((-π < ve) ∧ (ve < (-π) / 2) ∨ (0 < ve) ∧ (ve < π / 2), (-van) / (size - zp) - 3, van / (size - zp) + 3) → iz
70. Circle(O, size) → p_1
71. Circle(O, zp) → q_1
72. Intersect(q_1, p) → J_1, K_1
73. Dilate(K_1, iz, O) → H_1
74. Dilate(D_1, xpos, O) → I_1
75. Dilate(D_1, xneg, O) → L_1
76. Dilate(E_1, ypos, O) → M_1
77. Dilate(E_1, yneg, O) → N_1
78. Line(M_1, F_1) → m_1
79. Line(N_1, F_1) → n_1
80. Line(L_1, G_1) → r_1
81. Line(I_1, G_1) → s_1
82. Intersect(n_1, r_1) → O_1
83. Intersect(m_1, r_1) → P_1
84. Intersect(s_1, m_1) → Q_1
85. Intersect(s_1, n_1) → R_1
86. Polygon(P_1, O_1, R_1, Q_1) → mangekant4, p_2, o_1, r_2, q_2
87. Dilate(K_1, zpos, O) → S_1
88. Dilate(K_1, zneg, O) → T_1
89. Segment(I_1, L_1) → a_2
90. Segment(N_1, M_1) → b_2
91. Line(F_1, S_1) → c_2
92. Line(T_1, F_1) → d_2
93. Line(S_1, G_1) → e_2
94. Line(T_1, G_1) → f_2
95. Line(H_1, N_1) → g_2
96. Line(H_1, I_1) → h_2
97. Line(H_1, L_1) → i_2
98. Line(H_1, M_1) → j_2
99. Intersect(g_2, e_2) → V_1
100. Intersect(g_2, f_2) → W_1
101. Intersect(e_2, j_2) → Z_1
102. Intersect(f_2, j_2) → A_2
103. Line(V_1, F_1) → k_2
104. Line(Z_1, F_1) → l_2
105. Line(W_1, F_1) → m_2
106. Line(A_2, F_1) → n_2
107. Intersect(i_2, c_2) → B_2
108. Intersect(i_2, d_2) → C_2
109. Intersect(c_2, h_2) → D_2
110. Intersect(h_2, d_2) → E_2
111. Line(B_2, G_1) → s_2
112. Line(D_2, G_1) → t_2
113. Line(E_2, G_1) → a_3
114. Line(C_2, G_1) → b_3
115. Intersect(k_2, s_2) → F_2
116. Intersect(s_2, l_2) → G_2
117. Intersect(t_2, l_2) → H_2
118. Intersect(t_2, k_2) → I_2
119. Intersect(m_2, b_3) → J_2
120. Intersect(m_2, a_3) → K_2
121. Intersect(a_3, n_2) → L_2
122. Intersect(n_2, b_3) → M_2
123. Segment(F_2, G_2) → c_3
124. Segment(G_2, H_2) → d_3
125. Segment(H_2, I_2) → e_3
126. Segment(I_2, F_2) → f_3
127. Segment(F_2, J_2) → g_3
128. Segment(I_2, K_2) → h_3
129. Segment(L_2, H_2) → i_3
130. Segment(G_2, M_2) → j_3
131. Segment(M_2, L_2) → k_3
132. Segment(L_2, K_2) → l_3
133. Segment(K_2, J_2) → m_3
134. Segment(J_2, M_2) → n_3
135. Segment(T_1, S_1) → p_3
136. Dilate(I_1, enx, O) → N_2
137. Dilate(I_1, tox, O) → O_2
138. Dilate(I_1, trex, O) → P_2
139. Dilate(I_1, fix, O) → Q_2
140. Dilate(I_1, fex, O) → R_2
141. Dilate(I_1, enxm, O) → S_2
142. Dilate(I_1, six, O) → T_2
143. Dilate(I_1, sevx, O) → U_2
144. Dilate(I_1, eix, O) → V_2
145. Dilate(I_1, nix, O) → W_2
146. Dilate(I_1, tex, O) → Z_2
147. Dilate(I_1, toxm, O) → A_3
148. Dilate(I_1, trexm, O) → B_3
149. Dilate(I_1, fixm, O) → C_3
150. Dilate(I_1, fexm, O) → D_3
151. Dilate(I_1, sixm, O) → E_3
152. Dilate(I_1, sevxm, O) → F_3
153. Dilate(I_1, eixm, O) → G_3
154. Dilate(I_1, nixm, O) → H_3
155. Dilate(I_1, texm, O) → I_3
156. Line(Z_2, G_1) → q_3
157. Line(W_2, G_1) → r_3
158. Line(V_2, G_1) → s_3
159. Line(U_2, G_1) → t_3
160. Line(T_2, G_1) → a_4
161. Line(R_2, G_1) → b_4
162. Line(Q_2, G_1) → c_4
163. Line(P_2, G_1) → d_4
164. Line(O_2, G_1) → e_4
165. Line(N_2, G_1) → f_4
166. Line(S_2, G_1) → g_4
167. Line(A_3, G_1) → h_4
168. Line(B_3, G_1) → i_4
169. Line(C_3, G_1) → j_4
170. Line(D_3, G_1) → k_4
171. Line(E_3, G_1) → l_4
172. Line(F_3, G_1) → m_4
173. Line(G_3, G_1) → n_4
174. Line(H_3, G_1) → p_4
175. Line(I_3, G_1) → q_4
176. Intersect(q_2, q_4) → J_3
177. Intersect(q_2, p_4) → K_3
178. Intersect(q_2, n_4) → L_3
179. Intersect(q_2, m_4) → M_3
180. Intersect(q_2, l_4) → N_3
181. Intersect(q_2, k_4) → O_3
182. Intersect(q_2, j_4) → P_3
183. Intersect(q_2, i_4) → Q_3
184. Intersect(q_2, h_4) → R_3
185. Intersect(q_2, g_4) → S_3
186. Intersect(q_2, f_4) → T_3
187. Intersect(q_2, e_4) → U_3
188. Intersect(q_2, d_4) → V_3
189. Intersect(q_2, c_4) → W_3
190. Intersect(q_2, b_4) → Z_3
191. Intersect(q_2, a_4) → A_4
192. Intersect(q_2, t_3) → B_4
193. Intersect(q_2, s_3) → C_4
194. Intersect(q_2, r_3) → D_4
195. Intersect(q_2, q_3) → E_4
196. Intersect(o_1, q_3) → F_4
197. Intersect(o_1, r_3) → G_4
198. Intersect(o_1, s_3) → H_4
199. Intersect(o_1, t_3) → I_4
200. Intersect(o_1, a_4) → J_4
201. Intersect(o_1, b_4) → K_4
202. Intersect(o_1, c_4) → L_4
203. Intersect(o_1, d_4) → M_4
204. Intersect(o_1, e_4) → N_4
205. Intersect(o_1, f_4) → O_4
206. Intersect(o_1, g_4) → P_4
207. Intersect(o_1, h_4) → Q_4
208. Intersect(o_1, i_4) → R_4
209. Intersect(o_1, j_4) → S_4
210. Intersect(o_1, k_4) → T_4
211. Intersect(o_1, m_4) → W_4
212. Intersect(o_1, n_4) → Z_4
213. Intersect(o_1, p_4) → A_5
214. Intersect(o_1, q_4) → B_5
215. Segment(B_5, J_3) → r_4
216. Segment(A_5, K_3) → s_4
217. Segment(Z_4, L_3) → t_4
218. Segment(W_4, M_3) → a_5
219. Segment(T_4, O_3) → c_5
220. Segment(S_4, P_3) → d_5
221. Segment(R_4, Q_3) → e_5
222. Segment(Q_4, R_3) → f_5
223. Segment(P_4, S_3) → g_5
224. Segment(O_4, T_3) → h_5
225. Segment(N_4, U_3) → i_5
226. Segment(M_4, V_3) → j_5
227. Segment(L_4, W_3) → k_5
228. Segment(K_4, Z_3) → l_5
229. Segment(J_4, A_4) → m_5
230. Segment(I_4, B_4) → n_5
231. Segment(H_4, C_4) → p_5
232. Segment(G_4, D_4) → q_5
233. Segment(F_4, E_4) → r_5
234. Dilate(M_1, eny, O) → C_5
235. Dilate(M_1, toy, O) → D_5
236. Dilate(M_1, trey, O) → E_5
237. Dilate(M_1, firy, O) → F_5
238. Dilate(M_1, femy, O) → G_5
239. Dilate(M_1, sixy, O) → H_5
240. Dilate(M_1, sevy, O) → I_5
241. Dilate(M_1, eiy, O) → J_5
242. Dilate(M_1, niy, O) → K_5
243. Dilate(M_1, tey, O) → L_5
244. Dilate(M_1, toym, O) → M_5
245. Dilate(M_1, enym, O) → N_5
246. Dilate(M_1, treym, O) → O_5
247. Dilate(M_1, firym, O) → P_5
248. Dilate(M_1, sixym, O) → Q_5
249. Dilate(M_1, femym, O) → R_5
250. Dilate(M_1, sevym, O) → S_5
251. Dilate(M_1, eiym, O) → T_5
252. Dilate(M_1, niym, O) → U_5
253. Dilate(M_1, teym, O) → V_5
254. Line(V_5, F_1) → s_5
255. Line(U_5, F_1) → t_5
256. Line(T_5, F_1) → a_6
257. Line(S_5, F_1) → b_6
258. Line(Q_5, F_1) → c_6
259. Line(R_5, F_1) → d_6
260. Line(P_5, F_1) → e_6
261. Line(O_5, F_1) → f_6
262. Line(M_5, F_1) → g_6
263. Line(N_5, F_1) → h_6
264. Line(C_5, F_1) → i_6
265. Line(D_5, F_1) → j_6
266. Line(E_5, F_1) → k_6
267. Line(F_5, F_1) → l_6
268. Line(G_5, F_1) → m_6
269. Line(H_5, F_1) → n_6
270. Line(I_5, F_1) → p_6
271. Line(J_5, F_1) → q_6
272. Line(K_5, F_1) → r_6
273. Line(L_5, F_1) → s_6
274. Intersect(p_2, s_5) → W_5
275. Intersect(p_2, t_5) → Z_5
276. Intersect(p_2, a_6) → A_6
277. Intersect(p_2, b_6) → B_6
278. Intersect(p_2, c_6) → C_6
279. Intersect(p_2, d_6) → D_6
280. Intersect(p_2, e_6) → E_6
281. Intersect(p_2, f_6) → F_6
282. Intersect(p_2, g_6) → G_6
283. Intersect(p_2, h_6) → H_6
284. Intersect(p_2, i_6) → I_6
285. Intersect(p_2, j_6) → J_6
286. Intersect(p_2, k_6) → K_6
287. Intersect(p_2, l_6) → L_6
288. Intersect(p_2, m_6) → M_6
289. Intersect(p_2, n_6) → N_6
290. Intersect(p_2, p_6) → O_6
291. Intersect(p_2, q_6) → P_6
292. Intersect(p_2, r_6) → Q_6
293. Intersect(p_2, s_6) → R_6
294. Intersect(r_2, s_6) → S_6
295. Intersect(r_2, r_6) → T_6
296. Intersect(r_2, q_6) → U_6
297. Intersect(r_2, p_6) → V_6
298. Intersect(r_2, n_6) → W_6
299. Intersect(r_2, m_6) → Z_6
300. Intersect(r_2, l_6) → A_7
301. Intersect(r_2, k_6) → B_7
302. Intersect(r_2, j_6) → C_7
303. Intersect(r_2, i_6) → D_7
304. Intersect(r_2, h_6) → E_7
305. Intersect(r_2, g_6) → F_7
306. Intersect(r_2, f_6) → G_7
307. Intersect(r_2, e_6) → H_7
308. Intersect(r_2, d_6) → I_7
309. Intersect(r_2, c_6) → J_7
310. Intersect(r_2, b_6) → K_7
311. Intersect(r_2, a_6) → L_7
312. Intersect(r_2, t_5) → M_7
313. Intersect(r_2, s_5) → N_7
314. Segment(N_7, W_5) → t_6
315. Segment(M_7, Z_5) → a_7
316. Segment(L_7, A_6) → b_7
317. Segment(K_7, B_6) → c_7
318. Segment(J_7, C_6) → d_7
319. Segment(I_7, D_6) → e_7
320. Segment(H_7, E_6) → f_7
321. Segment(G_7, F_6) → g_7
322. Segment(F_7, G_6) → h_7
323. Segment(E_7, H_6) → i_7
324. Segment(D_7, I_6) → j_7
325. Segment(C_7, J_6) → k_7
326. Segment(B_7, K_6) → l_7
327. Segment(A_7, L_6) → m_7
328. Segment(Z_6, M_6) → n_7
329. Segment(W_6, N_6) → p_7
330. Segment(V_6, O_6) → q_7
331. Segment(U_6, P_6) → r_7
332. Segment(T_6, Q_6) → s_7
333. Segment(S_6, R_6) → t_7
334. Intersect(o_1, l_4) → U_4
335. Intersect(q_2, l_4) → V_4
336. Segment(U_4, V_4) → b_5
337. Dilate(S_1, enz, O) → O_7
338. Vector(O, N_2) → z
339. Vector(O, C_5) → u_1
340. Vector(O, O_7) → v_1
341. Dilate(I_1, xx1, O) → P_7
342. Dilate(M_1, yy1, O) → Q_7
343. Dilate(S_1, zz1, O) → R_7
344. Line(P_7, G_1) → a_8
345. Line(R_7, G_1) → b_8
346. Line(Q_7, F_1) → c_8
347. Line(R_7, F_1) → d_8
348. Line(H_1, P_7) → e_8
349. Line(H_1, Q_7) → f_8
350. Intersect(b_8, f_8) → S_7
351. Intersect(e_8, d_8) → T_7
352. Line(T_7, G_1) → g_8
353. Line(S_7, F_1) → h_8
354. Intersect(h_8, g_8) → P1
355. Intersect(c_8, a_8) → V_7
356. Segment(P1, R_7) → i_8
357. Segment(P1, V_7) → j_8
358. Segment(V_7, P_7) → k_8
359. Segment(V_7, Q_7) → l_8
360. Dilate(I_1, xx2, O) → L
361. Dilate(M_1, yy2, O) → W_7
362. Dilate(S_1, zz2, O) → Z_7
363. Line(H_1, L) → m_8
364. Line(H_1, W_7) → n_8
365. Line(W_7, F_1) → p_8
366. Line(Z_7, F_1) → q_8
367. Line(L, G_1) → r_8
368. Line(Z_7, G_1) → s_8
369. Intersect(m_8, q_8) → A_8
370. Intersect(n_8, s_8) → B_8
371. Line(A_8, G_1) → t_8
372. Line(B_8, F_1) → a_9
373. Intersect(t_8, a_9) → P2
374. Intersect(p_8, r_8) → D_8
375. Segment(W_7, D_8) → b_9
376. Segment(D_8, L) → c_9
377. Segment(D_8, P2) → d_9
378. Segment(P2, Z_7) → e_9
379. Dilate(I_1, xx3, O) → E_8
380. Dilate(M_1, yy3, O) → F_8
381. Dilate(S_1, zz3, O) → G_8
382. Line(H_1, F_8) → f_9
383. Line(H_1, E_8) → g_9
384. Line(F_8, F_1) → h_9
385. Line(G_8, F_1) → i_9
386. Line(E_8, G_1) → j_9
387. Line(G_8, G_1) → k_9
388. Intersect(g_9, i_9) → H_8
389. Intersect(f_9, k_9) → I_8
390. Line(H_8, G_1) → l_9
391. Line(I_8, F_1) → m_9
392. Intersect(m_9, l_9) → P3
393. Intersect(j_9, h_9) → K_8
394. Segment(F_8, K_8) → n_9
395. Segment(K_8, P3) → p_9
396. Segment(K_8, E_8) → q_9
397. Segment(P3, G_8) → r_9
398. Vector(P1, P2) → w_1
399. Vector(P1, P3) → z_1
400. Dilate(I_1, nnx, O) → U_7
401. Dilate(M_1, nny, O) → C_8
402. Dilate(S_1, nnz, O) → J_8
403. Line(H_1, U_7) → s_9
404. Line(H_1, C_8) → t_9
405. Line(C_8, F_1) → a_{10}
406. Line(J_8, F_1) → b_{10}
407. Line(U_7, G_1) → c_{10}
408. Line(J_8, G_1) → d_{10}
409. Intersect(s_9, b_{10}) → L_8
410. Intersect(t_9, d_{10}) → M_8
411. Line(L_8, G_1) → e_{10}
412. Line(M_8, F_1) → f_{10}
413. Intersect(e_{10}, f_{10}) → N_8
414. Intersect(c_{10}, a_{10}) → O_8
415. Vector(P1, N_8) → u_2