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球体扫描 by Juan Carlos Ponce Campuzano

球体扫描 by Juan Carlos Ponce Campuzano
几何画板及绘图内容加载中，请稍等……
2019-04-24 19:45
立体几何微积分参数方程几何作图函数图像
①本范例演示了球体与平面、多边形等几何元素的交互扫描过程，生成独特的数学艺术图形；②涉及的核心数学概念包括立体几何、导数、线性回归、参数方程、变换等；③作图要点提炼自构造摘要，使用了Polygon（多边形）、Translate（平移）、Sphere（球体）、Plane（平面）、IntersectPath（路径相交）等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者学习空间几何、参数方程及数学艺术创作。

GeoGebra 命令及参数

  1. Polygon(A, B, D, C) → p0, f, g, h, i
  2. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (1 - 1)) - 1, 0)]) → P1
  3. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (2 - 1)) - 1, 0)]) → P2
  4. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (3 - 1)) - 1, 0)]) → P3
  5. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (4 - 1)) - 1, 0)]) → P4
  6. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (5 - 1)) - 1, 0)]) → P5
  7. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (6 - 1)) - 1, 0)]) → P6
  8. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (7 - 1)) - 1, 0)]) → P7
  9. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (8 - 1)) - 1, 0)]) → P8
  10. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (9 - 1)) - 1, 0)]) → P9
  11. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (10 - 1)) - 1, 0)]) → P10
  12. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (11 - 1)) - 1, 0)]) → P11
  13. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (12 - 1)) - 1, 0)]) → P12
  14. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (13 - 1)) - 1, 0)]) → P13
  15. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (14 - 1)) - 1, 0)]) → P14
  16. Translate(p0, Vector[(0, -1, 0), (0, (2 / n * (15 - 1)) - 1, 0)]) → P15
  17. Sphere((0, t, 0), 0.75) → s
  18. Plane(P1) → PO1
  19. Plane(P2) → PO2
  20. Plane(P3) → PO3
  21. Plane(P4) → PO4
  22. Plane(P5) → PO5
  23. Plane(P6) → PO6
  24. Plane(P7) → PO7
  25. Plane(P8) → PO8
  26. Plane(P9) → PO9
  27. Plane(P10) → PO10
  28. Plane(P11) → PO11
  29. Plane(P12) → PO12
  30. Plane(P13) → PO13
  31. Plane(P14) → PO14
  32. Plane(P15) → PO15
  33. IntersectPath(PO1, s) → S1
  34. IntersectPath(PO2, s) → S2
  35. IntersectPath(PO3, s) → S3
  36. IntersectPath(PO4, s) → S4
  37. IntersectPath(PO5, s) → S5
  38. IntersectPath(PO6, s) → S6
  39. IntersectPath(PO7, s) → S7
  40. IntersectPath(PO8, s) → S8
  41. IntersectPath(PO9, s) → S9
  42. IntersectPath(PO10, s) → S10
  43. IntersectPath(PO11, s) → S11
  44. IntersectPath(PO12, s) → S12
  45. IntersectPath(PO13, s) → S13
  46. IntersectPath(PO14, s) → S14
  47. IntersectPath(PO15, s) → S15