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3D曲面图形

3D曲面图形
几何画板及绘图内容加载中，请稍等……
2020-01-26 17:00
解析几何立体几何参数方程
所属专题 Color 3D surfaces
该范例演示了多种3D曲面图形，包括阿斯多里亚、贝尔林戈特、波希米亚穹顶等。涉及的核心数学概念包括参数方程和立体几何。通过使用If语句、对象a, b, c等GeoGebra命令，可以构造出复杂的3D曲面图形。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. If(n ≟ 1, Surface[((a * cos(v)^(3)) * cos(u)^(3)), ((b * cos(v)^(3)) * sin(u)^(3)), (c * sin(v)^(3)), u, Umin, Umax, v, Vmin, Vmax]) → astroid
  2. If(n ≟ 2, Surface[((a * (1 + u)) * cos(v)), ((b * (1 - u)) * sin(v)), (c * u), u, Umin, Umax, v, Vmin, Vmax]) → berlingot
  3. If(n ≟ 3, Surface[(a * cos(u)), (b * cos(v)), (a * sin(u)) + (b * sin(v)), u, Umin, Umax, v, Vmin, Vmax]) → bohemianDome
  4. If(n ≟ 4, Surface[((a * cos(v)) * sin((2 * u))), ((b * sin(v)) * sin((2 * u))), (c * (sin(u)^(2) - (cos(u)^(2) * cos(v)^(2)))), u, Umin, Umax, v, Vmin, Vmax]) → crossCap
  5. If(n ≟ 5, Surface[((a * sin((2 * u))) * cos(v)), ((b * sin((2 * u))) * sin(v)), ((c * sin(u)^(2)) * sin((2 * v))), u, Umin, Umax, v, Vmin, Vmax]) → romaine
  6. If(n ≟ 1, Sequence[CurveCartesian[((a * cos(v)^(3)) * cos(u)^(3)), ((b * cos(v)^(3)) * sin(u)^(3)), (c * sin(v)^(3)), u, Umin, Umax], v, Vmin, Vmax, π / p]) → liste1
  7. If(n ≟ 1, Sequence[CurveCartesian[((a * cos(v)^(3)) * cos(u)^(3)), ((b * cos(v)^(3)) * sin(u)^(3)), (c * sin(v)^(3)), v, Umin, Umax], u, Vmin, Vmax, π / p]) → liste2
  8. If(n ≟ 2, Sequence[CurveCartesian[((a * (1 + u)) * cos(v)), ((b * (1 - u)) * sin(v)), (c * u), u, Umin, Umax], v, Vmin, Vmax, π / p]) → liste3
  9. If(n ≟ 2, Sequence[CurveCartesian[((a * (1 + u)) * cos(v)), ((b * (1 - u)) * sin(v)), (c * u), v, Vmin, Vmax], u, Umin, Umax, π / p]) → liste4
  10. If(n ≟ 3, Sequence[CurveCartesian[(a * cos(u)), (b * cos(v)), (a * sin(u)) + (b * sin(v)), u, Umin, Umax], v, Vmin, Vmax, π / p]) → liste5
  11. If(n ≟ 3, Sequence[CurveCartesian[(a * cos(u)), (b * cos(v)), (a * sin(u)) + (b * sin(v)), v, Vmin, Vmax], u, Umin, Umax, π / p]) → liste6
  12. If(n ≟ 4, Sequence[CurveCartesian[((a * cos(v)) * sin((2 * u))), ((b * sin(v)) * sin((2 * u))), (c * (sin(u)^(2) - (cos(u)^(2) * cos(v)^(2)))), u, Umin, Umax], v, Vmin, Vmax, π / p]) → liste7
  13. If(n ≟ 4, Sequence[CurveCartesian[((a * cos(v)) * sin((2 * u))), ((b * sin(v)) * sin((2 * u))), (c * (sin(u)^(2) - (cos(u)^(2) * cos(v)^(2)))), v, Vmin, Vmax], u, Umin, Umax, (0.5 * π / p)]) → liste8
  14. If(n ≟ 5, Sequence[CurveCartesian[((a * sin((2 * u))) * cos(v)), ((b * sin((2 * u))) * sin(v)), ((c * sin(u)^(2)) * sin((2 * v))), u, Umin, Umax], v, Vmin, Vmax, (0.5 * π / p)]) → liste9
  15. If(n ≟ 5, Sequence[CurveCartesian[((a * sin((2 * u))) * cos(v)), ((b * sin((2 * u))) * sin(v)), ((c * sin(u)^(2)) * sin((2 * v))), v, Vmin, Vmax], u, Umin, Umax, (0.5 * π / p)]) → liste10