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3D Surfaces

3D Surfaces
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2020-01-26 17:00
Coordinate GeometrySolid GeometryParametric Equation
In collections Color 3D surfaces
This example demonstrates various 3D surfaces, including Astroid, Berlingot, Bohemian Dome, etc. It involves parametric equations and solid geometry. Using If statements and objects a, b, c, etc., complex 3D surfaces can be constructed. Suitable for high school students and teachers.

GeoGebra Commands & Parameters

  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