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Curve Extrusion

Curve Extrusion
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2016-10-17 06:32
VectorCoordinate GeometrySolid GeometryParametric Equation
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates how to generate a 3D surface by extruding a curve, involving core math concepts like 3D geometry, vector operations, parametric equations, and surface creation. It uses GeoGebra commands such as CurveCartesian for curve plotting, Textfield and Surface for text and surface display, and objects like InputBox1, a, b, c, r, f for parameter control and interaction. Suitable for high school and above students learning spatial geometry and parametric surfaces.

GeoGebra Commands & Parameters

  1. CurveCartesian((sin(t), cos(t), t), t, -10, 10) → a
  2. Textfield(a) → InputBox1
  3. CurveCartesian(a'(t) ⊗ (1, 0, 0), t, -10, 10) → b
  4. CurveCartesian(b(t) ⊗ a'(t), t, -10, 10) → c
  5. Surface(a(t) + ((b(t) * sin(u)) * r) + ((c(t) * cos(u)) * r), t, -10, 10, u, (-π), π) → f