A Moving “Tube” at a Fixed Distance from a 3D Curve

This GeoGebra example demonstrates how to build a moving tube-like surface in 3D by taking a space curve and enforcing a constant distance offset from it. It visualizes how the generated solid surface evolves as the underlying curve is parameterized. The key math concepts are vector calculus on parametric space curves (derivatives of coordinate functions), constructing local direction/auxiliary vectors from the curve’s derivative information, and using a distance constraint (a prescribed offset radius) to define the tube surface relative to the curve. Construction highlights: it uses Derivative to compute derivatives of the curve components (fx, fy, fz and dfx, dfy, dfz), CurveCartesian to define the 3D curve, and Surface to render the resulting tube surface. Vector-related helper objects (vx, vy, vz, wx, wy, wz, ux, uy, uz, together with dvx/dvy/dvz and computed offset-related parameters like ldf/ldv) and a distance measure dis are used to keep the tube at the specified offset. Multiple InputBox controls (InputBox1–InputBox6) together with parameters (a, b, c, d, e, to/from) drive the animation/interaction. Suitable for advanced high-school and early university level topics in 3D analytic geometry and calculus (parametric curves and derivatives), and for interactive STEM visualization.