Tube Surface at a Fixed Distance from a 3D Curve

This example demonstrates how to construct a tube (a 3D surface) at a fixed distance from a given space curve, showing the resulting offset geometry around the curve (outer/inner sides depending on the chosen direction). The key math concepts are 3D vector geometry, parametric representation of curves, derivatives for extracting geometric direction information (tangent/normal-related vectors), and generating offset surfaces via a prescribed distance. Construction highlights in GeoGebra: Derivative is used to compute derivatives of the curve’s Cartesian components (fx, fy, fz → dfx, dfy, dfz), which then feed into direction/offset computations involving vector quantities (e.g., vx, vy, vz and related intermediate objects such as dvy, dvz, dvx, ldv/ldf, ux/uy/uz, and wx/wy/wz). The space curve itself is created with CurveCartesian, and the resulting tube surface is built with Surface. Parameters such as the distance (dis), the parameter interval (from/to), and user inputs (InputBox1–InputBox6, a/b/c/d) control the extent and radius of the tube. Suitable for advanced high school/early university learners studying 3D analytic geometry, vector calculus intuition, and geometric modeling.