Spline-Based Morphing of Curves

This example demonstrates how to build smooth curves from discrete control points using splines, then produce a continuous morphing animation by updating the corresponding geometry through geometric transformations. The key mathematics includes spline interpolation (Spline) for smooth curve fitting, parameterization via ordered point sets (Sequence) to ensure consistent correspondence during the transition, and transformation principles (e.g., similarity/geometry mapping) to move between shapes in a controlled way. Construction is driven by GeoGebra commands Spline to create the curve segments, Sequence and If to organize control-point sequences and switch logic across morph stages, and a dedicated Morphing result object to render the evolving shape. Many point objects (A–O, A_1–D_1, etc.) together with parameters (l1, l2, l3, a, b, etc.) serve as the adjustable anchors and length/position controls. Suitable for secondary advanced learners, early university courses, and teaching modules on parametric curves, curve sketching, and geometric transformation-based visualization.