Inertia Tensor and Eigenvectors (3D Visual Demo)

This example visualizes how an inertia tensor identifies the principal directions of a 3D object: the rotation-related behavior along different axes is governed by the eigenvectors (the principal axes). It connects geometry with linear algebra by illustrating that for symmetric shapes, meaningful directions emerge from the tensor’s spectral properties. The core concepts include the inertia tensor, eigenvalues/eigenvectors, and the diagonalization viewpoint that links algebraic structure to geometric orientation. Construction-wise, it uses Polygon to form the key boundaries/sections of the solid representation, Line to define the candidate axis directions, Intersect to compute crucial intersection points, and Point/Segment to organize the geometry. Vector is used to represent oriented quantities and direction data, while Midpoint helps locate symmetric or central positions needed for a consistent geometric setup. Suitable for high-school to early university learners studying linear algebra, 3D geometry, and modeling; also useful for courses or self-study focused on eigen-decomposition, symmetry, and vector-based geometric reasoning.