🎬the relationship between tangent vectors and the normal vector and the gradient vector of a 3D surfa

the relationship between tangent vectors and the normal vector and the gradient vector of a 3D surface

This visualization tool provides an interactive environment to explore the fundamental geometric relationships between tangent, normal, and gradient vectors across multiple 3D surfaces, including a static plane, a paraboloid, and a dynamic, traveling corrugated sheet. The demonstration shows that the surface normal, calculated as the cross product of two tangent vectors, is always perpendicular to the surface. Critically, the visualization and accompanying real-time numerical data confirm the core vector calculus principle: the gradient vector, calculated implicitly from the surface equation, is inherently parallel to the surface normal, a relationship visually reinforced by a static gradient arrow that remains perpendicular to the surface tangent plane even as the corrugated surface continuously shifts its position via animation.

🎬Narrated Video

🧵Related Derivation

🧄Surface Parametrisation and the Verification of the Gradient-Normal Relationship (SP-GNR)

⚒️Compound Page

the relationship between tangent vectors and the normal vector and the gradient vector of a 3D surface | Animated Resultsviadean on Notion