These resources outline a comprehensive framework for understanding 3D surfaces by linking theoretical vector calculus with computational visualization. The core mathematical insight is the gradient-normal relationship, which proves that the gradient vector $\nabla \phi$ of an implicit function is inherently orthogonal to the surface and parallel to the surface normal vector $n$. This concept is demonstrated through specific case studies-including planes, paraboloids, and corrugated sheets-where tangent vectors are used to derive the normal via cross products. To bridge theory and practice, the workflow suggests using Python for backend calculations and HTML for interactive web-based demonstrations, allowing for the visualization of dynamic effects like traveling waves and the real-time verification of vector orthogonality.