The Dual Basis for the Tangent Space of a 2D Surface
The Dual Basis for the Tangent Space of a 2D Surface
This Demonstration illustrates the tangent plane basis and the reciprocal basis at points along a few sample surfaces. The tangent plane itself is shown and a control is provided to alter the position of the tangent plane along the surface. This lets you see the normality of the tangent plane basis vectors and their alternate indexed reciprocal vector. You can also compare the orientations of the tangent plane basis vectors with their reciprocals, and see how these pairs of vectors are not necessarily collinear.